DFT
hi,
I have a signal x(t)=25cos(10*pi*t)cos(400*pi*t) . i sampled it at sampling frequency of 410 Hz which is just equal to the Nyquist rate. my matlab code to compute the DFT X(K) is
N=82;
n= 0:81;
Ts = 1/410;
t = n*Ts;
x=25*cos(10*pi*t).*cos(400*pi*t);
X=fft(x);
subplot(3,1,1)
stem(n, x)
axis tight
ylabel('x[n]');
xlabel('n');
subplot(3,1,2);
stem(n*410/N, abs(X));
axis tight
ylabel('DFT X(K),Magnitute');
xlabel('f in Hz');
subplot(3,1,3)
stem(n*410/N, angle(X))
ylabel('DFT X(K),Phase');
xlabel('f in Hz');
axis tight
The result is the DFT X(K) frequency spectrum show 3 frequency present in the signal. but i expect only two frequency present (195Hz and 205Hz) . where the hell this third frequency resulted. am i right to say that is it caused by aliasing.
Now if I sampled the signal at 810Hz and other parameter remain unchanged , my DFT X(K) in the frequency domain have duplicate copies( periodic) but the frequency spectrum is not what i expected to be 195Hz and 205Hz. I thought I have prevented Aliasing by sampling higher than the Nyquist Rate.
struggling to understand on this.