signal processing, fft, adding two cosine waves

Hi, I can individually retrieve the magnitude and frequency of two cosine waves (say 10*cos(w*t) and 30*cos(w*t)). Suppose the signal is 10*cos(w*t)+30*cos(w*t) how to retrieve the magnitudes (i.e, 10 and 30) from the fft. All suggestions welcome.

Answer 1

[Wayne King]

Then the magnitude will be 40 in this case if the frequencies and phases are the same. And there is no way to extract the 10 and the 30 separately.

 n = 0:199;
 x = 10*cos(pi/4*n)+30*cos(pi/4*n);
 xdft = fft(x);
 xdft = xdft(1:length(x)/2+1)/length(x);
 xdft(2:end-1) = 2*xdft(2:end-1);
 plot(abs(xdft))
 abs(xdft(26))

[Nani C]

t.y. !

Answer 2

[Wayne King]

The main thing will be figuring out the DFT bin that the frequency of interest falls on. The frequencies are spaced at Fs/N where N is the length of the input signal and Fs is the sampling frequency. Keep in mind that the first bin (unless you use fftshift) is the zero frequency, or DC. I'll do an example assuming a sampling frequency of 1 and two frequencies, 1/8 cycles/sec and 1/4 cycles per second. For a signal of length 200, we expect these frequencies in bins, 26 and 51.

n = 0:199;
x = 10*cos(pi/4*n)+30*sin(pi/2*n);
xdft = fft(x);
xdft = xdft(1:length(x)/2+1)/length(x);
xdft(2:end-1) = 2*xdft(2:end-1);
plot(abs(xdft))
abs(xdft(26))
abs(xdft(51))

[Nani C]

O.K. what about when both frequencies are same ?