《DSP using MATLAB》Problem 3.4

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf(‘\n***********************************************************\n‘);
fprintf(‘        <DSP using MATLAB> Problem 3.4 \n\n‘);

banner();
%% ------------------------------------------------------------------------

% ----------------------------------------------
%            Rectangle Window sequence
% ----------------------------------------------
M = 101;

n1_start = 0; n1_end = M;
n1 = [n1_start : n1_end - 1]; 

x1 =  ones(1, length(n1)); 

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 x1(n) Rectangle‘);
set(gcf,‘Color‘,‘white‘);
stem(n1, x1);
xlabel(‘n‘); ylabel(‘x1‘);
title(sprintf(‘x1(n) sequence, M = %d‘, M)); grid on;

MM = 500;
k = [-MM:MM];        % [-pi, pi]
%k = [0:M];        % [0, pi]
w = (pi/MM) * k;

[X1] = dtft(x1, n1, w);                            

magX1 = abs(X1); angX1 = angle(X1); realX1 = real(X1); imagX1 = imag(X1);

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 DTFT of Rm(n)‘);
set(gcf,‘Color‘,‘white‘);
subplot(2,1,1); plot(w/pi, magX1/max(magX1)); grid on;
title(‘Magnitude Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Magnitude‘);
subplot(2,1,2); plot(w/pi, angX1); grid on;
title(‘Angle Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Radians‘);

% --------------------------------------------------
%                Hanning Window Sequence
% --------------------------------------------------
%n2_start = -9; n2_end = 15;
%n2 = [n2_start : n2_end];
n2 = n1;
x2 = 0.5 * (1 - cos(2*pi*n1/(M-1))) .* x1; 

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 x2(n) Hanning‘);
set(gcf,‘Color‘,‘white‘);
stem(n2, x2);
xlabel(‘n‘); ylabel(‘x2‘);
title(sprintf(‘x2(n) sequence, M = %d‘, M)); grid on;

MM = 500;
k = [-MM:MM];        % [-pi, pi]
%k = [0:M];        % [0, pi]
w = (pi/MM) * k;

[X2] = dtft(x2, n2, w);                            

magX2 = abs(X2); angX2 = angle(X2); realX2 = real(X2); imagX2 = imag(X2);

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 DTFT of Cm(n)‘);;
set(gcf,‘Color‘,‘white‘);
subplot(2,1,1); plot(w/pi, magX2/max(magX2)); grid on;
title(‘Magnitude Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Magnitude‘);
subplot(2,1,2); plot(w/pi, angX2); grid on;
title(‘Angle Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Radians‘);

% --------------------------------------------------
%            Triangular Window Sequence
% --------------------------------------------------
%n3_start = -3; n3_end = 10;
%n3 = [n3_start : n3_end];
n3 = n1;
x3 = (1 - abs(M-1-2*n3)/(M-1)) .* x1; 

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 x3(n) Triangular‘);
set(gcf,‘Color‘,‘white‘);
stem(n3, x3);
xlabel(‘n‘); ylabel(‘x3‘);
title(sprintf(‘x3(n) sequence, M = %d‘, M)); grid on;

MM = 500;
k = [-MM:MM];        % [-pi, pi]
%k = [0:M];        % [0, pi]
w = (pi/MM) * k;

[X3] = dtft(x3, n3, w);                            

magX3 = abs(X3); angX3 = angle(X3); realX3= real(X3); imagX3 = imag(X3);

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 DTFT of Tm(n)‘);;
set(gcf,‘Color‘,‘white‘);
subplot(2,1,1); plot(w/pi, magX3/max(magX3)); grid on;
title(‘Magnitude Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Magnitude‘);
subplot(2,1,2); plot(w/pi, angX3); grid on;
title(‘Angle Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Radians‘);

% ---------------------------------------------
%            Hamming Window sequence
% ---------------------------------------------
%n4_start = 0; n4_end = 50;
%n4 = [n4_start : n4_end];
n4 = n1;
x4 = (0.54 - 0.46 * cos(2*pi*n4/(M-1))) .* x1; 

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 x4(n) Hamming‘);
set(gcf,‘Color‘,‘white‘);
stem(n4, x4, ‘filled‘);
xlabel(‘n‘); ylabel(‘x4‘);
title(sprintf(‘x4(n) sequence, M = %d‘, M)); grid on;

MM = 500;
k = [-MM:MM];        % [-pi, pi]
%k = [0:M];        % [0, pi]
w = (pi/MM) * k;

[X4] = dtft(x4, n4, w);                            

magX4 = abs(X4); angX4 = angle(X4); realX4= real(X4); imagX4 = imag(X4);

figure(‘NumberTitle‘, ‘off‘, ‘Name‘, ‘Problem 3.4 DTFT of Hm(n)‘);;
set(gcf,‘Color‘,‘white‘);
subplot(2,1,1); plot(w/pi, magX4/max(magX4)); grid on;
title(‘Magnitude Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Magnitude‘);
subplot(2,1,2); plot(w/pi, angX4); grid on;
title(‘Angle Part‘);
xlabel(‘frequency in \pi units‘); ylabel(‘Radians‘);

　　运行结果：

矩形窗：

汉宁窗：

三角窗：

汉明窗：