Spectrum of fm modulaton
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AbdAlla Hefny
on 8 Apr 2017
Answered: santy vega
on 28 Aug 2019
Is there a way to plot the spectrum of an fm modulated signal. I know that Fourier transform is not directly applicable for fm signals as they are not linear. So is there a direct method to do that [even for a tone modulation at least]?
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Accepted Answer
David Goodmanson
on 9 Apr 2017
Edited: David Goodmanson
on 9 Apr 2017
Hello AbdAlla, The generation of a real fm signal is not a linear process, but there is no problem with finding the resulting spectrum by fft since the fft can find the frequency components of any signal. The fft works out best with modulation by a tone or the sum of a small number of tones, AND when the carrier and all the tones have an exact number of cycles in the time array.
(revised) Here is a small example:
F = 1e6; % sampling frequency
f0 = 20000; % carrier
f1 = 200; % modulating tone
beta = 1; % modulation index
% signal, spectrum
N = 1e6;
t = (0:N-1)*(1/F); % delt = 1us
y = cos(2*pi*f0*t+beta*cos(2*pi*f1*t));
z = fftshift(fft(y))/N;
f = (-N/2:N/2-1)*(F/N);
% predicted sidebands for the positive frequencies only
n = 4;
sidamp = (1/2)*besselj(0:n,beta);
sidamp = [fliplr(sidamp(2:end)), sidamp];
sidf = (f0-n*f1):f1:(f0+n*f1);
figure(1)
plot (f,abs(z))
xlim([-2*f0 2*f0])
figure(2)
plot(f,abs(z),sidf,sidamp,'o')
xlim([f0-f1*10 f0+f1*10]) % sidebands at the pos frequencies
Fig 1 shows positive and negative frequencies. Most of the time people double the abs(amplitudes) and show positive frequencies only, in which case the sideband calculation does not have the factor of 1/2.
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venu dunde
on 26 Mar 2018
Edited: venu dunde
on 26 Mar 2018
clear all;
clc;
close all;
Fs_fm = 200e3; %%%%%% sampling rate of FM signal bw = 100e3; %%% signal bandwidth
F_carrier = 98e6; %%%%% FM carrier
fc = 98e6; % Operating frequency fs = Fs_fm; % Waveform
[y_song,Fs_audio] = audioread('song.mp3');
%Fs_audio = 44100;
%y_fm = resample(y_song,Fs_fm,Fs_audio);
%%%%%%%%%%%%%%%%% %%%% time of simulations , sec %%%%%%%%%%%%%%%%%%
deltaT =40;
%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%% creating FM stereo signal %%%%%%%%%%%%%%%%%%%%%%%%%%%
audio_signal = y_song(1:deltaT*Fs_audio,:);
%rc = rcosine(Fs_audio,16*Fs_audio);
%audio_signal = filter(rc,1,randn(deltaT*Fs_audio,2));
audio_signal = resample(audio_signal, Fs_fm, Fs_audio);
t_vect = [0:length(audio_signal)-1]'/Fs_fm;
sum_ch= 0.5 *(audio_signal(:,1)+audio_signal(:,2));
diff_ch = 0.5 *(audio_signal(:,1)-audio_signal(:,2));
stereophonic_signal = sum_ch + 0.1*cos(2*pi*19e3*t_vect) + diff_ch.*cos(2*pi*38e3*t_vect);
CE_FM_radio_signal = exp(1j*2*pi*75e3*cumsum(stereophonic_signal/Fs_fm));
s_wav = CE_FM_radio_signal( 8.45e4:end);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%% Source characterization %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
figure(1)
plot(fft(s_wav),Fs_fm,'b');
title('FM signal spectral density');
xlabel('Frequency KHz');
ylabel('Magnitude dB'); grid
figure(2)
fm_acor = abs(xcorr(s_wav));
plot(10*log10(fm_acor));
title('Autocorrelation Function');
xlabel('Autocorrelation Lags');
ylabel('magnitude');
grid
venu dunde
on 26 Mar 2018
plot the frequency spectrum of FM signal ( which is almost real-time signal), i am facing problem at figure(1) plot(s_wav,Fs_fm,'b');title('FM signal spectral density');xlabel('Frequency KHz');ylabel('Magnitude dB');grid, figure-1
update the file (use any short .mp3 file, here i am unable to attach the .mp3 file) thank you,
More Answers (1)
santy vega
on 28 Aug 2019
hello,
excuse me and if I want to get the fm bandwitch of this signal,How could I do it? thanks
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