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

Question

Devon Rose 2022-3-7

0
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https://ww2.mathworks.cn/matlabcentral/answers/1666044-how-to-use-besselj-function-to-plot-spectrum-of-single-tone-fm-signal

编辑： Saarthak Gupta 2023-12-18

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

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Answer 1

Saarthak Gupta 2023-12-18

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https://ww2.mathworks.cn/matlabcentral/answers/1666044-how-to-use-besselj-function-to-plot-spectrum-of-single-tone-fm-signal#answer_1373522

编辑：Saarthak Gupta 2023-12-18

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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: