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

%%            Output Info about this m-file

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

fprintf('        <DSP using MATLAB> Problem 3.7 \n\n');

banner();

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

n_start = -10; n_end = 20;

n = [n_start:n_end];

x = 2 * (0.9 .^(-n)) .* (cos(0.1*pi*n) + j*sin(0.9*pi*n)) .* (stepseq(0, n_start, n_end)-stepseq(10, n_start, n_end)); 

[xe,xo,m] = evenodd_cv(x,n);

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 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;

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 xe(m)')

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

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

xlabel('m'); ylabel('Real[xe(m)]');

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

grid on

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

xlabel('m'); ylabel('Imag[xe(m)]');

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

grid on

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 xo(m)')

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

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

xlabel('m'); ylabel('Real[xo(m)]');

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

grid on

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

xlabel('m'); ylabel('Imag[xo(m)]');

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

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 3.7 DTFT of x(n)');

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

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

title('Magnitude Part');

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

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

title('Angle Part');

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 Real and Imag of X(jw)');

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

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

title('Real Part');

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

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

title('Imaginary Part');

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

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

%                   DTFT of xe(m)

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

MM = 500;

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

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

w = (pi/MM) * k;

[XE] = dtft(xe, m, w);                            

magXE = abs(XE); angXE = angle(XE); realXE = real(XE); imagXE = imag(XE);

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 DTFT of xe(m)');

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

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

title('Magnitude Part');

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

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

title('Angle Part');

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 Real and Imag of XE(jw)');

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

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

title('Real Part');

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

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

title('Imaginary Part');

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

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

%                   DTFT of xo(m)

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

MM = 500;

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

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

w = (pi/MM) * k;

[XO] = dtft(xo, m, w);                            

magXO = abs(XO); angXO = angle(XO); realXO = real(XO); imagXO = imag(XO);

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 DTFT of xo(m)');

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

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

title('Magnitude Part');

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

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

title('Angle Part');

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 Real and Imag of XO(jw)');

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

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

title('Real Part');

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

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

title('Imaginary Part');

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

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

%             Verify

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 RealX and RealXE');

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

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

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

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

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

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

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

figure('NumberTitle', 'off', 'Name', 'Problem 3.7 ImagX and ImagXO');

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

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

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

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

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

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

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