Using the Tustin equivalence with the prewarping method, fnd the discrete equivalent of the
following H(s): H s s s s s ( ) = + + + + 2 5 7 3 8 2 2 With h = 0.5, conduct a Bode plot
comparison of continuous, Tustin equivalent, and backward differences.
Solution
Tustin Approximation
The Tustin or bilinear approximation yields the best frequency-domain match between the
continuous-time and discretized systems. This method relates the s-domain and z-domain
transfer functions using the approximation:
z=esTs1+sTs/21sTs/2.
In c2d conversions, the discretization Hd(z) of a continuous transfer function H(s) is:
Hd(z)=H(s),s=2Tsz1z+1
Similarly, the d2c conversion relies on the inverse correspondence
H(s)=Hd(z),z=1+sTs/21sTs/2
When you convert a state-space model using the Tustin method, the states are not preserved. The
state transformation depends upon the state-space matrices and whether the system has time
delays. For example, for an explicit (E = I) continuous-time model with no time delays, the state
vector w[k] of the discretized model is related to the continuous-time state vector x(t) by:
w[kTs]=(IATs2)x(kTs)Ts2Bu(kTs)=x(kTs)Ts2(Ax(kTs)+Bu(kTs)).
Ts is the sample time of the discrete-time model. A and B are state-space matrices of the
continuous-time model.
Tustin Approximation with Frequency Prewarping
If your system has important dynamics at a particular frequency that you want the transformation
to preserve, you can use the Tustin method with frequency prewarping. This method ensures a
match between the continuous- and discrete-time responses at the prewarp frequency.
The Tustin approximation with frequency prewarping uses the following transformation of
variables:
Hd(z)=H(s),s=tan(Ts/2)z1z+1
This change of variable ensures the matching of the continuous- and discrete-time frequency
responses at the prewarp frequency , because of the following correspondence:
H(j)=Hd(ejTs)
Tustin Approximation for Systems with Time Delays
You can use the Tustin approximation to discretize SISO or MIMO continuous-time models with
time delays.
By default, the Tustin method rounds any time delay to the nearest multiple of the sample time.
Therefore, for any time delay tau, the integer portion of the delay, k*Ts, maps to a delay of k
sampling periods in the discretized model. This approach ignores the residual fractional delay,
tau - k*Ts.
You can to approximate the fractional portion of the delay by a discrete all-pass filter (Thiran
filter) of specified order. To do so, use the FractDelayApproxOrder option ofc2dOptions.
To understand how the Tustin method handles systems with time delays, consider the following
SISO state-space model G(s). The model has input delay i, output delay o, and internal delay .
The following figure shows the general result of discretizing G(s) using the Tustin method.
By default, c2d converts the time delays to pure integer time delays. The c2d command
computes the integer delays by rounding each time delay to the nearest multiple o.
Multi carrier equalization by restoration of redundanc y (merry) for adaptive...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The
performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed
DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated
and less complexity also involved by the simulation of the DST-DMT system.
Improved Timing Estimation Using Iterative Normalization Technique for OFDM S...IJECEIAES
Conventional timing estimation schemes based on autocorrelation experience perfor- mance degradation in the multipath channel environment with high delay spread. To overcome this problem, we proposed an improvement of the timing estimation for the OFDM system based on statistical change of symmetrical correlator. The new method uses iterative normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. Thus, it increases the detection probability and achieves better performance than previously published methods in the multipath environment. Computer simulation shows that our method is very robust in the fading multipath channel.
An identification of the tolerable time-interleaved analog-todigital convert...IJECEIAES
High-speed Terahertz communication systems has recently employed orthogonal frequency division multiplexing approach as it provides high spectral efficiency and avoids inter-symbol interference caused by dispersive channels. Such high-speed systems require extremely high-sampling time-interleaved analog-to-digital converters at the receiver. However, timing mismatch of time-interleaved analog-to-digital converters significantly causes system performance degradation. In this paper, to avoid such performance degradation induced by timing mismatch, we theoretically determine maximum tolerable mismatch levels for orthogonal frequency division multiplexing communication systems. To obtain these levels, we first propose an analytical method to derive the bit error rate formula for quadrature and pulse amplitude modulations in Rayleigh fading channels, assuming binary reflected gray code (BRGC) mapping. Further, from the derived bit error rate (BER) expressions, we reveal a threshold of timing mismatch level for which error floors produced by the mismatch will be smaller than a given BER. Simulation results demonstrate that if we preserve mismatch level smaller than 25% of this obtained threshold, the BER performance degradation is smaller than 0.5 dB as compared to the case without timing mismatch.
Computing f-Divergences and Distances of\\ High-Dimensional Probability Densi...Alexander Litvinenko
Talk presented on SIAM IS 2022 conference.
Very often, in the course of uncertainty quantification tasks or
data analysis, one has to deal with high-dimensional random variables (RVs)
(with values in $\Rd$). Just like any other RV,
a high-dimensional RV can be described by its probability density (\pdf) and/or
by the corresponding probability characteristic functions (\pcf),
or a more general representation as
a function of other, known, random variables.
Here the interest is mainly to compute characterisations like the entropy, the Kullback-Leibler, or more general
$f$-divergences. These are all computed from the \pdf, which is often not available directly,
and it is a computational challenge to even represent it in a numerically
feasible fashion in case the dimension $d$ is even moderately large. It
is an even stronger numerical challenge to then actually compute said characterisations
in the high-dimensional case.
In this regard, in order to achieve a computationally feasible task, we propose
to approximate density by a low-rank tensor.
Multi carrier equalization by restoration of redundanc y (merry) for adaptive...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The
performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed
DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated
and less complexity also involved by the simulation of the DST-DMT system.
Improved Timing Estimation Using Iterative Normalization Technique for OFDM S...IJECEIAES
Conventional timing estimation schemes based on autocorrelation experience perfor- mance degradation in the multipath channel environment with high delay spread. To overcome this problem, we proposed an improvement of the timing estimation for the OFDM system based on statistical change of symmetrical correlator. The new method uses iterative normalization technique to the correlator output before the detection based on statistical change of symmetric correlator is applied. Thus, it increases the detection probability and achieves better performance than previously published methods in the multipath environment. Computer simulation shows that our method is very robust in the fading multipath channel.
An identification of the tolerable time-interleaved analog-todigital convert...IJECEIAES
High-speed Terahertz communication systems has recently employed orthogonal frequency division multiplexing approach as it provides high spectral efficiency and avoids inter-symbol interference caused by dispersive channels. Such high-speed systems require extremely high-sampling time-interleaved analog-to-digital converters at the receiver. However, timing mismatch of time-interleaved analog-to-digital converters significantly causes system performance degradation. In this paper, to avoid such performance degradation induced by timing mismatch, we theoretically determine maximum tolerable mismatch levels for orthogonal frequency division multiplexing communication systems. To obtain these levels, we first propose an analytical method to derive the bit error rate formula for quadrature and pulse amplitude modulations in Rayleigh fading channels, assuming binary reflected gray code (BRGC) mapping. Further, from the derived bit error rate (BER) expressions, we reveal a threshold of timing mismatch level for which error floors produced by the mismatch will be smaller than a given BER. Simulation results demonstrate that if we preserve mismatch level smaller than 25% of this obtained threshold, the BER performance degradation is smaller than 0.5 dB as compared to the case without timing mismatch.
Computing f-Divergences and Distances of\\ High-Dimensional Probability Densi...Alexander Litvinenko
Talk presented on SIAM IS 2022 conference.
Very often, in the course of uncertainty quantification tasks or
data analysis, one has to deal with high-dimensional random variables (RVs)
(with values in $\Rd$). Just like any other RV,
a high-dimensional RV can be described by its probability density (\pdf) and/or
by the corresponding probability characteristic functions (\pcf),
or a more general representation as
a function of other, known, random variables.
Here the interest is mainly to compute characterisations like the entropy, the Kullback-Leibler, or more general
$f$-divergences. These are all computed from the \pdf, which is often not available directly,
and it is a computational challenge to even represent it in a numerically
feasible fashion in case the dimension $d$ is even moderately large. It
is an even stronger numerical challenge to then actually compute said characterisations
in the high-dimensional case.
In this regard, in order to achieve a computationally feasible task, we propose
to approximate density by a low-rank tensor.
Low rank tensor approximation of probability density and characteristic funct...Alexander Litvinenko
Very often one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (\pdf) and/or by the corresponding probability characteristic functions (\pcf), or by a function representation. Here the interest is mainly to compute characterisations like the entropy, or
relations between two distributions, like their Kullback-Leibler divergence, or more general measures such as $f$-divergences,
among others. These are all computed from the \pdf, which is often not available directly, and it is a computational challenge to even represent it in a numerically feasible fashion in case the dimension $d$ is even moderately large. It is an even stronger numerical challenge to then actually compute said characterisations in the high-dimensional case.
In this regard, in order to achieve a computationally feasible task, we propose to represent the density by a high order tensor product, and approximate this in a low-rank format.
Direct split-radix algorithm for fast computation of type-II discrete Hartley...TELKOMNIKA JOURNAL
In this paper, a novel split-radix algorithm for fast calculation the discrete Hartley transform of type-II (DHT-II) is intoduced. The algorithm is established through the decimation in time (DIT) approach, and implementedby splitting a length N of DHT-II into one DHT-II of length N/2 for even-indexed samples and two DHTs-II of length N/4 for odd-indexed samples. The proposed algorithm possesses the desired properties such as regularity, inplace calculation and it is represented by simple closed form decomposition sleading to considerable reductions in the arithmetic complexity compared to the existing DHT-II algorithms. Additionally, the validity of the proposed algorithm has been confirmed through analysing the arithmetic complexityby calculating the number of real additions and multiplications and associating it with the existing DHT-II algorithms.
Multi-carrier Equalization by Restoration of RedundancY (MERRY) for Adaptive ...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated and less complexity also involved by the simulation of the DST-DMT system.
I am Grey Nolan. Currently associated with matlabassignmentexperts.com as an assignment helper. After completing my master's from the University of British Columbia, I was in search for an opportunity that expands my area of knowledge hence I decided to help students with their Signals and Systems assignments. I have written several assignments till date to help students overcome numerous difficulties they face in Signals and Systems Assignments.
Discretizing of linear systems with time-delay Using method of Euler’s and Tu...IJERA Editor
Delays deteriorate the control performance and could destabilize the overall system in the theory of discretetime
signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control
applications, the data as seen from the computer and systems involved are naturally discrete-time because a
computer executes program code at discrete points of time. Theory of discrete-time dynamic signals and systems
is useful in design and analysis of control systems, signal filters, state estimators and model estimation from
time-series of process data system identification. In this paper, a new approximated discretization method and
digital design for control systems with delays is proposed. System is transformed to a discrete-time model with
time delays. To implement the digital modeling, we used the z-transfer functions matrix which is a useful model
type of discrete-time systems, being analogous to the Laplace-transform for continuous-time systems. The most
important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended
discrete-time. The proposed method can closely approximate the step response of the original continuous timedelayed
control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate
the effectiveness of the developed method.\
Wavelets are mathematical functions. The wavelet transform is a tool that cuts up data, functions or operators into different frequency components and then studies each component with a resolution matched to its scale. It is needed, because analyzing discontinuities and sharp spikes of the signal and applications as image compression, human vision, radar, and earthquake prediction. Wai Mar Lwin | Thinn Aung | Khaing Khaing Wai "Applications of Wavelet Transform" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27958.pdfPaper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/27958/applications-of-wavelet-transform/wai-mar-lwin
Why do you believe money laundering is a difficult fraud to investig.pdffsenterprises
Why do you believe money laundering is a difficult fraud to investigate
Solution
Money laundering is mostly a difficult situation to Investigate as sometimes it miss the clue
chain for tracking Criminals, Sometimes Criminals not have a identity/social security to trace
and the funds moved through offshore accounts is still unavailable for accessing any kind of
information to whom transferred and whom to be transferred.
It is very difficult to trace when governmental authority or Person or Agent or Agency of
authority support / help such kinds of frauds or Money laundering situations. They are looting
and transferring the money within seconds and closing the accounts for unidentity.
Sometimes It may not be difficult to investigate but difficult to gather the evidence We all know
facts so happened but difficult to get evidence and prove in the court of law as because of
unauthorised way of activity and transaction, If it is authorised then all documents are available.
Every Country may not follow transparency rather they follow their own rules and regulations
depending upon the situations it is facing around the world. some of the countries indirectly
encouraging by not laying appropriate controls by way of regulations.
Most of the Money Laundering happening in the united states are belonging too or linked to
another country which results in gathering the evidence from other countries which is so risky
and lot of intrications are involved and very tricky situations. Some of the countries still
following anonymous way to open bank account and close the same, The country indirectly
promoting money laundering thereby terrorism thereby harming world economy and peace.
Bitcoin is one of the example , is it authorised to issue such kind of currency or paper, where
funds are unknowly investing thereby increasing the value of bitcoin and realised gains are
transferring as a real earned Money.
The rules and Regulations and dual economy business treaty which always impact the
investigation in many ways which results in lack of evidence thereby relieving the case without
any proper action and prosecutions..
Which of the following is a characteristic of Baroque instrumental m.pdffsenterprises
Which of the following is a characteristic of Baroque instrumental music?
a. use of the direct ancestors of modern instruments
b. development of the orchestra
c. use of multi-movement works
d. all of the abovea.b.c.d.
Solution
Answer:
D.All of the above given characterize the Baroque instrumental music.
It uses direct ancestors of modern instruments with multi-movement works there were
development of the orchestra..
More Related Content
Similar to Using the Tustin equivalence with the prewarping method, fnd the dis.pdf
Low rank tensor approximation of probability density and characteristic funct...Alexander Litvinenko
Very often one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described by its probability density (\pdf) and/or by the corresponding probability characteristic functions (\pcf), or by a function representation. Here the interest is mainly to compute characterisations like the entropy, or
relations between two distributions, like their Kullback-Leibler divergence, or more general measures such as $f$-divergences,
among others. These are all computed from the \pdf, which is often not available directly, and it is a computational challenge to even represent it in a numerically feasible fashion in case the dimension $d$ is even moderately large. It is an even stronger numerical challenge to then actually compute said characterisations in the high-dimensional case.
In this regard, in order to achieve a computationally feasible task, we propose to represent the density by a high order tensor product, and approximate this in a low-rank format.
Direct split-radix algorithm for fast computation of type-II discrete Hartley...TELKOMNIKA JOURNAL
In this paper, a novel split-radix algorithm for fast calculation the discrete Hartley transform of type-II (DHT-II) is intoduced. The algorithm is established through the decimation in time (DIT) approach, and implementedby splitting a length N of DHT-II into one DHT-II of length N/2 for even-indexed samples and two DHTs-II of length N/4 for odd-indexed samples. The proposed algorithm possesses the desired properties such as regularity, inplace calculation and it is represented by simple closed form decomposition sleading to considerable reductions in the arithmetic complexity compared to the existing DHT-II algorithms. Additionally, the validity of the proposed algorithm has been confirmed through analysing the arithmetic complexityby calculating the number of real additions and multiplications and associating it with the existing DHT-II algorithms.
Multi-carrier Equalization by Restoration of RedundancY (MERRY) for Adaptive ...IJNSA Journal
This paper proposes a new blind adaptive channel shortening approach for multi-carrier systems. The performance of the discrete Fourier transform-DMT (DFT-DMT) system is investigated with the proposed DST-DMT system over the standard carrier serving area (CSA) loop1. Enhanced bit rates demonstrated and less complexity also involved by the simulation of the DST-DMT system.
I am Grey Nolan. Currently associated with matlabassignmentexperts.com as an assignment helper. After completing my master's from the University of British Columbia, I was in search for an opportunity that expands my area of knowledge hence I decided to help students with their Signals and Systems assignments. I have written several assignments till date to help students overcome numerous difficulties they face in Signals and Systems Assignments.
Discretizing of linear systems with time-delay Using method of Euler’s and Tu...IJERA Editor
Delays deteriorate the control performance and could destabilize the overall system in the theory of discretetime
signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control
applications, the data as seen from the computer and systems involved are naturally discrete-time because a
computer executes program code at discrete points of time. Theory of discrete-time dynamic signals and systems
is useful in design and analysis of control systems, signal filters, state estimators and model estimation from
time-series of process data system identification. In this paper, a new approximated discretization method and
digital design for control systems with delays is proposed. System is transformed to a discrete-time model with
time delays. To implement the digital modeling, we used the z-transfer functions matrix which is a useful model
type of discrete-time systems, being analogous to the Laplace-transform for continuous-time systems. The most
important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended
discrete-time. The proposed method can closely approximate the step response of the original continuous timedelayed
control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate
the effectiveness of the developed method.\
Wavelets are mathematical functions. The wavelet transform is a tool that cuts up data, functions or operators into different frequency components and then studies each component with a resolution matched to its scale. It is needed, because analyzing discontinuities and sharp spikes of the signal and applications as image compression, human vision, radar, and earthquake prediction. Wai Mar Lwin | Thinn Aung | Khaing Khaing Wai "Applications of Wavelet Transform" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-5 , August 2019, URL: https://www.ijtsrd.com/papers/ijtsrd27958.pdfPaper URL: https://www.ijtsrd.com/mathemetics/applied-mathematics/27958/applications-of-wavelet-transform/wai-mar-lwin
Why do you believe money laundering is a difficult fraud to investig.pdffsenterprises
Why do you believe money laundering is a difficult fraud to investigate
Solution
Money laundering is mostly a difficult situation to Investigate as sometimes it miss the clue
chain for tracking Criminals, Sometimes Criminals not have a identity/social security to trace
and the funds moved through offshore accounts is still unavailable for accessing any kind of
information to whom transferred and whom to be transferred.
It is very difficult to trace when governmental authority or Person or Agent or Agency of
authority support / help such kinds of frauds or Money laundering situations. They are looting
and transferring the money within seconds and closing the accounts for unidentity.
Sometimes It may not be difficult to investigate but difficult to gather the evidence We all know
facts so happened but difficult to get evidence and prove in the court of law as because of
unauthorised way of activity and transaction, If it is authorised then all documents are available.
Every Country may not follow transparency rather they follow their own rules and regulations
depending upon the situations it is facing around the world. some of the countries indirectly
encouraging by not laying appropriate controls by way of regulations.
Most of the Money Laundering happening in the united states are belonging too or linked to
another country which results in gathering the evidence from other countries which is so risky
and lot of intrications are involved and very tricky situations. Some of the countries still
following anonymous way to open bank account and close the same, The country indirectly
promoting money laundering thereby terrorism thereby harming world economy and peace.
Bitcoin is one of the example , is it authorised to issue such kind of currency or paper, where
funds are unknowly investing thereby increasing the value of bitcoin and realised gains are
transferring as a real earned Money.
The rules and Regulations and dual economy business treaty which always impact the
investigation in many ways which results in lack of evidence thereby relieving the case without
any proper action and prosecutions..
Which of the following is a characteristic of Baroque instrumental m.pdffsenterprises
Which of the following is a characteristic of Baroque instrumental music?
a. use of the direct ancestors of modern instruments
b. development of the orchestra
c. use of multi-movement works
d. all of the abovea.b.c.d.
Solution
Answer:
D.All of the above given characterize the Baroque instrumental music.
It uses direct ancestors of modern instruments with multi-movement works there were
development of the orchestra..
What was the energy that was not passed on to the next trophic le.pdffsenterprises
What was the energy that was not passed on to the next trophic level used for?
What was the energy that was not passed on to the next trophic level used for?
Solution
The energy is used for the various metabolic reactions occuring in the body such as digestion,
respiration and other metabolic reactions and so at each level some energy is lost..
What sort of religious ideas does the megalith Stonehenge suggest A.pdffsenterprises
What sort of religious ideas does the megalith Stonehenge suggest? Are these religious ideas
similar to or different from those of Egypt and Mesopotamia? Are Egypt and Mesopotamia
similar or different in their cultural ideas? What accounts for these similarities or differences?
Include examples and evidence to support your conclusions.
Solution.
What are successful approaches to forecasting and creating a needed .pdffsenterprises
What are successful approaches to forecasting and creating a needed public sector budget? How
much should we train personnel in budget forecasting and creation?
Solution
The successful approaches of forecasting and creating public sector budget are as follows:
The personnel training is necessary for the budget forecast.
What are the major challenges for managing health care information t.pdffsenterprises
What are the major challenges for managing health care information technology in the context of
health care reform? How should existing and future health care information technology be
managed?
Solution
Tha Major Challenges :
There are Mainly 5 Information Technology Challenges Faced by Healthcare Organizations
Healthcare is among the economic sectors facing the most significant challenges in
implementing effective IT solutions.
Chief information officers in healthcare settings must balance strict privacy and security
requirements with the need to constantly improve IT infrastructure and performance. From small
doctor’s offices to major hospitals, the healthcare IT environment is increasingly complex and, if
not managed appropriately, can negatively impact patient care.
A Growing Flood of Data
Healthcare data usage is growing at an exponential pace for a variety of reasons. Digital imaging
technologies, electronic medical records, and resource-taxing applications are placing a strain on
existing data infrastructures. Mobile applications and a growing use of telemedicine technologies
also are increasing data generation and the need for its secure storage and management.
Federal HIPAA Privacy Requirements
The Health Insurance Portability and Accountability Act, or HIPAA, requires medical providers
to safeguard patients’ private medical information. The federal law requires stringent procedures
for backing up data along with recovering data in disaster and emergency situations. The Health
Information Technology for Economic and Clinical Health act, or HITECH, strengthened
HIPAA and increased penalties and requirements for mandatory notifications when data
breaches occur.
Inadequate Data Storage Capacity
Data storage needs for healthcare double approximately every 18 months, largely due to
regulatory pressure to keep patient information indefinitely. Forward-thinking medical
organizations have begun implementing strategic, multi-tiered storage plans that include on-site,
off-site and virtual storage. But improving overall storage capacity also requires more efficient
software solutions for managing the massive and growing amounts of data that now exist in
diverse medical environments.
Lack of Communication among Healthcare Systems
Only in the past few years have electronic medical records become the standard, and data
systems that smoothly interface between all medical providers remain years away. While the
industry regularly rolls out innovations to improve patient care and facility operations, the
advances often have limited capability to “talk” to each other. This lack of ability to interface
across systems restricts the ability to automate processes and to capture and use data effectively,
decreasing the return on investment for technology.
Increasing Costs of IT Projects in Healthcare
Healthcare organizations are facing rapidly increasing IT costs from a number of drivers,
including government regulations, growing energy needs and pressure t.
Use Java programming Thank you very much Programing requirement for.pdffsenterprises
Use Java programming Thank you very much Programing requirement for: Safety Alert System
Version 01 I. Project and class name Create a new project name: yourfirst lastname program01
(you must include your name in the project name) Create a new class name: Safety Alert V0 1 II.
Requirement i. Input Prompt appropriate messages that asking use to enter: city name, season,
temperature, and raining. Input validation: your program has to valid the user input and prompt
specific message when user enter invalid input. Base on following validation: City name: only
can be string of letters, not containing number. Maximum length is 20 Season: only can be either
SUMMER or WINTER Temperature is in double Raining is in integer number if the program
found an invalid input, prompt a specific message that tell which input is invalid and what is the
correction format ofthat input should be, then STOP the program. That Page 2 of 4
Solution
import java.util.*;
class Safety_Alert_VO_1
{
private static double CONST_MIN_TEMP_WINTER = -20;
private static double CONST_MAX_TEMP_SUMMER = 127;
public static void main (String[] args)
{
Scanner scan = new Scanner(System.in);
boolean road_ice,call_for_help,flood,tminchange,tmaxchange;
road_ice = false;
call_for_help = false;
tminchange = false;
tmaxchange = false;
String stay_inside = \"no\";
System.out.println(\"Enter city name \");
String city = scan.next();
if ((city.contains(\"[a-zA-Z]+\") == true) || (city.length() > 20))
{
System.out.println(\"Error: city name should be a string with not more than 20
characters\");
System.exit(0);
}
System.out.println(\"Enter season : \");
String season = scan.next();
if(!(season.equals(\"WINTER\") || season.equals(\"SUMMER\")))
{
System.out.println(\"Error Season can be SUMMER or WINTER\");
System.exit(0);
}
System.out.println(\"Enter temperature : \");
double temp = scan.nextDouble();
System.out.println(\"Enter raining : \");
int rain = scan.nextInt();
switch(season)
{
case \"WINTER\": if((temp < 32)&&(rain > 0))
road_ice = true;
if((temp < 5)||(rain>250))
stay_inside = \"yes\";
else
stay_inside = \"no\";
if((temp<-15)||(rain>500))
call_for_help = true;
if(temp350)
flood = true;
if((temp>120)||(rain>250))
stay_inside = \"yes\";
else
stay_inside = \"no\";
if((temp>125)||(rain>500))
call_for_help = true;
if(temp>CONST_MAX_TEMP_SUMMER)
{
CONST_MAX_TEMP_SUMMER =
Math.max(temp,CONST_MAX_TEMP_SUMMER);
tmaxchange = true;
}
}
System.out.println(\"CS103 Spring 2017\");
System.out.println(\"Student : first and last name \");
System.out.println(\"Index Number : \");
System.out.println(\"The Cities Safety Alert System V01\");
System.out.println(\"City Name : \"+city);
System.out.println(\"Season : \"+season);
System.out.println(\"Temperature : \"+temp+ \" Raining : \"+rain);
System.out.println(\"Road icing : \"+road_ice+\" Stay inside : \"+stay_inside);
if(tminchange == true)
System.out.println(\"This is the new minimum temperature record\");
if(tmaxchange == true)
System.out.println(\"This is.
Translate the following C++ code segment into Mic-1 IJVM machine lan.pdffsenterprises
Translate the following C++ code segment into Mic-1 IJVM machine language, assuming i, j,
and k are the first, the second and third local variables, respectively.
i=i-j; if (i==8) ksiEEJ; =1 else k=i | j; k-1 | | j; ji&- fk1k
Solution
step 1 :first declare the variables i,j,k in the main section.
Here we assumed that i,j,k have values initially. Otherwise we need to push the value onto the
stack and store it in the variables before starting the operations.
step 2: write the code after ending the variables declaration section
step3: write halt before ending main
.main
.var
i
j
k
.end-var
ILOAD i
ILOAD j
ISUB
ISTORE i
ILOAD i
BIPUSH 8
IF_ICMPEQ L1 // if(i==8)
ILOAD i
ILOAD j
IOR // k=i||j
ISTORE k
GOTO L2
L1: ILOAD i
ILOAD j
IAND // k=i&&j
ISTORE k
L2:
HALT
.end-main.
Transactions On September 1 of the current year, Joy Tucker estab.pdffsenterprises
Transactions
On September 1 of the current year, Joy Tucker established a business to manage rental
property. She completed the following transactions during September:
Required:
1. Indicate the effect of each transaction and the balances after each transaction:
For those boxes in which no entry is required, leave the box blank.
For those boxes in which you must enter subtractive or negative numbers use a minus sign.
(Example: -300)
2. Stockholders\' equity is the right of stockholders\' to the assets of the business. These rights are
increased by issuing common stock and revenues and decreased by dividends and expenses.
3. Determine the net income for September.
$
4. How much did September\'s transactions (a-j) increase or decrease retained earnings?
Increased by $Assets=Liabilities+Stockholders\' EquityItemCash+Accounts
Receivable+Supplies=Accounts Payable+Common Stock-Dividends+Fees Earned-Rent
Expense-Sal. Expense-Supp. Expense-Auto Expense-Misc. ExpenseItem a. a. b. b. Bal. Bal.
c. c. Bal. Bal. d. d. Bal. Bal. e. e. Bal. Bal. f. f. Bal. Bal. g. g. Bal. Bal. h. h. Bal.
Bal. i. i. Bal. Bal. j. j. Bal. Bal.
Solution.
To correct the vision of a person who is nearR sighted, we use a div.pdffsenterprises
To correct the vision of a person who is nearR sighted, we use a diverging lens to cause the rays
from the distant object to diverge slightly, as if they were coming from a closer object, allowing
the eye to focus the image on the retina. In this example, a nearRsighted eye has near and far
points of 12 cm and 17 cm, respectively. Assume that the prescribed lens is 2.0 cm from the eye.
a) What lens power is needed for this person to see a distant object clearly? For a distant object,
the lens must put the image at the far point of the eye so that the person can focus
on it.
i) What is the object distance?
ii) What is the image distance?
iii) Now you can use the thin lens equation to find the focal length of the lens that must be
prescribed:
iv) What is the power of the lens?
Solution
i) Object distance is u= infinity
ii) Now the image from the lens should be at the far point. Since the image is in front of the lens,
it is negative
Image distance is v= -15cm
iii) Thin lens equation => 1/f=1/u+1/v
=>1/f=1/inf+1/(-15)
=>f=-15cm
iv) Power =1/f(in m)=-1/0.15=-6.67D.
The height of the water in the tank pictured below 7 ft. The tank is.pdffsenterprises
The height of the water in the tank pictured below 7 ft. The tank is emptied from a pump at the
top of the tank. Set up an integral to determine how much work is done by the pump. dont need
to evaluate.
Solution
there is no picture displayed ( picture mentioned in the question).. please post again
with the picture...
Suppose that a classroom has 4 light bulbs. The probability that eac.pdffsenterprises
Suppose that a classroom has 4 light bulbs. The probability that each individual light bulbs work
is 0.6. Suppose that each light bulb works independently of the other light bulbs. What is the
probability that none of the 4 light bulbs work?
Solution
Probabiltiy that bulb lights=0.6
probability that bulb doesnot light=1-0.6=0.4
P(None works)=0.4*0.4*0.4*0.4=0.0256.
Security Standards Please respond to the following A number of .pdffsenterprises
\"Security Standards\" Please respond to the following: A number of organizations exist to define
information security standards. Explain the importance of standards organizations with regard to
both information systems and information systems security. Provide a rationale for your
response. Determine two (2) specific concerns that you believe exist for cloud deployments, and
ascertain whether or not data breaches, such as the Snowden Incident have heightened concerns.
Justify your answer.
Solution
Information security for information systems are key for sustaining the organization and its
identity in the information technology environment. As per the continues improvement on
sustaining system, information systems security standardization was created huge importance to
secure the organization information and to maintain certain guidelines to mitigate problems.
The following standard organizations provide guidelines and required certifications for business
organizations to ensure the security of information systems.
American National Standards Institute (ANSI)
Global Engineering Documents
British Standards Institute (BSi)
British Standard 7799 (BS7799)
Center for Internet Security (CIS)
Institute of Electrical and Electronic Engineers (IEEE)
IEEE standards that relate to Security
International Information Systems Security Certification Consortium, Inc. (ISC)2
International Organization for Standardization (ISO)
ISO/IEC 17799:2000
ISO 17799 Community Forum
Internet Architecture Board (IAB)
Internet Assigned Numbers Authority (IANA)
National Institute of Standards and Technology (NIST)
Computer Security Resource Center (CSRC)
Guide to NIST Information Security Documents
Federal Information Processing Standard 200 (FIPS 200)
Federal Information Processing Standard 201 (FIPS 201-1)
Guide for Developing Security Plans for Federal Information Systems
Federal Desktop Core Configuration (FDCC)
National Security Agency (NSA)
Rationale: It is always recommend to apply at least to follow any of the applicable
standardization guidelines, in order to keep sustainable information systems in organization.
Standardization always says and improves the security and controls on allowing security
breaches to our MIS.
Recent times could computing has become the predominant growth for small and medium scale
organization to mitigate the cost of implementation on information systems. Security of the same
and allowing access to external agents is so critical which is directly granting access to important
data. Like the above standard guidelines tell us to maintain the NDAs, system access controls..
Real Estate Finance essay questionWhy did observers at first belie.pdffsenterprises
Real Estate Finance essay question
Why did observers at first believe that the damage from the impending subprime mortgage crisis
would be too small to cause a recession?
Solution
Subprime lending is the loan\'s, given by the banks to the people based on there creditworthiness,
banks initially thought that they will earn high profits by giving loans at higher rate of interest to
the people, in case if they fail to deposit the loaned amount back, the bank will profit by selling
the land/home, they assumed that real state prices will rise with respect to time. Sooner the
borrowers started to default on there EMI\'s, as well the availability of houses increased at such a
level that nobody seemed to be interested, thus this asset is called toxic asset or the bubble burst
has occured in the economy.
Initially, it is beleived that this subprime crisis would be too small to cause a recession because
the market was on the peak, real state prices are high, investors worldwide are investing in USA,
mortgage backed securities to stronghold securitization process, governments supportive policies
etc are some of the factors that led to this mirage like situation.
As the borrowers defaulted, the creditors lost there confidence in the american banking system,
soon the stocks crashed, people started taking there money back from the banks, the liquidity
disbalanced, also it lead to the cascading effect, other european economies also affected as
investors from this countries also occured big losses, in order to sustain this shock, there is high
unemployement, cost cutting etc which further elevated the problems..
Provide your key points of Setup Reducation Provide your key points.pdffsenterprises
Provide your key points of Setup Reducation? Provide your key points of Kanban? Provide
how a Kaizen event works? What are the benefts?
Solution
Key points for setup reduction
1.Documentation of the setup
2.Divide events into internal and external events
3.Convert internal to external events
4.Streamline internal events by simplifying,reducing and eliminating.
Please help. C++ The program is an interactive program th.pdffsenterprises
Please help. C++
The program is an interactive program that reads input from the keyboard. Several instructions
(listed below) may be entered by the user. For each input, the program will give a short response
printed to cout. Each response to cout is followed by a single endl.
Important: The program must not try to store all the numbers in a single big array. In fact, it is
outlawed by the CSI police that you have any array that is larger than 100 elements. Instead, you
should create a frequency array which has indexes from [0] to [99]. A location, such as
frequency[i], tells you how many times the number i has occurred in the input. This frequency
array should be initialized to all zeros, and each time a number is read, the program will add one
to the corresponding array location. For example, frequency[42] begins at zero. When one 42 is
read, frequency[42] is increased to one. If another 42 is read, frequency[42] is increased to two,
and so on. All of the statistics that you need to calculate can be computed based on the frequency
array (so that you don\'t need to store all those numbers separately).
• Input: The letter N followed by an integer in the range 0 to 99. The biggest possible input
number is 99. The specification does not care what the program does for numbers that are
outside of the legal range.
Output: The word \"OK\".
• Input: The letter S.
Output: The output is the SUM of all the input numbers read so far. This output is 0 if there has
not yet been any numbers read by the program.
• Input: The letter A.
Output: The output is the AVERAGE of all the input numbers read so far, calculated as a double
number. For example, if there have been four input numbers 2, 2, 6 and 5, then the average is
3.75. If there has not yet been any input numbers, then the program should print the word
\"ERROR\" instead of an average.
• Input: The letter B.
Output: The output is the BIGGEST of all the input numbers read so far, For example, if there
have been four input numbers 2, 2, 6 and 5, then the biggest is 6. If there has not yet been any
input numbers, then the program should print the word \"ERROR\" instead of a number.
• Input: The letter F.
Output: The output is the most FREQUENT of all the input numbers read so far--in other words,
the number that has been read most often (also called the \"mode\"). If there are several numbers
that are equally often, then the smallest number is printed. For example, if there have been four
input numbers 2, 2, 6 and 5, then the most frequent is 2. If there has not yet been any input
numbers, then the program should print the word \"ERROR\" instead.
• Input: The letter H.
Output: The output is a count of HOW MANY numbers have been input so far. This could be as
small as zero.
• Input: The letter M.
Output: The output is the MEDIAN of all the input numbers read so far. The median is a number
that has no more than half of the input numbers below it and no more than half the input numbers
above it. For example.
please answer this case using down picturein business ethics emplo.pdffsenterprises
please answer this case using down picture
in business ethics employee benefits CASE 4: Richard and Conway are talking in the hallway
about the program. Conway, who has had some recent financial trouble, explains to Richard how
the benefits program has a loophole that will allow him to receive some financial assistance that
he really needs to help pay health care costs for his mother. Cathy, a fellow worker, overhears
the conversation. Later, Cathy is approached by her supervisor who says he heard a rumor that
some people were Ataking advantage of the company benefits program
Solution
1. The ethical issue or problem in this case is that Conway has found a loophole in the employee
benefits program. Cathy overheard the conversation between Conway and Richard and the
ethical issue that she is facing her is that should she inform her supervisor that Conway has
found a loophole and thus violate Conway\'s rights or should she keep quiet about the issue and
let the employees take advantage of the program.
2. The facts that have most bearing on the case are: Conway had told Richard about his financial
troubles. Conway\'s mother\'s health, and the possibility of the company losing money due to the
loophole are the factors that have a bearing on the case.
3. Conway will be affected if Cathy informs the supervisor and he may get fired. In this case
Cathy will get an award. Richard can also be fired as he has the information and selects not to
pass on this information to his supervisor.
4. Conway would expect that the supervisor is not informed so that he can use the financial
assistance for the treatment of his mother. Cathy would expect an award for informing about the
loophole. Richard was just a listener and will expect nothing from me.
5. 3 alternatives (i) Inform the supervisor about the loophole. In this case, the best case scenario
is that the supervisor will plug the loophole and award Cathy for the information. As Conway
was in real need of money for his mother\'s treatment, he will not be punished and will be let off
with a warning. The worst case scenario is that Conway will be fired.
(ii) do not inform the supervisor about the loophole but confront Conway so as to not take any
unwarranted advantage of this loophole in future. The best case scenario is that Conway will use
the loophole to get his mother\'s treatment and the loophole will not be abused by him in future.
The worst case is that Conway and Richard start abusing the loophole for their personal
advantage. (iii) The last alternative is to do nothing. The best case scenario is that Conway will
use the loophole to get his mother\'s treatment and the loophole will not be abused by him in
future. The worst case is that Conway and Richard start abusing the loophole for their personal
advantage.
6. The course of action determined by me is to plug the loopholes. This will ensure that the
company does not lose money in future. However, Conway should be allowed by HR to take
some financial a.
Al has three times as much money as Bill. Bill has two times as much.pdffsenterprises
Al has three times as much money as Bill. Bill has two times as much money as Charlie. If
Charlie has $5.89, how much money does Al have?
A. $11.78
B. $19.79
C. $29.24
D. $35.34
Solution
D. Create equations to solve this problem.
Al=3(Bill)
Bill = 2(Charlie)
Charlie=$5.98
Solve for Al. Substitute what you know into the formulas.
Bill = 2($5.89)
Bill = $11.78
To find Al, substitute what you know about Bill.
Al = 3($11.78)
Al = $35.34.
A SURVEY is a tool used to collect information about a population. L.pdffsenterprises
A SURVEY is a tool used to collect information about a population. List 2 strengths and 2
weaknesses of this tool.
Solution
Surveys are economical
They collect huge amount of data.with simple means like proper questionnaire.and not needing
any advanced equipment,
They help in providing overall idea regarding any issue
But they are time consuming
and the outcome depends on the effectivenes of the questions, approach to the people and their
response...So any communication gap leads to inaccurate studies..
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Using the Tustin equivalence with the prewarping method, fnd the dis.pdf
1. Using the Tustin equivalence with the prewarping method, fnd the discrete equivalent of the
following H(s): H s s s s s ( ) = + + + + 2 5 7 3 8 2 2 With h = 0.5, conduct a Bode plot
comparison of continuous, Tustin equivalent, and backward differences.
Solution
Tustin Approximation
The Tustin or bilinear approximation yields the best frequency-domain match between the
continuous-time and discretized systems. This method relates the s-domain and z-domain
transfer functions using the approximation:
z=esTs1+sTs/21sTs/2.
In c2d conversions, the discretization Hd(z) of a continuous transfer function H(s) is:
Hd(z)=H(s),s=2Tsz1z+1
Similarly, the d2c conversion relies on the inverse correspondence
H(s)=Hd(z),z=1+sTs/21sTs/2
When you convert a state-space model using the Tustin method, the states are not preserved. The
state transformation depends upon the state-space matrices and whether the system has time
delays. For example, for an explicit (E = I) continuous-time model with no time delays, the state
vector w[k] of the discretized model is related to the continuous-time state vector x(t) by:
w[kTs]=(IATs2)x(kTs)Ts2Bu(kTs)=x(kTs)Ts2(Ax(kTs)+Bu(kTs)).
Ts is the sample time of the discrete-time model. A and B are state-space matrices of the
continuous-time model.
Tustin Approximation with Frequency Prewarping
If your system has important dynamics at a particular frequency that you want the transformation
to preserve, you can use the Tustin method with frequency prewarping. This method ensures a
match between the continuous- and discrete-time responses at the prewarp frequency.
The Tustin approximation with frequency prewarping uses the following transformation of
variables:
Hd(z)=H(s),s=tan(Ts/2)z1z+1
This change of variable ensures the matching of the continuous- and discrete-time frequency
responses at the prewarp frequency , because of the following correspondence:
H(j)=Hd(ejTs)
Tustin Approximation for Systems with Time Delays
You can use the Tustin approximation to discretize SISO or MIMO continuous-time models with
time delays.
2. By default, the Tustin method rounds any time delay to the nearest multiple of the sample time.
Therefore, for any time delay tau, the integer portion of the delay, k*Ts, maps to a delay of k
sampling periods in the discretized model. This approach ignores the residual fractional delay,
tau - k*Ts.
You can to approximate the fractional portion of the delay by a discrete all-pass filter (Thiran
filter) of specified order. To do so, use the FractDelayApproxOrder option ofc2dOptions.
To understand how the Tustin method handles systems with time delays, consider the following
SISO state-space model G(s). The model has input delay i, output delay o, and internal delay .
The following figure shows the general result of discretizing G(s) using the Tustin method.
By default, c2d converts the time delays to pure integer time delays. The c2d command
computes the integer delays by rounding each time delay to the nearest multiple of the sample
time Ts. Thus, in the default case, mi = round(i /Ts), mo = round(o/Ts), and m = round(/Ts)..
Also in this case, Fi(z) = Fo(z) = F(z) = 1.
If you set FractDelayApproxOrder to a non-zero value, c2d approximates the fractional portion
of the time delays by Thiran filters Fi(z), Fo(z), and F(z).
The Thiran filters add additional states to the model. The maximum number of additional states
for each delay is FractDelayApproxOrder.
for the input delay i, the order of the Thiran filter Fi(z) is:
order(Fi(z)) = max(ceil(i /Ts), FractDelayApproxOrder).
If ceil(i /Ts) < FractDelayApproxOrder, the Thiran filter Fi(z) approximates the entire input
delay i. If ceil(i/Ts) > FractDelayApproxOrder, the Thiran filter only approximates a portion of
the input delay. In that case, c2d represents the remainder of the input delay as a chain of unit
delays z–mi, where
mi = ceil(i /Ts) – FractDelayApproxOrder.
c2d uses Thiran filters and FractDelayApproxOrder in a similar way to approximate the output
delay o and the internal delay .
When you discretizetf and zpk models using the Tustin method, c2d first aggregates all input,
output, and transfer delays into a single transfer delay TOT for each channel. c2dthen
approximates TOT as a Thiran filter and a chain of unit delays in the same way as described for
each of the time delays in ss models.
Zero-Pole Matching Equivalents
The method of conversion by computing zero-pole matching equivalents applies only to SISO
systems. The continuous and discretized systems have matching DC gains. Their poles and zeros
are related by the transformation:
zi=esiTszzz
where:
3. Zero-Pole Matching for Systems with Time Delays
You can use zero-pole matching to discretize SISO continuous-time models with time delay,
except that the method does not support ss models with internal delays. The zero-pole matching
method handles time delays in the same way as the Tustin approximation.
Tustin Approximation
The Tustin or bilinear approximation yields the best frequency-domain match between the
continuous-time and discretized systems. This method relates the s-domain and z-domain
transfer functions using the approximation:
z=esTs1+sTs/21sTs/2.
In c2d conversions, the discretization Hd(z) of a continuous transfer function H(s) is:
Hd(z)=H(s),s=2Tsz1z+1
Similarly, the d2c conversion relies on the inverse correspondence
H(s)=Hd(z),z=1+sTs/21sTs/2
When you convert a state-space model using the Tustin method, the states are not preserved. The
state transformation depends upon the state-space matrices and whether the system has time
delays. For example, for an explicit (E = I) continuous-time model with no time delays, the state
vector w[k] of the discretized model is related to the continuous-time state vector x(t) by:
w[kTs]=(IATs2)x(kTs)Ts2Bu(kTs)=x(kTs)Ts2(Ax(kTs)+Bu(kTs)).
Ts is the sample time of the discrete-time model. A and B are state-space matrices of the
continuous-time model.
Tustin Approximation with Frequency Prewarping
If your system has important dynamics at a particular frequency that you want the transformation
to preserve, you can use the Tustin method with frequency prewarping. This method ensures a
match between the continuous- and discrete-time responses at the prewarp frequency.
The Tustin approximation with frequency prewarping uses the following transformation of
variables:
Hd(z)=H(s),s=tan(Ts/2)z1z+1
This change of variable ensures the matching of the continuous- and discrete-time frequency
responses at the prewarp frequency , because of the following correspondence:
H(j)=Hd(ejTs)
Tustin Approximation for Systems with Time Delays
You can use the Tustin approximation to discretize SISO or MIMO continuous-time models with
time delays.
By default, the Tustin method rounds any time delay to the nearest multiple of the sample time.
Therefore, for any time delay tau, the integer portion of the delay, k*Ts, maps to a delay of k
sampling periods in the discretized model. This approach ignores the residual fractional delay,
4. tau - k*Ts.
You can to approximate the fractional portion of the delay by a discrete all-pass filter (Thiran
filter) of specified order. To do so, use the FractDelayApproxOrder option ofc2dOptions.
To understand how the Tustin method handles systems with time delays, consider the following
SISO state-space model G(s). The model has input delay i, output delay o, and internal delay .
The following figure shows the general result of discretizing G(s) using the Tustin method.
By default, c2d converts the time delays to pure integer time delays. The c2d command
computes the integer delays by rounding each time delay to the nearest multiple of the sample
time Ts. Thus, in the default case, mi = round(i /Ts), mo = round(o/Ts), and m = round(/Ts)..
Also in this case, Fi(z) = Fo(z) = F(z) = 1.
If you set FractDelayApproxOrder to a non-zero value, c2d approximates the fractional portion
of the time delays by Thiran filters Fi(z), Fo(z), and F(z).
The Thiran filters add additional states to the model. The maximum number of additional states
for each delay is FractDelayApproxOrder.
for the input delay i, the order of the Thiran filter Fi(z) is:
order(Fi(z)) = max(ceil(i /Ts), FractDelayApproxOrder).
If ceil(i /Ts) < FractDelayApproxOrder, the Thiran filter Fi(z) approximates the entire input
delay i. If ceil(i/Ts) > FractDelayApproxOrder, the Thiran filter only approximates a portion of
the input delay. In that case, c2d represents the remainder of the input delay as a chain of unit
delays z–mi, where
mi = ceil(i /Ts) – FractDelayApproxOrder.
c2d uses Thiran filters and FractDelayApproxOrder in a similar way to approximate the output
delay o and the internal delay .
When you discretizetf and zpk models using the Tustin method, c2d first aggregates all input,
output, and transfer delays into a single transfer delay TOT for each channel. c2dthen
approximates TOT as a Thiran filter and a chain of unit delays in the same way as described for
each of the time delays in ss models.
Zero-Pole Matching Equivalents
The method of conversion by computing zero-pole matching equivalents applies only to SISO
systems. The continuous and discretized systems have matching DC gains. Their poles and zeros
are related by the transformation:
zi=esiTszzz
where:
Zero-Pole Matching for Systems with Time Delays
You can use zero-pole matching to discretize SISO continuous-time models with time delay,
except that the method does not support ss models with internal delays. The zero-pole matching