DSP using MATLAB 示例 Example3.10

用到的性质

上代码：

n = -5:10; x = rand(1,length(n)) + j * rand(1,length(n));
k = -100:100; w = (pi/100)*k;                 % freqency between -pi and +pi  ,   [0,pi] axis divided into 101 points.
X = x * (exp(-j*pi/100)) .^ (n'*k);           % DTFT of x

% conjugation property
y = conj(x);                                  % signal conjugation
Y = y * (exp(-j*pi/100)) .^ (n'*k);           % DTFT of y 

magX = abs(X); angX = angle(X); realX = real(X); imagX = imag(X);
magY = abs(Y); angY = angle(Y); realY = real(Y); imagY = imag(Y);

%verification
Y_check = conj(fliplr(X));                    % conj(X(-w))    DTFT flip first, then conjugation
error = max(abs(Y-Y_check));                  % Difference

figure('NumberTitle', 'off', 'Name', 'x & y sequence')
set(gcf,'Color','white');
subplot(2,2,1); stem(n,real(x)); title('x sequence Real Part');         xlabel('n'); ylabel('Real x(n)'); grid on;
subplot(2,2,2); stem(n,imag(x)); title('x sequence Imaginary Part');    xlabel('n'); ylabel('Imaginary x(n))'); grid on;
subplot(2,2,3); stem(n,real(y)); title('y sequence Real Part');         xlabel('n'); ylabel('Real y(n)'); grid on;
subplot(2,2,4); stem(n,imag(y)); title('y sequence Imaginary Part');    xlabel('n'); ylabel('Imaginary y(n))'); grid on;

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%%        START Graphical verification
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figure('NumberTitle', 'off', 'Name', 'X Y compare theirs Magnitude and Angle');
set(gcf,'Color','white');
subplot(2,2,1); plot(w/pi,magX); grid on; axis([-1,1,0,12]);
xlabel('frequency in \pi units'); ylabel('|X|'); title('Magnitude of X ');
subplot(2,2,2); plot(w/pi,angX/pi); grid on; axis([-1,1,-1,1]);
xlabel('frequency in \pi units'); ylabel('Radians/\pi'); title('Angle of X ');

subplot(2,2,3); plot(w/pi,magY); grid on; axis([-1,1,0,12]);
xlabel('frequency in \pi units'); ylabel('|Y|'); title('Magnitude of Y ');
subplot(2,2,4); plot(w/pi,angY/pi); grid on; axis([-1,1,-1,1]);
xlabel('frequency in \pi units'); ylabel('Radians/\pi'); title('Angle of Y ');

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%%        END Graphical verification
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　运行结果：