This post list two MATLAB codes and their outputs that represent the ensemble and median filtering concepts in Signals & System.

Task 1: Ensemble

MATLAB Code

r=50

m=0:r-1;

s=2*m.*(0.9.^m);

d=rand(r,1)-0.5;

x1=s+d’;

stem(m,x1,’g’)

xlabel (‘Time’)

ylabel(‘Amplitude’)

title(‘Noisy Signal’)

pause

for n=1:50

    d=rand(r,1)-0.5

    x=s+d’;

    x1=x1+x

end

x1=x1/50

stem(m,x1,’r’)

xlabel(‘Time’)

ylabel(‘Amplitude’)

title(‘Ensemble Average’)

Task 2: Median Filtering

MATLAB Code

n=input(‘Median Filter Input’)

r=50;

a=rand(1,r)-0.4;

b=round(a);

m=0:r-1;

s=2*m.*(0.9.^m);

x=s+b;

y=medfilt1(x,3)

subplot(211)

stem(m,x,’r’)

axis([0 50 -1 8])

xlabel(‘Time’)

ylabel(‘Amplitude’)

title(‘Impulse Noise Corrupt Signal’)

subplot(212)

stem(m,y,’b’)

xlabel(‘Time’)

ylabel(‘Amplitude’)

title(‘Output of Median Filter’)