Project FEDS

7/28/2019 Project FEDS

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Adaptive Line Enhancer (ALE)

using Fast EDS

Presented by:

Sarita Mishra-11528017

Vivek Surana -11550017


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Project 12 : Adaptive Line Enhancer (ALE) using Fast EDS

Generate a signal of the form where Ts is the sampling frequency and thefrequencies f1 and f2 can be chosen as desired. Choose Ts so that the sinusoidappears smooth. A noise w(n) is added to the signal to produce the noisy signal

d(n) = s(n) + w(n).

The noise is a white uniformly distributed sequence with zero mean. The SNR ofthis signal should be about -7 dB. The desired signal (or primary signal) is d(n). Thereference signal is d(n-1) and is applied to the input of an N-tap FIR filter thatproduces the output y(n), which should be the estimate of the signal. Use theFast EDS algorithm for adaptation. Experiment with different values of N and theforgetting factor . submit the following for your best case.

(a) Plot the MSE for an ensemble of 100 runs.

(b) Plot a few cycles of s(n) for one run.

(c) Plot a few cycles of y(n) after convergence (one run).

(d) Plot the impulse response and the frequency response of the filter afterconvergence (one run). I)

(e) Find the SNR of the filtered signal. Make sure you correct for phase, if necessary.

(f) Discuss the effects of N and on the performance of the algorithm.

Provide all block diagrams, equations, and algorithms in your report. Discuss yourresults. Are they as expected? Are there any variations from your expectations?Comment on the convergence rate in your experiments.

(g) Discuss the rate of convergence of the Fast EDS in relation to the EDS algorithm.


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What are Adaptive Filter?

Filters with changing coefficients are called Adaptive filters .

Adaptive filters consists of the following two basic elements:

A digital filter, which produces an output in response to an input

signal.

An adaptive algorithm, which adjusts the coefficients of the

digital filter.


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The effects of on the performance of the

algorithm:

If =1 all the data are weighted equally and the algorithm has infinite

memory length, which is optimal with respect to suppressing the estimation

noise effect alone. If is small the algorithm has shorter memory length.

Or

Larger will reduce the estimation noise and small value reduces the

equalization error due to lag effect. The optimal value of depends on

channel fading dynamics and the extent of input noise on the equalization

error.


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The effects of N on the performance

of the algorithm:

FEDS has O(N) computational complexity (4N+2). In this algorithm only

one directional search is performed for each sample of data so it has slow

rate of convergence and as we increase the no of N the computational

complexity will increase and rate of convergence will decrease.

Rate of convergence of EDS is very much higher than FEDS. Because

in EDS, N directions are searched for every sample.


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Applications

System identification

Sinusoidal tracking

Noise cancellation Channel equalizer


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Advantage:

It reduces the computational complexity i.e.O(N) and required 4N+2 multiplications.

Disadvantage:

Its convergence rate is very low in comparison

to EDS and RLS.


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Adaptive line enhancher


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Input signal

f1=input('enter the frequency of first signal')

f2=input('enter the frequency of second signal')

Ts1=1/(10*f1);

Ts2=1/(10*f2);

%%input signal...

for i=1:1000

a(i)=5*sin(2*pi*f1*Ts1*i);

b(i)=6*sin(2*pi*f2*Ts2*i);

end

s=a+b;

Figure;

plot(s)

title('input signal')

%%desired signal...

ln=length(s);

w=(10*rand(ln,1)-.5)';


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Input signal (cont.)

Figure;

plot(w)

title('uniform white noise with 0 mean')

Figure;d=s+w;;

plot(d)

title('desired signal d=s+w')


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%%calculation of SNR

p1=sum(s.^2);

p1db=10*log10(p1); p2=sum(w.^2);

p2db=10*log10(p2)

SNR=p1db-p2db

OUTPUT

p1db =

33.0103

p2db =

40.7973

SNR =

-7.7870


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Project FEDS

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