Filters can be classified based on the range of frequencies they allow to pass. Butterworth filters provide maximally flat frequency response in the passband. They are designed by determining the filter order based on the required stopband attenuation. The poles are then calculated and the transfer function is the ratio of polynomials formed from the poles. Butterworth filter design involves converting specifications to a lowpass prototype, finding the poles, and transforming the prototype to the desired filter type.
Salient Features:
The magnitude response is nearly constant(equal to 1) at lower frequencies
There are no ripples in passband and stop band
The maximum gain occurs at Ω=0 and it is H(Ω)=1
The magnitude response is monotonically decreasing
As the order of the filter ‘N’ increases, the response of the filter is more close to the ideal response
Bilinear z-transformation is the most common method for converting the transfer function H(s) of the analog filter to the transfer function H(z) of the digital filter and vice versa. In this work, introducing the relationship between the digital coefficients and the analog coefficients in the matrix equation definitely involves the Pascal’s triangle.
Salient Features:
The magnitude response is nearly constant(equal to 1) at lower frequencies
There are no ripples in passband and stop band
The maximum gain occurs at Ω=0 and it is H(Ω)=1
The magnitude response is monotonically decreasing
As the order of the filter ‘N’ increases, the response of the filter is more close to the ideal response
Bilinear z-transformation is the most common method for converting the transfer function H(s) of the analog filter to the transfer function H(z) of the digital filter and vice versa. In this work, introducing the relationship between the digital coefficients and the analog coefficients in the matrix equation definitely involves the Pascal’s triangle.
Analysis of Butterworth and Chebyshev Filters for ECG Denoising Using WaveletsIOSR Journals
Abstract: A wide area of research has been done in the field of noise removal in Electrocardiogram signals.. Electrocardiograms (ECG) play an important role in diagnosis process and providing information regarding heart diseases. In this paper, we propose a new method for removing the baseline wander interferences, based on discrete wavelet transform and Butterworth/Chebyshev filtering. The ECG data is taken from non-invasive fetal electrocardiogram database, while noise signal is generated and added to the original signal using instructions in MATLAB environment. Our proposed method is a hybrid technique, which combines Daubechies wavelet decomposition and different thresholding techniques with Butterworth or Chebyshev filter. DWT has good ability to decompose the signal and wavelet thresholding is good in removing noise from decomposed signal. Filtering is done for improved denoising performence. Here quantitative study of result evaluation has been done between Butterworth and Chebyshev filters based on minimum mean squared error (MSE), higher values of signal to interference ratio and peak signal to noise ratio in MATLAB environment using wavelet and signal processing toolbox. The results proved that the denoised signal using Butterworth filter has a better balance between smoothness and accuracy than the Chebvshev filter. Keywords: Electrocardiogram, Discrete Wavelet transform, Baseline Wandering, Thresholding, Butterworth, Chebyshev
Design of Filter Circuits using MATLAB, Multisim, and ExcelDavid Sandy
The purpose of this project was to design crossover active filter circuits, in order to drive music through three different types of speakers. So, high frequencies would be sent through a Tweeter speaker, low frequencies would be sent through a Woofer speaker, and middle frequencies would be sent through a Midbass driver speaker. Three circuits were created to drive these speakers. Multisim, MATLAB, and Excel, were all used in the design process in order to create the filter circuits correctly.
Embedded systems increasingly employ digital, analog and RF signals all of which are tightly synchronized in time. Debugging these systems is challenging in that one needs to measure a number of different signals in one or more domains (time, digital, frequency) and with tight time synchronization. This session will discuss how a digital oscilloscope can be used to effectively debug these systems, and some of the instrumentation considerations that go along with this.
Analysis of Butterworth and Chebyshev Filters for ECG Denoising Using WaveletsIOSR Journals
Abstract: A wide area of research has been done in the field of noise removal in Electrocardiogram signals.. Electrocardiograms (ECG) play an important role in diagnosis process and providing information regarding heart diseases. In this paper, we propose a new method for removing the baseline wander interferences, based on discrete wavelet transform and Butterworth/Chebyshev filtering. The ECG data is taken from non-invasive fetal electrocardiogram database, while noise signal is generated and added to the original signal using instructions in MATLAB environment. Our proposed method is a hybrid technique, which combines Daubechies wavelet decomposition and different thresholding techniques with Butterworth or Chebyshev filter. DWT has good ability to decompose the signal and wavelet thresholding is good in removing noise from decomposed signal. Filtering is done for improved denoising performence. Here quantitative study of result evaluation has been done between Butterworth and Chebyshev filters based on minimum mean squared error (MSE), higher values of signal to interference ratio and peak signal to noise ratio in MATLAB environment using wavelet and signal processing toolbox. The results proved that the denoised signal using Butterworth filter has a better balance between smoothness and accuracy than the Chebvshev filter. Keywords: Electrocardiogram, Discrete Wavelet transform, Baseline Wandering, Thresholding, Butterworth, Chebyshev
Design of Filter Circuits using MATLAB, Multisim, and ExcelDavid Sandy
The purpose of this project was to design crossover active filter circuits, in order to drive music through three different types of speakers. So, high frequencies would be sent through a Tweeter speaker, low frequencies would be sent through a Woofer speaker, and middle frequencies would be sent through a Midbass driver speaker. Three circuits were created to drive these speakers. Multisim, MATLAB, and Excel, were all used in the design process in order to create the filter circuits correctly.
Embedded systems increasingly employ digital, analog and RF signals all of which are tightly synchronized in time. Debugging these systems is challenging in that one needs to measure a number of different signals in one or more domains (time, digital, frequency) and with tight time synchronization. This session will discuss how a digital oscilloscope can be used to effectively debug these systems, and some of the instrumentation considerations that go along with this.
Digital Implementation of Costas Loop with Carrier RecoveryIJERD Editor
Demodulator circuit is a basic building block of wireless communication. Digital implementation of
demodulator is attracting more attention for the significant advantages of digital systems than analog systems.
The carrier signal extraction is the main problem in synchronous demodulation in design of demodulator based
on Software Defined Radio. When transmitter or receiver in motion, it is difficult for demodulator to generate
carrier signal same in frequency and phase as transmitter carrier signal due to Doppler shift and Doppler rate.
Here the digital implementation of Costas loop for QPSK demodulation in continuous mode is discussed with
carrier recovery using phase locked loop.
- Obtained the Fast Fourier Transform of signals.
- Designed and Validated Low Pass, High Pass, and Band Pass filters in compliance with the specifications.
- Produced and compared graphs of the results upon processing.
A Low power discrete time sigma delta ADC consisting of a second order sigma delta modulator and third order Cascaded Integrated Comb (CIC) filter is proposed. The second order modulator is designed to work at a signal band of 20K Hz at an oversampling ratio of 64 with a sampling frequency of 2.56 MHz. It achieves a signal to noise ratio of 85.2dB and a resolution of 14 bits. The CIC digital filter is designed to implement a decimation factor of 64, operating at a maximum sampling frequency of 2.56 MHz. A second order sigma delta modulator is implemented in 0.18micron CMOS technology using full custom design and the third order digital CIC decimation filter is implemented in verilog HDL. The complete Sigma Delta ADC, consisting of analog block of second order modulator and digital block of decimator consumes a
total power 1.96mW.
Performance Analysis and Simulation of Decimator for Multirate ApplicationsIJEEE
In this paper, a decimator design has been presented for multirate digital signal processing. The decimator design has been analysed and simulated for performance comparison in terms of filter order and ripple factor. Direct form-I with decimation factor 2 have been used for performance and ripple analysis. The decimators have been designed & simulated using MATLAB. It can be observed from the simulated results that as we increase the filter order, ripple factor decreases, for the same filter structure. On the other hand, increasing filter order will increase its area and implementation cost.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
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Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
2. ٢
Slide ٣
Digital Signal Processing
Filter types
Slide ٤
Digital Signal Processing
Filter types according to its frequency response
Butterworth filter
Chebychev I filter
Chebychev II filter
Elliptic filter
Filter types
3. ٣
Slide ٥
Digital Signal Processing
Butterworth filter
Ideal lowpass filter is shown in the figure
The passband is normalised to one.
Tolerance in passband and stopband are allowed to enable
the construction of the filter.
Slide ٦
Digital Signal Processing
Lowpass prototype filter
Lowpass prototype filter: it is a lowpass filter with
cutoff frequency p=1.
Lowpass
prototype
filter
Frequency
Transformation
Lowpass filter
Highpass filter
Bandpass filter
Bandreject filter
The frequency scale is normalized by p. We use = / p.
4. ٤
Slide ٧
Digital Signal Processing
Lowpass prototype filter
Notation
In analogue filter design we will use
s to denote complex frequency
to denote analogue frequency
p to denote complex frequency at lowpass prototype
frequencies.
to denote analogue frequency at the lowpass prototype
frequencies.
Slide ٨
Digital Signal Processing
Magnitude Approximation of Analog Filters
The transfer function of analogue filter is given as rational
function of the form
The Fourier transform is given by
nm
sdsdsdd
scscscc
sH n
n
m
mo
2
210
2
21
n
n
n
m
m
m
o
js
djdjdd
cjcjcc
sHH
2
210
2
21
)(
j
ejHH )(
5. ٥
Slide ٩
Digital Signal Processing
Magnitude Approximation of Analog Filters
Analogue filter is usually expressed in term of
Example
Consider the transfer function of analogue filter, find
jHjHjH *2
22
1
2
ss
s
sH
jsjs
ss
s
ss
s
sHsHjH
22
1
22
1
22
2
42
1
2 4
2
jH
2
jH
jH
Slide ١٠
Digital Signal Processing
In order to approximate the ideal filter
1) The magnitude at = 0 is normalized to one
2) The magnitude monotonically decreases from this value to
zero as ∞.
3) The maximum number of its derivatives evaluated at = 0
are zeros.
This can be satisfied if
Butterworth filter
n
n
m
mo
DDD
CCCC
H 2
2
4
4
2
2
2
2
4
4
2
22
1
)(
Will have only even powers of , or
N
ND
H 2
2
2
1
1
)(
2
jH
6. ٦
Slide ١١
Digital Signal Processing
The following specification is usually given for a lowpass
Butterworth filter is
1) The magnitude of H0 at = 0
2) The bandwidth p.
3) The magnitude at the bandwidth p.
4) The stopband frequency s.
5) The magnitude at the stopband frequency s.
6) The transfer function is given by
Butterworth filter
N
ND
H
H 2
2
02
1
)(
Slide ١٢
Digital Signal Processing
To achieve the equivalent lowpass prototype filter
1) We scale the cutoff frequency to one using transformation
= / p.
2) We scale the magnitude to 1 to one by dividing the magnitude
by H0 .
The transfer function become
We denotes D2N as 2 where is the ripple factor, then
Butterworth filter
N
ND
H 2'
2
2
1
1
)(
N
H 22
2
1
1
)(
7. ٧
Slide ١٣
Digital Signal Processing
If the magnitude at the bandwidth = p = 1 is given as (1 - p)2
or −Ap decibels,
the value of 2 is computed by
If we choose Ap = -3dB 2 = 1. this is the most common case
and gives
Butterworth filter
pAH
p
2)(log20
2
1
pA
2
1
1
log10
110
1.02
pA
N
H 2
2
1
1
)(
Slide ١٤
Digital Signal Processing
If we use the complex frequency representation
The poles of this function occurs at
Or in general
Poles occurs in complex conjugates
Poles which are located in the LHP are the poles of H(s)
Butterworth filter
Njp
p
HpH
2/
22
1
1
)(
even,2,...,2,1
odd,2,...,2,1
2/12
2/2
nNke
nNke
p Nk
Nk
k
Nkep NNkj
k 2,...,2,12/)12(
Nkep NNkj
k ,...,2,12/)12(
8. ٨
Slide ١٥
Digital Signal Processing
When we found the N poles we can construct the filter transfer
function as
The denominator polynomial D (p) is calculated by
Butterworth filter
pD
pH
1
n
k
kpppD
1
Slide ١٦
Digital Signal Processing
Butterworth filter
Another method to calculate D (p ) using
The coefficients dk is calculated recursively where d0 = 1
k
kpppD )(
n
n pdpdpdpD 2
211)(
Nkd
N
k
k
d kk ,,3,2,1
2
sin
2/1cos
1
9. ٩
Slide ١٧
Digital Signal Processing
Butterworth filter
The minimum attenuation as dB is usually given at certain
frequency s.
The order of the filter can be calculated from the filter
equation
s (rad/sec)
H()
dB
N
s
ss AH
2
2
1log10
)(log10
s
As
N
log2
110log 10/
Slide ١٨
Digital Signal Processing
Design Steps of Butterworth Filter
1. Convert the filter specifications to their equivalents in the
lowpass prototype frequency.
2. From Ap determine the ripple factor .
3. From As determine the filter order, N.
4. Determine the left-hand poles, using the equations given.
5. Construct the lowpass prototype filter transfer function.
6. Use the frequency transformation to convert the LP
prototype filter to the given specifications.
10. ١٠
Slide ١٩
Digital Signal Processing
Butterworth filter
Example:
Design a lowpass Butterworth filter with a maximum gain of 5 dB
and a cutoff frequency of 1000 rad/s at which the gain is at least
2 dB and a stopband frequency of 5000 rad/s at which the
magnitude is required to be less than −25dB.
Solution:
p = 1000 rad/s , s = 5000 rad/s,
By normalization,
p = p/ p = 1 rad/s,
s = s / p = 5 rad/s,
And the stopband attenuation As = 25+ 5 =30 dB
The filter order is calculated by
3146.2
)5log(2
)110log( 10/
sA
N
Slide ٢٠
Digital Signal Processing
Butterworth filter
The pole positions are:
3,2,16/22
kep kj
k
866.05.0,1,866.05.0,, 3/43/2
jjeeep jjj
k
866.05.01866.05.0)( jppjppD
11)( 2
ppppD
122)( 23
ppppD
Hence the transfer function of the normalized prototype
filter of third order is
122
1
)( 23
ppp
pH
11. ١١
Slide ٢١
Digital Signal Processing
Butterworth filter
To restore the magnitude, we multiply be H0
20logH0 = 5dB which leads H0 = 1.7783
To restore the frequency we replace p by s/1000
122
)( 23
0
ppp
H
pH
1
1000
2
1000
2
1000
7783.1
)( 231000/
sss
pHsH sp
9623
9
101022000
10.7783.1
)(
sss
sH
Slide ٢٢
Digital Signal Processing
Butterworth filter
If the passband edge is defined for Ap 3 dB (i.e. 1).
The design equation needs to be modified. The formula for
calculating the order will become
And the poles are given by
Home Study: Repeat the previous example if Ap = 0.5 dB
s
As
N
log2
110log 10/
Nkep NNkjN
k ,...,2,12/)12(/1