Demodulate using FM method
object™ demodulates an FM modulated signal.
To FM demodulate a signal:
Starting in R2016b, instead of using the
to perform the operation defined by the System
object™, you can
call the object with arguments, as if it were a function. For example,
= step(obj,x) and
y = obj(x) perform
H = comm.FMDemodulator creates a demodulator System
that frequency demodulates an input signal.
H = comm.FMDemodulator(mod) creates an
FM demodulator object whose properties are determined by the corresponding
FM modulator object,
H = comm.FMDemodulator( creates
an FM demodulator object with each specified property
to the specified
appear inside single quotes. You can specify additional name-value
pair arguments in any order as (
Peak deviation of the output signal frequency (Hz)
Specify the frequency deviation of the FM demodulator in Hz
as a positive real scalar. The default value is
Sample rate of input signal (Hz)
Specify the sample rate in Hz as a positive real scalar. The
default value is
|reset||Reset states of the FM demodulator object|
|step||Applies FM baseband demodulation|
|Common to All System Objects|
Allow System object property value changes
Modulate and demodulate a sinusoidal signal. Plot the demodulated signal and compare it to the original signal.
Set the example parameters.
fs = 100; % Sample rate (Hz) ts = 1/fs; % Sample period (s) fd = 25; % Frequency deviation (Hz)
Create a sinusoidal input signal with duration 0.5s and frequency 4 Hz.
t = (0:ts:0.5-ts)'; x = sin(2*pi*4*t);
Create an FM modulator System object™.
MOD = comm.FMModulator('SampleRate',fs,'FrequencyDeviation',fd);
FM modulate the input signal and plot its real part. You can see that the frequency of the modulated signal changes with the amplitude of the input signal.
y = step(MOD,x); plot(t,[x real(y)])
Demodulate the FM modulated signal.
DEMOD = comm.FMDemodulator('SampleRate',fs,'FrequencyDeviation',fd); z = step(DEMOD,y);
Plot the input and demodulated signals. The demodulator output signal exactly aligns with the input signal.
plot(t,x,'r',t,z,'ks') legend('Input Signal','Demod Signal') xlabel('Time (s)') ylabel('Amplitude')
Create an FM demodulator System object? from an FM modulator object. Modulate and demodulate audio data loaded from a file and compare its spectrum with that of the input data.
Set the example parameters.
fd = 50e3; % Frequency deviation (Hz) fs = 300e3; % Sample rate (Hz)
Create an FM modulator System object.
MOD = comm.FMModulator('FrequencyDeviation',fd,'SampleRate',fs);
Create a companion demodulator object based on the modulator.
DEMOD = comm.FMDemodulator(MOD);
Verify that the properties are identical in the two System objects.
MOD = comm.FMModulator with properties: SampleRate: 300000 FrequencyDeviation: 50000 DEMOD = comm.FMDemodulator with properties: SampleRate: 300000 FrequencyDeviation: 50000
Load audio data into structure variable,
S = load('handel.mat'); data = S.y; fsamp = S.Fs;
Create a spectrum analyzer System object.
SA = dsp.SpectrumAnalyzer('SampleRate',fsamp,'ShowLegend',true);
FM modulate and demodulate the audio data.
modData = step(MOD,data); demodData = step(DEMOD,modData);
Verify that the spectrum plot of the input data (Channel 1) is aligned with that of the demodulated data (Channel 2).
Playback an audio file after applying FM modulation and demodulation. The example takes advantage of the characteristics of System objects™ to process the data in streaming mode.
Load the audio file,
guitartune.wav, using an audio file reader object.
AUDIO = dsp.AudioFileReader... ('guitartune.wav','SamplesPerFrame',4410);
Create an audio device writer object for audio playback.
AUDIOPLAYER = audioDeviceWriter;
Create modulator and demodulator objects having default properties.
MOD = comm.FMModulator; DEMOD = comm.FMDemodulator;
Read audio data, FM modulate, FM demodulate, and playback the demodulated signal,
while ~isDone(AUDIO) x = step(AUDIO); % Read audio data y = step(MOD,x); % FM modulate z = step(DEMOD,y); % FM demodulate step(AUDIOPLAYER,z); % Playback the demodulated signal end
 Chakrabarti, I. H., and Hatai, I. “A New High-Performance Digital FM Modulator and Demodulator for Software-Defined Radio and Its FPGA Implementation.” International Journal of Reconfigurable Computing. Vol. 2011, No. 10.1155/2011, 2011, p. 10.
 Taub, Herbert, and Donald L. Schilling. Principles of Communication Systems. New York: McGraw-Hill, 1971, pp. 142–155.
Represent a frequency modulated passband signal, Y(t), as
where A is the carrier amplitude, fc is the carrier frequency, x(τ) is the baseband input signal, and fΔ is the frequency deviation in Hz. The frequency deviation is the maximum shift from fc in one direction, assuming |x(t)| ≤ 1.
A baseband FM signal can be derived from the passband representation by downconverting it by fc such that
Removing the component at -2fc from ys(t) leaves the baseband signal representation, y(t), which is expressed as
The expression for y(t) is rewritten as
where , which implies that the input signal is a scaled version of the derivative of the phase, ϕ(t).
A baseband delay demodulator is used to recover the input signal from y(t).
A delayed and conjugated copy of the received signal is subtracted from the signal itself,
where T is the sample period. In discrete terms, wn=w(nT), and
The signal vn is the approximate derivative of ϕn, such that vn ≈ xn.
Usage notes and limitations:
See System Objects in MATLAB Code Generation (MATLAB Coder).