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; %% ---------------------------------------------------------------- %% START Graphical verification %% ---------------------------------------------------------------- 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 '); %% ---------------------------------------------------------------- %% END Graphical verification %% ----------------------------------------------------------------
运行结果: