《DSP using MATLAB》Problem 3.8

2018年元旦，他乡加班中，外面尽是些放炮的，别人的繁华与我无关。

代码：

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

%%            Output Info about this m-file

fprintf('\n***********************************************************\n');

fprintf('        <DSP using MATLAB> Problem 3.8 \n\n');

banner();

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n_start = -5; n_end = 30;

n = [n_start:n_end];

x = exp(j*0.1*pi*n) .* (stepseq(0, n_start, n_end)-stepseq(20, n_start, n_end)); 

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 x(n)')

set(gcf,'Color',[1,1,1])                  % 改变坐标外围背景颜色

subplot(2,1,1); stem(n, real(x)); title('x sequence Real Part');

xlabel('n'); ylabel('Real[x(n)]') ;

% axis([-10,10,0,1.2])

grid on

subplot(2,1,2); stem(n, imag(x)); title('x sequence Imag Part');

xlabel('n'); ylabel('Imag[x(n)]');

grid on;

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

%                       DTFT of x(n)

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

MM = 500;

k = [-MM:MM];        % [-pi, pi]

%k = [0:M];          % [0, pi]

w = (pi/MM) * k;

[X] = dtft(x, n, w);                            

magX = abs(X); angX = angle(X); realX = real(X); imagX = imag(X);

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 X(w)--DTFT of x(n)');

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

subplot(2,1,1); plot(w/pi, magX); grid on;

title('Magnitude Part of X(w)');

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

subplot(2,1,2); plot(w/pi, angX); grid on;

title('Angle Part of X(w)');

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 Real and Imag of X(w)');

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

subplot('2,1,1'); stem(w/pi, realX); grid on;

title('Real Part of X(w)');

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

subplot('2,1,2'); stem(w/pi, imagX); grid on;

title('Imaginary Part of X(w)');

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

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

%%            Even and Odd part of X(jw)

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

[XE, XO, m] = evenodd_cv(X, w/pi*500);

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 XE(m)--Even of X(w)')

set(gcf,'Color',[1,1,1])

subplot(2,1,1); stem(m/500, real(XE)); title('Real Part of Even Sequence');

xlabel('m in \pi units'); ylabel('Real[XE(m)]');

%axis([-10,10,0,1.2])

grid on

subplot(2,1,2); stem(m/500, imag(XE)); title('Imag Part of Even Sequence');

xlabel('m in \pi units'); ylabel('Imag[XE(m)]');

%axis([-10,10,0,1.2])

grid on

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 XO(m)--Odd of X(w)')

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

subplot(2,1,1); stem(m/500, real(XO)); title('Real Part of Odd Sequence');

xlabel('m in \pi units'); ylabel('Real[XO(m)]');

%axis([-10,10,0,1.2])

grid on

subplot(2,1,2); stem(m/500, imag(XO)); title('Imag Part of Odd Sequence');

xlabel('m in \pi units'); ylabel('Imag[XO(m)]');

%axis([-10,10,0,1.2])

grid on

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

%                   DTFT of Realx(n)

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

MM = 500;

k = [-MM:MM];        % [-pi, pi]

%k = [0:M];        % [0, pi]

w = (pi/MM) * k;

[RX] = dtft(real(x), n, w);                            

magRX = abs(RX); angRX = angle(RX); realRX = real(RX); imagRX = imag(RX);

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 RX(w)--DTFT of Realx(n)');

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

subplot(2,1,1); plot(w/pi, magRX); grid on;

title('Magnitude Part');

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

subplot(2,1,2); plot(w/pi, angRX); grid on;

title('Angle Part');

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 Real and Imag of RX(w)');

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

subplot('2,1,1'); plot(w/pi, realRX); grid on;

title('Real Part');

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

subplot('2,1,2'); plot(w/pi, imagRX); grid on;

title('Imaginary Part');

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

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

%                      DTFT of Imagx(n)

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

MM = 500;

k = [-MM:MM];        % [-pi, pi]

%k = [0:M];        % [0, pi]

w = (pi/MM) * k;

[IX] = dtft(j*imag(x), n, w);                            

magIX = abs(IX); angIX = angle(IX); realIX = real(IX); imagIX = imag(IX);

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 IX(w)--DTFT of Imagx(n)');

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

subplot(2,1,1); plot(w/pi, magIX); grid on;

title('Magnitude Part');

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

subplot(2,1,2); plot(w/pi, angIX); grid on;

title('Angle Part');

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 Real and Imag of IX(w)');

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

subplot('2,1,1'); plot(w/pi, realIX); grid on;

title('Real Part');

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

subplot('2,1,2'); plot(w/pi, imagIX); grid on;

title('Imaginary Part');

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

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

%             Verify

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 RX(w) and RealXE');

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

subplot('2,1,1'); plot(w/pi, realRX); grid on;

title('Real Part of RX(w)');

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

subplot('2,1,2'); plot((m/500), real(XE)); grid on;

title('Real Part of XE(w)');

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.8 IX(w) and ImagXO');

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

subplot('2,1,1'); plot(w/pi, imagIX); grid on;

title('Imaginary Part of IX(w)');

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

subplot('2,1,2'); plot((m/500), imag(XO)); grid on;

title('Imaginary Part of XO(w)');

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