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% MATLAB script for Illustrative Problem 7, Chapter 1. echo on df=0.01; % freq. resolution fs=5; % sampling frequency ts=1/fs; % sampling interval t=[-5:ts:5]; % time vector x=zeros(1,length(t)); % input signal initiation x(16:26)=t(16:26)+2; x(27:31)=2*ones(1,5); x(32:41)=2+2*cos(0.5*pi*t(32:41)); x(42:46)=2*ones(1,5); % Part 1 [X,x1,df1]=fftseq(x,ts,df); % spectrum of the input f=[0:df1:df1*(length(x1)-1)]-fs/2; % frequency vector X1=X/fs; % scaling % Part 2 % Filter transfer function H=[ones(1,ceil(1.5/df1)),zeros(1,length(X)-2*ceil(1.5/df1)),ones(1,ceil(1.5/df1))]; Y=X.*H; % output spectrum y1=ifft(Y); % output of the filter % Part 3 % LTI system impulse response h=[zeros(1,ceil(5/ts)),t(ceil(5/ts)+1:ceil(6/ts)),ones(1,ceil(7/ts)-ceil(6/ts)),zeros(1,51-ceil(7/ts))]; y2=conv(h,x); % output of the LTI system pause % Press a key to see spectrum of the input plot(f,fftshift(abs(X1))) pause % Press a key to see the output of the lowpass filter. plot(t,abs(y1(1:length(t)))); pause % Press a key to see the output of the LTI system. plot([-10:ts:10],y2);