代码:
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%% Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf(' <DSP using MATLAB> Problem 5.11 \n\n'); banner();
%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ % --------------------------------------------------------------
% 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;
运行结果:
只会第1小题。
8点DFT基本能反映DTFT的幅度谱,但相位谱感觉稍有欠缺。
第2小题不会做。