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：
