《DSP using MATLAB》Problem 5.11

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%%            Output Info about this m-file
fprintf(‘\n***********************************************************\n‘);
fprintf(‘        <DSP using MATLAB> Problem 5.11 \n\n‘);

banner();
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% --------------------------------------------------------------
%              1  h(n) = [0.9^n]   n=[0:5]                                     
% --------------------------------------------------------------
 
nn1 = [0:5];
hh1 = 0.9 .^ nn1;
NN1 = length(hh1);                              % length is 6


%m = mod_1(nn1, NN1);
h = [hh1 zeros(1, 2)];                        % padding zeros
n = [nn1 max(nn1)+1:max(nn1)+2];


figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘P5.11.1 Causal Real LSI h(n)‘)
set(gcf,‘Color‘,‘white‘); 
subplot(2,1,1); stem(nn1, hh1);
xlabel(‘n‘); ylabel(‘h(n)‘);
title(‘h(n)=0.9^n ori sequence‘);  grid on;
subplot(2,1,2); stem(n, h);
xlabel(‘n‘); ylabel(‘h(n)‘);
title(‘h(n) padding zeros‘);  grid on;


%% =============================================================================
%%                 DTFT H(w) of hn sequence, w=[0:2pi], 
%% =============================================================================
MM = 500;
[Hw_DTFT, w] = dtft1(h, n, MM);

 magHw_DTFT = abs(Hw_DTFT);   angHw_DTFT = angle(Hw_DTFT)/pi; 
realHw_DTFT = real(Hw_DTFT); imagHw_DTFT = imag(Hw_DTFT);


%% --------------------------------------------------------------
%%        START H_DTFT‘s  mag ang real imag
%% --------------------------------------------------------------
figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘P5.11.1 H(w) DTFT of h(n)‘);
set(gcf,‘Color‘,‘white‘); 
subplot(2,2,1); plot(w/pi,magHw_DTFT); grid on;  % axis([-2,2,0,15]); 
title(‘Magnitude Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Magnitude  |H\_DTFT|‘); 
subplot(2,2,3); plot(w/pi, angHw_DTFT); grid on;  % axis([-2,2,-1,1]);
title(‘Angle Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Rad \pi‘); %axis([-200,200,0,2]);

subplot(‘2,2,2‘); plot(w/pi, realHw_DTFT); grid on;
title(‘Real Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Real‘);
subplot(‘2,2,4‘); plot(w/pi, imagHw_DTFT); grid on;
title(‘Imaginary Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Imaginary‘);
%% --------------------------------------------------------------
%%        END H_DTFT‘s  mag ang real imag
%% --------------------------------------------------------------


%% ------------------------------------------------------------------
%%                 DFT(k) of hn sequence, k=[0:N-1]
%%                      w=2pi*k/N       k=Nw/(2pi)
%% ------------------------------------------------------------------
N1 = length(h);
k1 = [0 : N1-1];
%k2 = [-N : N-1];
%k3 = [-N/2 : N/2];
Hk_DFT = dft(h, N1);                                        % DFT
    magHk_DFT = abs( Hk_DFT )                          % DFT magnitude
    angHk_DFT = angle( Hk_DFT )/pi                      % DFT angle
   realHk_DFT = real(Hk_DFT); imagHk_DFT = imag(Hk_DFT);

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘P5.11.1 DFT(k) of h(n)‘)
set(gcf,‘Color‘,‘white‘); 
subplot(2,1,1); stem(k1, magHk_DFT); hold on; plot(N1*w/(2*pi), magHw_DTFT,‘r--‘); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel(‘k‘); ylabel(‘magnitude(k)‘);
title(‘DFT magnitude of h(n), N=8‘);  grid on;
subplot(2,1,2); stem(k1, angHk_DFT);  hold on; plot(N1*w/(2*pi), angHw_DTFT,‘r--‘); hold off;
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel(‘k‘); ylabel(‘angle(k)‘);
title(‘DFT angle of h(n), N=8‘);  grid on;