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The MATLAB source code for the Sparse Signal Recovery in the Presence of Noise collection.

Code

The following is the MATLAB source code for each of the components of our project.

Addnoise.m

function out = addNoise(sig,mean,sd,Plot) %addNoise%adds noise with given mean and sd to the signal rand=randn(1,1000)*sd+mean;out=sig+rand; if(Plot==1)plot(1:1000,out,1:1000,sig); endend

Sample.m

function out = sample(sd,plot,sig) %sample%samples a manually constructed signal, and adds gaussian noise to it %with a standard deviation that is providedout=fft(addNoise(sig,0,sd,plot)); end

Init.m

function [out,samp]=init(sig,sd)%averages the signal and the noise over a number of samples to make the %noise level manageableout=sig+randn(1,1000).*sd; %optimize number of samplesif sd<76 val=6.25;else val=9;end samp=floor((ceil(sd))^2/(val));for n=2:samp out=(out.*(n-1)+sig+randn(1,1000).*sd)/n;end out=fft(out);end

Simpleiterate.m

function [mask, NSig,runT] = simpleIterate(sigMask,threshold,run,n,sd,sig)%simpleIterate(sigMask,threshold,run,n) %computes an iteration of the thresholding, with a running average of run,%on iteration n, with the current signal mask of sigMask %returns the new signal mask, the current signal(non-masked) NSig and the%running average of the signal runT siz=size(sigMask);temp=zeros(1,siz(2)); for i=1:4NSig=sample(sd,0,sig).*sigMask; if(n==1)runT=NSig; elserunT=(run.*(n-1)+NSig)/n; end%temp=temp+(max(abs(real(NSig)),abs(imag(NSig)))>threshold); temp=temp+(max(abs(real(runT)),abs(imag(runT)))>threshold); %temp=temp+(abs(NSig)>threshold); endmask=zeros(1,siz(2)); for l=1:siz(2)if(temp(l)<2) mask(l)=0;else mask(l)=sigMask(l);end endend

Testarbitary.m

function [flag,samples,time]=testArbitrary(sig,sd)%Simulates the transmission of a signal in the library, and tests whether %or not it can be recovered.siglib=cat(1,sin(0:pi/500:(1000*pi-1)/500),sin(0:pi/250:(2000*pi-1)/500),sin(0:pi/125:(4000*pi-1)/500),sin(0:pi/50:(10000*pi-1)/500),sin(0:pi/25:(20000*pi-1)/500)); siglib=cat(1,siglib,sin(0:pi/500:(1000*pi-1)/500)+sin(0:pi/50:(10000*pi-1)/500),cos(0:pi/500:(1000*pi-1)/500),cos(0:pi/250:(2000*pi-1)/500),cos(0:pi/125:(4000*pi-1)/500),cos(0:pi/50:(10000*pi-1)/500));siglib=cat(1,siglib,cos(0:pi/25:(20000*pi-1)/500),cos(0:pi/25:(20000*pi-1)/500)+sin(0:pi/500:(1000*pi-1)/500),sin(0:pi/500:(1000*pi-1)/500)+sin(0:pi/125:(4000*pi-1)/500)+cos(0:pi/25:(20000*pi-1)/500)); sigmax=max(abs(fft(siglib(sig,:))));threshhold=sigmax-3*max(abs(real(fft(randn(1,1000))))); tolerance=.5;A=ones(1,1000); flag=0;tic [C,samples]=init(siglib(sig,:),sd); for i=1:10000[A,B,C]=simpleIterate(A,threshhold,C,i+samples,sd,siglib(sig,:));for j=1:size(siglib) if(abs(ifft(A.*C)-siglib(j,:))<tolerance) flag=j;break; endend if(flag>0) break;end endsamples=samples+i; time=toc;end

Controller.m

function accepted = Controller(enteredpassword,sd) %Tests whether or not a transmission of a password will activate the system%This simulates the noise and processing as well as the values actualpassword=cat(1,13,5,10,4,2,8);accepted=1; redundancy=3;for i=1:size(actualpassword); flag=0;%while flag==0 for j=1:redundancy [flag,runs]=testArbitrary(enteredpassword(i),sd); endif(flag~=actualpassword(i)) accepted=-i;break; endend end

Controller2.m

function Controller2() %Helper function used to graph trendssig=1; for sd=0:30passed=0; for reps=1:50if(testArbitrary(sig,3+sd/10)==sig) passed=passed+1;end endtemp(sd*10-29)=passed endsubplot(1,1,1); plot(temp);end

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Source:  OpenStax, Sparse signal recovery in the presence of noise. OpenStax CNX. Dec 14, 2009 Download for free at http://cnx.org/content/col11144/1.1
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