《DSP using MATLAB》示例Example5.7

代码：

x = [1, 1, 1, 1, zeros(1,4)];

N = 8;                                                 % zero-padding operation

X_DFT = dft(x,N);                                      % DFT of x(n)

magX_DFT = abs(X_DFT)

phaX_DFT = angle(X_DFT)*180/pi                         % degrees

realX_DFT = real(X_DFT); imagX_DFT = imag(X_DFT);

angX_DFT = angle(X_DFT);                               % radias

n = 0:(N - 1);

k = 0:1000; w = (pi/500)*k;                            % [0,2pi] axis divided into 501 points.

%k = 0:500; w = (pi/500)*k;                            % [0,pi] axis divided into 501 points.

X_DTFT = x * (exp(-j*pi/500)) .^ (n'*k);               % DTFT of x(n)

magX_DTFT = abs(X_DTFT); angX_DTFT = angle(X_DTFT); realX_DTFT = real(X_DTFT); imagX_DTFT = imag(X_DTFT);

figure('NumberTitle', 'off', 'Name', 'Exameple5.7 x sequence')

set(gcf,'Color','white');

stem(n,x); title('x sequence'); axis([0,N,-0.5,1.5]);

xlabel('n'); ylabel('x(n)'); grid on;

%% --------------------------------------------------------------

%%        START X_DTFT's  mag ang real imag

%% --------------------------------------------------------------

figure('NumberTitle', 'off', 'Name', 'X_DTFT its Magnitude and Angle, Real and Imaginary Part');

set(gcf,'Color','white');

subplot(2,2,1); plot(w/pi,magX_DTFT); grid on;  % axis([-2,2,0,15]);

title('Magnitude Part');

xlabel('frequency in \pi units'); ylabel('Magnitude  |X\_DTFT|');

subplot(2,2,3); plot(w/pi, angX_DTFT*180/pi); grid on;  % axis([-2,2,-1,1]);

title('Angle Part');

xlabel('frequency in \pi units'); ylabel('Degrees'); %axis([-200,200,0,2]);

subplot('2,2,2'); plot(w/pi, realX_DTFT); grid on;

title('Real Part');

xlabel('frequency in \pi units'); ylabel('Real');

subplot('2,2,4'); plot(w/pi, imagX_DTFT); grid on;

title('Imaginary Part');

xlabel('frequency in \pi units'); ylabel('Imaginary');

%% --------------------------------------------------------------

%%        END X_DTFT's  mag ang real imag

%% --------------------------------------------------------------

%% --------------------------------------------------------------

%%        START X_DFT's  mag ang real imag

%% --------------------------------------------------------------

figure('NumberTitle', 'off', 'Name', 'Example5.7 X_DFT its Magnitude and Angle');

set(gcf,'Color','white');

subplot(2,1,1); stem(n,magX_DFT); hold on; plot(4*w/pi,magX_DTFT,'--'); hold off;

grid on;   axis([-0.5,8.2,-1,5]);

title('Magnitude Part of the DFT: N = 8');

xlabel('k'); ylabel('Magnitude  |X\_DFT|');

subplot(2,1,2); stem(n, phaX_DFT); hold on; plot(4*w/pi,angX_DTFT*180/pi,'--'); hold off;

grid on;   axis([-0.5,8.2,-200,200]);

title('Angle Part of the DFT: N = 8');

xlabel('k'); ylabel('Degrees'); %axis([-200,200,0,2]);

%subplot('2,2,2'); stem(n, realX_DFT); grid on;

%title('Real Part');

%xlabel('frequency in \pi units'); ylabel('Real');

%subplot('2,2,4'); stem(n, imagX_DFT); grid on;

%title('Imaginary Part');

%xlabel('frequency in \pi units'); ylabel('Imaginary');

%% --------------------------------------------------------------

%%        END X_DFT's  mag ang real imag

%% --------------------------------------------------------------

　　结果：

将序列末尾补12个零，长度达到16位

代码：

x = [1, 1, 1, 1, zeros(1,12)];                         % append 12 zeros to the end of x(n)

N = 16;                                                % zero-padding operation

X_DFT = dft(x,N);                                      % DFT of x(n)

magX_DFT = abs(X_DFT)

phaX_DFT = angle(X_DFT)*180/pi                         % degrees

realX_DFT = real(X_DFT); imagX_DFT = imag(X_DFT);

angX_DFT = angle(X_DFT);                               % radias

n = 0:(N - 1);

k = 0:1000; w = (pi/500)*k;                            % [0,2pi] axis divided into 501 points.

%k = 0:500; w = (pi/500)*k;                            % [0,pi] axis divided into 501 points.

X_DTFT = x * (exp(-j*pi/500)) .^ (n'*k);               % DTFT of x(n)

magX_DTFT = abs(X_DTFT); angX_DTFT = angle(X_DTFT); realX_DTFT = real(X_DTFT); imagX_DTFT = imag(X_DTFT);

figure('NumberTitle', 'off', 'Name', 'Exameple5.7 x sequence')

set(gcf,'Color','white');

stem(n,x); title('x sequence, N = 16'); axis([0,N,-0.5,1.5]);

xlabel('n'); ylabel('x(n)'); grid on;

%% --------------------------------------------------------------

%%        START X_DTFT's  mag ang real imag

%% --------------------------------------------------------------

figure('NumberTitle', 'off', 'Name', 'X_DTFT its Magnitude and Angle, Real and Imaginary Part');

set(gcf,'Color','white');

subplot(2,2,1); plot(w/pi,magX_DTFT); grid on;  % axis([-2,2,0,15]);

title('Magnitude Part');

xlabel('frequency in \pi units'); ylabel('Magnitude  |X\_DTFT|');

subplot(2,2,3); plot(w/pi, angX_DTFT*180/pi); grid on;  % axis([-2,2,-1,1]);

title('Angle Part');

xlabel('frequency in \pi units'); ylabel('Degrees'); %axis([-200,200,0,2]);

subplot('2,2,2'); plot(w/pi, realX_DTFT); grid on;

title('Real Part');

xlabel('frequency in \pi units'); ylabel('Real');

subplot('2,2,4'); plot(w/pi, imagX_DTFT); grid on;

title('Imaginary Part');

xlabel('frequency in \pi units'); ylabel('Imaginary');

%% --------------------------------------------------------------

%%        END X_DTFT's  mag ang real imag

%% --------------------------------------------------------------

%% --------------------------------------------------------------

%%        START X_DFT's  mag ang real imag

%% --------------------------------------------------------------

figure('NumberTitle', 'off', 'Name', 'Example5.7 X_DFT its Magnitude and Angle');

set(gcf,'Color','white');

subplot(2,1,1); stem(n,magX_DFT); hold on; plot(8*w/pi,magX_DTFT,'--'); hold off;

grid on;   axis([-0.5,16.2,-1,5]);

title('Magnitude Part of the DFT: N = 16');

xlabel('k'); ylabel('Magnitude  |X\_DFT|');

subplot(2,1,2); stem(n, phaX_DFT); hold on; plot(8*w/pi,angX_DTFT*180/pi,'--'); hold off;

grid on;   axis([-0.5,16.2,-200,200]);

title('Angle Part of the DFT: N = 16');

xlabel('k'); ylabel('Degrees'); %axis([-200,200,0,2]);

%subplot('2,2,2'); stem(n, realX_DFT); grid on;

%title('Real Part');

%xlabel('frequency in \pi units'); ylabel('Real');

%subplot('2,2,4'); stem(n, imagX_DFT); grid on;

%title('Imaginary Part');

%xlabel('frequency in \pi units'); ylabel('Imaginary');

%% --------------------------------------------------------------

%%        END X_DFT's  mag ang real imag

%% --------------------------------------------------------------

　　结果：

继续补零，长度N=128，

代码：

x = [1, 1, 1, 1, zeros(1,124)];                        % append 124 zeros to the end of x(n)

N = 128;                                               % zero-padding operation

X_DFT = dft(x,N);                                      % DFT of x(n)

magX_DFT = abs(X_DFT)

phaX_DFT = angle(X_DFT)*180/pi                         % degrees

realX_DFT = real(X_DFT); imagX_DFT = imag(X_DFT);

angX_DFT = angle(X_DFT);                               % radias

n = 0:(N - 1);

k = 0:1000; w = (pi/500)*k;                            % [0,2pi] axis divided into 501 points.

%k = 0:500; w = (pi/500)*k;                            % [0,pi] axis divided into 501 points.

X_DTFT = x * (exp(-j*pi/500)) .^ (n'*k);               % DTFT of x(n)

magX_DTFT = abs(X_DTFT); angX_DTFT = angle(X_DTFT); realX_DTFT = real(X_DTFT); imagX_DTFT = imag(X_DTFT);

figure('NumberTitle', 'off', 'Name', 'Exameple5.7 x sequence')

set(gcf,'Color','white');

stem(n,x); title('x sequence, N = 128'); axis([0,N,-0.5,1.5]);

xlabel('n'); ylabel('x(n)'); grid on;

%% --------------------------------------------------------------

%%        START X_DTFT's  mag ang real imag

%% --------------------------------------------------------------

figure('NumberTitle', 'off', 'Name', 'X_DTFT its Magnitude and Angle, Real and Imaginary Part');

set(gcf,'Color','white');

subplot(2,2,1); plot(w/pi,magX_DTFT); grid on;  % axis([-2,2,0,15]);

title('Magnitude Part');

xlabel('frequency in \pi units'); ylabel('Magnitude  |X\_DTFT|');

subplot(2,2,3); plot(w/pi, angX_DTFT*180/pi); grid on;  % axis([-2,2,-1,1]);

title('Angle Part');

xlabel('frequency in \pi units'); ylabel('Degrees'); %axis([-200,200,0,2]);

subplot('2,2,2'); plot(w/pi, realX_DTFT); grid on;

title('Real Part');

xlabel('frequency in \pi units'); ylabel('Real');

subplot('2,2,4'); plot(w/pi, imagX_DTFT); grid on;

title('Imaginary Part');

xlabel('frequency in \pi units'); ylabel('Imaginary');

%% --------------------------------------------------------------

%%        END X_DTFT's  mag ang real imag

%% --------------------------------------------------------------

%% --------------------------------------------------------------

%%        START X_DFT's  mag ang real imag

%% --------------------------------------------------------------

figure('NumberTitle', 'off', 'Name', 'Example5.7 X_DFT its Magnitude and Angle');

set(gcf,'Color','white');

subplot(2,1,1); stem(n,magX_DFT); hold on; plot(64*w/pi,magX_DTFT,'--'); hold off;

grid on;   axis([-0.5,128.2,-1,5]);

title('Magnitude Part of the DFT: N = 128');

xlabel('k'); ylabel('Magnitude  |X\_DFT|');

subplot(2,1,2); stem(n, phaX_DFT); hold on; plot(64*w/pi,angX_DTFT*180/pi,'--'); hold off;

grid on;   axis([-0.5,128.2,-200,200]);

title('Angle Part of the DFT: N = 128');

xlabel('k'); ylabel('Degrees'); %axis([-200,200,0,2]);

%subplot('2,2,2'); stem(n, realX_DFT); grid on;

%title('Real Part');

%xlabel('frequency in \pi units'); ylabel('Real');

%subplot('2,2,4'); stem(n, imagX_DFT); grid on;

%title('Imaginary Part');

%xlabel('frequency in \pi units'); ylabel('Imaginary');

%% --------------------------------------------------------------

%%        END X_DFT's  mag ang real imag

%% --------------------------------------------------------------

　　运行结果：

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