How to use besselj function to plot spectrum of single tone FM signal

close all;
clear all;
clc;

fs = 10000;
fc = 1500; 
fm=100;
m=5;
n=1:1:m;

for n=1:1:m
x(n)=fs-fc-n*fm;
y(n)=fs+fc+n*fm;
z(n)=x(n)+y(n);
B(n)=besselj(n,z(n));
end

Answer 1

[Saarthak Gupta]

Hi Devon,

I understand you wish to plot the power spectrum of a single tone FM signal.

For a single tone FM signal of the form

the spectrum in the frequency domain is given as:

This FM spectrum can be plotted as a series of delta functions of height

A negative amplitude in a frequency component indicates a 180-degree phase shift for that component. Usually, we only need to compare the relative intensities of the sidebands for which we plot the amplitudes' absolute values.

Refer to the following code:

% parameter values
fc = 1500; 
fm = 100;
M = 5;
beta = 2;
A = 10;

% sideband frequencies
freqs = fc + (-M:M)*fm;
% freqs = -freqs;   % negative frequencies

% amplitudes for a given value of beta (modulation index), and sideband frequencies
amps = A/2.*abs(besselj(-M:M,beta));

% plot spectrum
scatter(freqs,amps);

for i=1:numel(freqs)
    line([freqs(i) freqs(i)], [0 amps(i)], 'Color', 'red');
end

In case you need to do power calculations, make sure to plot the negative frequencies as well. This can be easily achieved by negating the frequencies vector (code provided).

Refer to the following MATLAB documentation for further reference:

• https://www.mathworks.com/help/matlab/ref/besselj.html

Hope this helps!

Best regards,

Saarthak