DSPHW2 - THE UNIVERSITY OF AKRON Engineering Faculty...

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THE UNIVERSITY OF AKRON Engineering Faculty ELECTRICAL AND COMPUTER DEPARTMENT Digital Signal Processing-1 Dr.Roberto J Acosta Course #4400:646 Homework#2 DSP-1 Name: Krishna Namburi Student Number: 2351944 Due Date: 02/05/2010 Grade:
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Problem 1: Given Frequency response 3 3 10 ( ) 1 0 0 db jw db ww H e w w otherwise 1. Compute impulse response(closed form solution) Soln : To find the impulse response we should apply Inverse Discrete Fourier Transform( IDTFT ). Which is 1 ( ) ( ) 2 jw jwn H e e dw h n Hence 33 1 ( ) 0* 1* 2 w db w db jwn jwn jwn w db w db h n e dw e dw e dw = 3 3 1 2 w db jwn w db e jn = 1 2 jnw db jnw db ee nj = 1 sin( 3 ) nw db n At n=0; 3 3 3 *cos( ) () db db db w nw w hn
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2. Plot the time domain impulse response(very large number of coefficients) Matlab Code: clc; clear all ; close all ; w3db=pi*0.2; n=-1000:1000; x=zeros(length(n)); for k=1:length(n) if n(k)==0 x(k)=w3db/pi; else x(k)=(sin(w3db*n(k)))/(n(k)*pi); end end k=1:length(n); stem(n,x(k)); title( 'Impulse response' ); xlabel( 'No of samples' ); ylabel( 'h(n)' ); -1000 -800 -600 -400 -200 0 200 400 600 800 1000 -0.05 0 0.05 0.1 0.15 0.2 Impulse response No of samples h(n)
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3. Applied a rectangular window to the time domain impulse response of a total of 2N+1 points(N points on the negative axis , N points on the positive axis and the value at n=0). Plot the filter coefficients for N=500, 250, 125, 50. Matlab code: clc; clear all ; close all ; %plotting the impulse response: w3db=pi*0.3; N=800; p=zeros(1,2*N+1); k=1; x=zeros(1,2*N+1); for n=-N:1:N x(k)=(sin(w3db*n))/(n*pi); k=k+1; end n=-N:1:N; l=(length(n)+1)/2; x(l)=w3db/pi; %Creating a window for various number of points: for k1=[500,250,125,50] p=zeros(1,2*N+1); k=N-k1; for j=-k1:1:k1; p(k)=1; k=k+1; end y=zeros(1,2*N+1); for k=1:1:(2*N+1) y(k)=x(k)*p(k); end figure() plot(n,y)
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Plotting the filter coefficients for N=500 : Plotting the filter coefficients for N=250 : -400 -200 0 200 400 600 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Applied a window for N=500 No of samples Amplitude,h(n) -500 -400 -300 -200 -100 0 100 200 300 400 500 -0.04 -0.02 0 0.02 0.04 0.06 0.08 Applied a window for N=250 No of samples
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DSPHW2 - THE UNIVERSITY OF AKRON Engineering Faculty...

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