This document discusses various methods for modeling signals, including deterministic and stochastic processes. It covers topics like the least mean square direct method, Pade approximation, Prony's method, Shanks method, and stochastic processes like ARMA, MA, and AR. It also discusses an application of signal modeling for designing a least squares inverse FIR filter. Model order estimation is noted as an important problem in signal modeling when the correct model order is unknown.
Optimum Receiver corrupted by AWGN ChannelAWANISHKUMAR84
Optimum Receiver corrupted by AWGN Channel
This topic is related to Advance Digital Communication Engineering. In this ppt, you will get all details explanations of the receiver how to get affected by white Noise.
introduction to pulse shaping and equalization in advanced digital communication, it's characterisation, signal design of band limited signal, design of bandlimited signal for no ISI and design of bandlimited signal with controlled ISI-partial response, linear equalization,
Optimum Receiver corrupted by AWGN ChannelAWANISHKUMAR84
Optimum Receiver corrupted by AWGN Channel
This topic is related to Advance Digital Communication Engineering. In this ppt, you will get all details explanations of the receiver how to get affected by white Noise.
introduction to pulse shaping and equalization in advanced digital communication, it's characterisation, signal design of band limited signal, design of bandlimited signal for no ISI and design of bandlimited signal with controlled ISI-partial response, linear equalization,
In telecommunication, an eye pattern, also known as an eye diagram, is an oscilloscope display in which a digital signal from a receiver is repetitively sampled and applied to the vertical input, while the data rate is used to trigger the horizontal sweep. It is so called because, for several types of coding, the pattern looks like a series of eyes between a pair of rails. It is a tool for the evaluation of the combined effects of channel noise and intersymbol interference on the performance of a baseband pulse-transmission system. It is the synchronised superposition of all possible realisations of the signal of interest viewed within a particular signaling interval.
link of a reference: http://www.slideshare.net/zena_mohammed/advanced-digital-signal-processing-book. digital_signal_processing__a_practical_approach. this reference for asked me for pictures in presentation of Multirate Digital Signal Processing.
the presentation consists of a brief description about ADAPTIVE LINEAR EQUALIZER , its classification and the associated attributes of ZERO FORCING EQUALIZER and MMSE EQUALIZER
In this chapter we examine the capacity of a single-user wireless channel where transmitter and/or receiver have a single antenna. We will discuss capacity for channels that are both time invariant and time varying. We first look at the well-known formula for capacity of a time-invariant additive white Gaussian noise (AWGN) channel and then consider capacity of time-varying flat fading channels. We will first consider flat fading channel capacity where only the fading distribution is known at the transmitter and receiver. We will also treat capacity of frequency-selective fading channels. For time -invariant frequency-selective channels the capacity is known and is achieved with an optimal power allocation that water-fills over frequency instead of time. We will consider only discrete-time systems in this chapter.
In telecommunication, an eye pattern, also known as an eye diagram, is an oscilloscope display in which a digital signal from a receiver is repetitively sampled and applied to the vertical input, while the data rate is used to trigger the horizontal sweep. It is so called because, for several types of coding, the pattern looks like a series of eyes between a pair of rails. It is a tool for the evaluation of the combined effects of channel noise and intersymbol interference on the performance of a baseband pulse-transmission system. It is the synchronised superposition of all possible realisations of the signal of interest viewed within a particular signaling interval.
link of a reference: http://www.slideshare.net/zena_mohammed/advanced-digital-signal-processing-book. digital_signal_processing__a_practical_approach. this reference for asked me for pictures in presentation of Multirate Digital Signal Processing.
the presentation consists of a brief description about ADAPTIVE LINEAR EQUALIZER , its classification and the associated attributes of ZERO FORCING EQUALIZER and MMSE EQUALIZER
In this chapter we examine the capacity of a single-user wireless channel where transmitter and/or receiver have a single antenna. We will discuss capacity for channels that are both time invariant and time varying. We first look at the well-known formula for capacity of a time-invariant additive white Gaussian noise (AWGN) channel and then consider capacity of time-varying flat fading channels. We will first consider flat fading channel capacity where only the fading distribution is known at the transmitter and receiver. We will also treat capacity of frequency-selective fading channels. For time -invariant frequency-selective channels the capacity is known and is achieved with an optimal power allocation that water-fills over frequency instead of time. We will consider only discrete-time systems in this chapter.
The tuning of Microwave Circulators utilizing gyromagnetic materials requires the calibration of the biasing magneto-static field, which is mostly supplied by permanent magnets. The permanent magnets have to be tuned down from saturation to an appropriate magnetization stage by means of specialized magnetizing and tuning equipment. A tuning procedure suited for automated adjustment of the saturation level of permanent magnets is described, based on S-parameter measurements. Eigenvalues of the measured 3x3 S-matrices are used to determine a required setting on a computer controllable magnetizer. This will enable a quick and accurate automated tuning process.
non parametric methods for power spectrum estimatonBhavika Jethani
non-parametric methods for power spectrum estimation which includes bartlett method, welch method , blackman and tukey methods and also the comparision of all these methods
Bayesian modelling and computation for Raman spectroscopyMatt Moores
Raman spectroscopy can be used to identify molecules by the characteristic scattering of light from a laser. Each Raman-active dye label has a unique spectral signature, comprised by the locations and amplitudes of the peaks. The Raman spectrum is discretised into a multivariate observation that is highly collinear, hence it lends itself to a reduced-rank representation. We introduce a sequential Monte Carlo (SMC) algorithm to separate this signal into a series of peaks plus a smoothly-varying baseline, corrupted by additive white noise. By incorporating this representation into a Bayesian functional regression, we can quantify the relationship between dye concentration and peak intensity. We also estimate the model evidence using SMC to investigate long-range dependence between peaks. These methods have been implemented as an R package, using RcppEigen and OpenMP.
These slides deal with the basic problem of channel equalization and exposes the issue related to it and shows how it can be balanced by the usage of effective and robust algorithms.
PROGRAMMA ATTIVITA’ DIDATTICA A.A. 2016/17
DOTTORATO DI RICERCA IN INGEGNERIA STRUTTURALE E GEOTECNICA
____________________________________________________________
STOCHASTIC DYNAMICS AND MONTE CARLO SIMULATION IN EARTHQUAKE ENGINEERING APPLICATIONS
Lecture Series by
Agathoklis Giaralis, Ph.D., M.ASCE., P.E. City, University of London
Visiting Professor Sapienza University of Rome
A review of literature shows that there is a variety of adaptive filters. In this research study, we propose a new type of an adaptive filter that increases the diversification used to compensate the chan-nel distortion effect in the MC-CDMA transmission. First, we show the expressions of the filter’s impulse responses in the case of a perfect channel. The adaptive filter has been simulated and experienced by blind equalization for different cases of Gaussian white noise in the case of an MC-CDMA transmission with orthogonal frequency baseband for a mobile radio downlink channel Bran A. The simulation results show the performance of the proposed identification and blind equalization algorithm for MC-CDMA transmission chain using IFFT.
Trend removal from raman spectra with local variance estimation and cubic spl...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed
algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and
cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to
remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems
than other techniques that use wavelet transformation to suppress noise.
TREND REMOVAL FROM RAMAN SPECTRA WITH LOCAL VARIANCE ESTIMATION AND CUBIC SPL...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise
Trend Removal from Raman Spectra With Local Variance Estimation and Cubic Spl...csijjournal
Abstract
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise.
Keywords
Raman spectroscopy, Background correction method, Local variance, Cubic spline interpolation.
TREND REMOVAL FROM RAMAN SPECTRA WITH LOCAL VARIANCE ESTIMATION AND CUBIC SPL...csijjournal
Trend removal is an important problem in most communication systems. Here, we show a proposed algorithm for trend (background) removal from Raman Spectra by merging local variance estimation and cubic spline interpolation methods. We found that Raman spectrum does not need a smoothing process to remove trend from noisy signals. Employing this technique results in more speedy and noiseless systems than other techniques that use wavelet transformation to suppress noise.
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International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
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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.
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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.
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2. CONTENTS
Introduction
1.Title description
2.Need and importance of signal modeling
Theory
1.Least mean square direct method.
1.1. Brief Overview
1.2. Disadvantages
2.Pade Approximation
3.Prony’s Approximation
4.Shanks Method
5.Stochastic process-ARMA,MA,AR
Application
Least Mean Square Inverse FIR filter
Conclusion
References
3. WHAT IS MODELING:
Modelling of signal is basically mathematical
representation of signal.
Fourier series, Fourier transform are kind of signal
models.
WHY MODELLING
NEED OF MODELING:
1.EFFICIENCY OF TRANSMISSION
2.PREDICTION
8. TYPES OF SIGNAL TO BE MODELLED
DETERMINISTIC
SIGNALS
INPUT WILL BE
STOCHASTIC
RANDOM
PROCESS,WHITE
NOISE
9. MODEL PARAMETER
Models must be computationally efficient procedure for
deriving the model parameters.
Various approaches to signal modeling
THE LEAST SQUARE DIRECT METHOD
THE PADE APPROXIMATION
PRONY’S METHOD
1. Pole-Zero modeling
2. Shanks method
3. All-Pole Modeling DETERMINISTIC
4. Linear Prediction
ITERATIVE PREFILTERING
FINITE DATA RECORDS
1.The Autocorrelation Method
2.The Covariance Method
THE STOCHASTIC MODELS-ARMA,AR,MA RANDOM
11. LEAST SQUARE (CONTINUED)
Using Parseval writing in frequency domain
Setting the partial derivative w.r.t ap*(k) equal to zero we have
Treating ap(k) and ap*(k) as independent variable
For k=1,2…..q,differentiating w.r.t bq(k)
13. PADE APPROXIMATION
Pade approximation only requires solving a set linear equation.
In Pade we force the filter output h(n) to be equal to given signal x(n)
for p+q+1 values of n.
In time domain,
Where h(n)=0 for n<0 and n>q.To find the cofficients ap(k) and bq(k)
that gives an exact fit of data model in [0,p+q] we set h(n)=x(n)
14. In matrix form,
For soving the equation we use two step approach first solving for
denominator ap(k) and then bq(k).ap(k) last p equations
15. CONCLUSIONS ON PADE APPROXIMATION
The model formed from Pade approximation will
produce an exact fit to data over the
interval[0,p+q].But has no guarantee on how
accurate the model will be for n>p+q.
Pade approximation will give correct model
parameters provided the model order is chosen to
be large enough.
Since the Pade approximation forces the model to
match the signal only over limited range of
values,the model generated is not stable
16. PRONY’S METHOD
The limitation of Pade approximation-Only uses values of the
signal x(n) over the interval [0,p+q] to determine model
parameter and over this interval, it models the signal without
error.
There is no guarantee on how well the model will
approximate the signal for n>p+q
POLE ZERO MODELLING:
Similar to pade x(n)=0 for n<0.A least square minimization of e’(n)
results in set of non-linear equation for filter cofficient
Multiplying by Ap(z) we have new error
That is linear cofficients.In time domain:
17. Since bq(n)=0 for n>q,error can be explicitly written as
Instead of setting e(n)=0 for n=0,1,…….p+q as in Pade
approximation,Prony’s method begins by finding the cofficient
ap(k) that minimizes squared error.
19. ESTIMATION OF ERROR IN PRONY’S
Minimun value of modeling error:
e(n) and x*(n) are uncorrelated so from orthogonality principle
the second term is zero.
Thus the minimum value:
22. SHANKS APPROXIMATION
In Prony e(n)=0 for n=1, 2,….q.Although this allows the model to be exact
over [0,q],this does not take into account data for n>q.
Shanks performs mininization of model error over entire length of data record.
Filter can be viewed as cascade of two filter Ap(z) and Bq(z)
g(n) can be computed using the equation:
23. To compute cofficient filter Bq(z),which produces the approximation x(n)
when input to filter g(n).Instead of forcing e(n) to zero for first q+1 values of n
as in Prony,Shank minimizes the squared error.
……..(1)
………….(2)
Substituting (1) in (2)
24. MSE AND COMPARISION WITH PRONY
Minimum squared error
1.Shanks method is more involved than Prony’s method.
2.Extra compution of sequence g(n),autocorretion of
g(n),cross correlation of g(n) and x(n).But in shank the
mean square error reduces considerably
25. STOCHASTIC PROCESS:AR,MA,ARMA
Signals whose time evolution is governed by unknown factors
like electrocardiogram,unvoiced speech,population
statistics,economic data and seismograph
ARMA:
White noise is filtered with causal Linear shift invariant filter
having p poles and q zeros.
YULE WALKER
26. STOCHASTIC PROCESS CONTINUED..
MODIFIED YULE WALKER
Here k=q+1,…..q+p
Comparing above eq with Pade approximation the data consist of a sequence
of autocorrelations rx(k) .
AR:
A WSS AR process of order p is a special case of ARMA(p,q) process in which q=0.
27. STOCHASTIC CONTINUED….
In matrix form
MA: A MA process is generated by filtering unit variance white noise
with an FIR filter order q
:
28. APPLICATION OF SIGNAL MODELLING
FIR LEAST SQUARES INVERSE FILTER
Given a FIR filter the inverse filter relation can be written as
NEED:
Equalization filter in digital communicatilon.Assume that channeal
transfer function is G(z),the eqalization filter is found by relation.
Procedure:
g(n) is causal filter to be equalized,the problem is to find FIR filter
hN(n) of length N such that
The equation is same as shank,the solution of least square inverse filter
is
29. FIR LS INVERSE FILTER CONTINUED
where
Matrix form:
From shank’s it follows the concise form: …………..(1)
31. PROBLEM CONTINUED
With squared error of
The system function of least square inverse filter is
Which has a zero at
Least square inverse from equation 1 is
For n=1,2….N these equation may be represented in homogeneous form
The general solution to this equation is
………….(2)
32. PROBLEM
c1,c2 are constants and determined from boundary condition at n=0 and n=N-1
i.e first and last equation
…(3)
Substituting (2) in (3)
Which after cancelling common term can be simplified to
34. CONCLUSION
The various methods of signal modelling for both
deterministic and stochastic process are discussed.
PROBLEM IN SIGNAL MODELING
MODEL ORDER ESTIMATION:
In the cases assumed so far we have assumed that a model of given
order to be found.In the absence of any information about the correct
model order ,it becomes necessary to estimate what an appropiate
model order should be.Misleading information may result in an
inappropiate model order.
35. REFERENCES
STATISTICAL SIGNAL PROCESSING AND MODELING…
MONSON H.HAYES
Signal Modeling Techniques In Speech Recognition
by,Joseph Picone
Spectrum Estimation and Modeling by Petar M. Djuri´c State
University of New York at Stony Brook Steven M. Kay
University of Rhode Island
SOME REMARKS ON PADÉ-APPROXIMATIONS M.Vajta
Comparing Autoregressive Moving Average(ARMA)
coefficients determination using Artificial Neural Networks with
other techniques Abiodun M. Aibinu, Momoh J. E. Salami,
Amir A. Shafie and Athaur Rahman Najeeb