Modulation of Sinusoids in Matlab (Frequency Domain Problems)

[halcyon626]

The Problem
Hi, I am trying to modulate two sinusoids in Matlab. I have some

x = sin(2*pi*fx*t)

and some

y = cos(2*pi*fc*t)

, where fx and fc are different frequencies. I then modulate them together, using dot multiplication,

z = x.*y

. I then plot each in the time domain using

plot(t,x)

and I obtained the correct solution. The problem comes with plotting the Fourier Transform of the resulting signal.

My Attempt
I have let some xf , yf, and zf be each of the signals in the magnitude domain. I let

xf = 2*abs(fft(xf))/N

(getting the one-sided magnitude spectrum of x). N is the length of my time vector. The same is done for y and z.

I know I have to compute my "x-axis", and not just plot xf/yf/zf, but even when plotting them I know I *should* get two spikes each in x and y, and four spikes in the resulting modulated signal. The problem is my modulated signal only has two spikes.

I don't want to post an exact homework question here, but rather understand what I am doing wrong in Matlab to get this incorrect answer. If I let fx = 10 and fc = 2, the modulated signal (one-sided) should show spikes at -2, 2, 8,12 (we won't see the -2 in the one-sided).

Thank you for the help, and please let me know if I need to post more information, or be clearer on the question.

 

[Valkarie]

SolutionYou need to multiply the FFTs rather than the time-domain functions. That is, instead of z = x.*y, you should do zf = xf.*yf. This will give you the correct four-spike result.