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explain FSK spectrum plot

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jess17

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can some one explain to me why are there M peaks when I plot the fft of a FSK modulated signal, following is the matlab code

M = 4; freqsep = 8; nsamp = 8; Fs = 32;
x = randint(1000,1,M); % Random signal
y = fskmod(x,M,freqsep,nsamp,Fs); % Modulate.
ly = length(y);
% Create an FFT plot.
plot(abs(fft(y)))
 

Follows Bessel function.

There is infinite series but generally the number of significant peaks is dependent on modulation index.

Mod Index of 0.01 -> J0(beta) = 0.995 (carrier component), J1(beta) = 0.005

Mod Index of 2.0 -> J0(beta) = 0.220 (carrier component), J1(beta) = 0.580, J2(beta) = 0.35, J3(beta) = 0.13, J4(beta) = 0.03 ; has 4 significant sidebands with RF bandwidth of 8 x freq of modulation.

One accurate way of measuring modulation index is to look for particular sideband nulls.
 

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