demod

Demodulation for communications simulation

Syntax

x = demod(y,fc,fs,method)

x = demod(y,fc,fs,method,opt)

Description

x = demod(y,fc,fs,method) demodulates the real carrier signal y with a carrier frequency fc and sample rate fs using the method specified in method.

x = demod(y,fc,fs,method,opt) demodulates the real carrier signal y using the additional options specified in opt.

Examples

Frequency Modulation and Demodulation

Generate a 150 Hz sinusoid sampled at 8 kHz for 1 second. Embed the modulated signal in white Gaussian noise of variance 0.1².

fs = 8e3;

t = 0:1/fs:1-1/fs;
s = cos(2*pi*150*t) + randn(size(t))/10;

Frequency modulate the signal at a carrier frequency of 3 kHz using a modulation constant of 0.1.

fc = 3e3;
rx = modulate(s,fc,fs,'fm',0.1);

Frequency demodulate the signal using the same carrier frequency and modulation constant. Compute and plot power spectrum estimates for the transmitted, received, and demodulated signals.

y = demod(rx,fc,fs,'fm',0.1);

pspectrum([s;rx;y]',fs,'Leakage',0.85)

legend('Transmitted signal','Received signal','Demodulated signal','Location','best')

Input Arguments

y — Modulated signal

real vector | real matrix

Modulated message signal, specified as a real vector or matrix. Except for the methods pwm and ppm, y is the same size as x.

fc — Carrier frequency

real positive scalar

Carrier frequency used to modulate the message signal, specified as a real positive scalar.

fs — Sample rate

real positive scalar

Sample rate, specified as a real positive scalar.

method — Method of modulation used

'am' (default) | 'amdsb-tc' | 'amssb' | 'fm' | 'pm' | 'pwm' | 'ppm' | 'qam'

Method of modulation used, specified as one of:

• am or amdsb-sc — Amplitude demodulation, double sideband, suppressed carrier. Multiplies y by a sinusoid of frequency fc and applies a fifth-order Butterworth lowpass filter using filtfilt.

  x = y.*cos(2*pi*fc*t);
  [b,a] = butter(5,fc*2/fs);
  x = filtfilt(b,a,x);

• amdsb-tc — Amplitude demodulation, double sideband, transmitted carrier. Multiplies y by a sinusoid of frequency fc and applies a fifth-order Butterworth lowpass filter using filtfilt.

  x = y.*cos(2*pi*fc*t);
  [b,a] = butter(5,fc*2/fs);
  x = filtfilt(b,a,x);

  If you specify opt, demod subtracts scalar opt from x. The default value for opt is 0.

• amssb — Amplitude demodulation, single sideband. Multiplies y by a sinusoid of frequency fc and applies a fifth-order Butterworth lowpass filter using filtfilt..

  x = y.*cos(2*pi*fc*t);
  [b,a] = butter(5,fc*2/fs);
  x = filtfilt(b,a,x);

• fm — Frequency demodulation. Demodulates the FM waveform by modulating the Hilbert transform of y by a complex exponential of frequency -fc Hz and obtains the instantaneous frequency of the result..

  y=cos(2*pi*fc*t + opt*cumsum(x))

  cumsum is a rectangular approximation of the integral of x. modulate uses opt as the constant of frequency modulation. If you do not specify the opt parameter, modulate uses a default of opt = (fc/fs)*2*pi/(max(max(x))) so the maximum frequency excursion from fc is fc Hz.

• pm — Phase demodulation. Demodulates the PM waveform by modulating the Hilbert transform of y by a complex exponential of frequency -fc Hz and obtains the instantaneous phase of the result.

  y=cos(2*pi*fc*t + opt*x)

  modulate uses opt as the constant of phase modulation. If you do not specify the opt parameter, modulate uses a default of opt = pi/(max(max(x))) so the maximum phase excursion is π radians.

• pwm — Pulse-width demodulation. Finds the pulse widths of a pulse-width modulated signal y. demod returns in x a vector whose elements specify the width of each pulse in fractions of a period. The pulses in y should start at the beginning of each carrier period, that is, they should be left justified. modulate(x,fc,fs,'pwm','centered') yields pulses centered at the beginning of each period. The length of y is length(x)*fs/fc.

• ppm — Pulse-position demodulation. Finds the pulse positions of a pulse-position modulated signal y. For correct demodulation, the pulses cannot overlap. x is length length(t)*fc/fs.

• qam— Quadrature amplitude demodulation. [x1,x2] = demod(y,fc,fs,'qam') multiplies y by a cosine and a sine of frequency fc and applies a fifth-order Butterworth lowpass filter using filtfilt.

  x1 = y.*cos(2*pi*fc*t);
  x2 = y.*sin(2*pi*fc*t);
  [b,a] = butter(5,fc*2/fs);
  x1 = filtfilt(b,a,x1);
  x2 = filtfilt(b,a,x2);

  The input argument opt must be the same size as y.

opt — Optional input for some methods

real vector

Optional input, specified for some methods. Refer to method for more details on how to use opt.

Output Arguments

x — Demodulated message signal

real vector | real matrix

Demodulated message signal, returned as a real vector or matrix.