how to calculate central frequency from fft of wave function

hi all, is there any difference between central freq and maximum freq of a wave function. how i can calculate central frequency of this function using fft in matlab y=0.5(1-cos(2*pi*f*t)*sin(2*pi*f*t)

Answer 1

[Wayne King]

Are you trying to show us an AM signal? If so, are the two f's really the same frequency, or did you mean something like this:

    t = 0:1e-4:1-1e-4; 
    f0 = 50;
    fc = 1e3;
    y=0.5*(1-cos(2*pi*f0*t)).*sin(2*pi*fc*t);
    ydft = fft(y);
    ydft = ydft(1:length(y)/2+1);
    freq = 0:1e4/length(y):1e4/2;
   plot(freq,abs(ydft))

[kavya saxena]

these two are same frequency. let it wiil be 20Khz then i did

f=20e3;

fs=f*100;

ts=1/fs;

n=3;

t=0:ts:n/f;

y=0.5*(1-cos(2*pi*f*t)).*sin(2*pi*f*t);

ydft = fft(y);

now how i get central freq?

Answer 2

[Wayne King]

It appears to me that just rewriting that using trigonometric identities you see that it equals

1/2*sin(2*pi*f*t)-1/4*sin(2*pi*2*f*t)

So you get a line component at 20 kHz and one at 40 kHz with 1/2 the amplitude of the component at 20 kHz.

    freq = 0:fs/length(y):fs/2;
    ydft = fft(y);
    ydft = ydft(1:ceil(length(y)/2));
    plot(freq,abs(ydft))

So I'm guessing you call the center frequency 30 kHz.