Modulation for communications simulation
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Syntax
y = modulate(x,fc,fs)
[y,t] = modulate(x,fc,fs)
[___] = modulate(x,fc,fs,method)
[___] = modulate(x,fc,fs,method,opt)
Description
y = modulate(x,fc,fs) modulates the real message signal x with a carrier frequency fc and sample rate fs. If x is a matrix, the modulated signal is computed independently for each column and stored in the corresponding column of y.
[y,t] = modulate(x,fc,fs) also returns the internal time vector t.
example
[___] = modulate(x,fc,fs,method) modulates the real message signal using the modulation technique specified by method. You can use these inputs with either of the previous output syntaxes.
example
[___] = modulate(x,fc,fs,method,opt) uses the additional options specified in opt for some modulation methods.
Examples
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Single-Sideband Amplitude Modulation
Open Live Script
Generate a 10 Hz sinusoidal signal sampled at a rate of 200 Hz for 1 second. Embed the sinusoid in white Gaussian noise of variance 0.01.
fs = 200;t = 0:1/fs:1;x = sin(2*pi*10*t) + randn(size(t))/10;
Single-sideband amplitude modulate the signal with a carrier frequency of 50 Hz. Compute and display the new Welch's power spectral density estimates.
y = modulate(x,50,fs,'amssb');pwelch([x;y]',hamming(100),80,1024,fs,'centered')
Quadrature Amplitude Modulation of Two Sinusoidal Signals
Open Live Script
Generate two sinusoidal signals frequencies of 10 Hz and 20 Hz, sampled at a rate of 200 Hz for 1 second. Embed the sinusoids in white Gaussian noise of variance 0.01.
fs = 200;t = 0:1/fs:1;i = sin(2*pi*10*t) + randn(size(t))/10;q = sin(2*pi*20*t) + randn(size(t))/10;
Create a quadrature amplitude modulated signal from signals i and q using a carrier frequency of 70 Hz. Compute the Welch power spectral density estimates of the original and modulated sequences. Use a 100-sample Hamming window with 80 samples of overlap. Specify an FFT length of 1024.
y = modulate(i,70,fs,'qam',q);pwelch([i;q;y]',hamming(100),80,1024,fs,'centered') legend('In-phase signal','Quadrature signal','Modulated signal')
Input Arguments
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x — Message signal
real vector | real matrix
Message signal, specified as a real vector or matrix.
Example: sin(2*pi*25*[0:(1/200):1])
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:
amdsb-scoram— Amplitude modulation, double sideband, suppressed carrier. Multipliesxby a sinusoid of frequencyfc.y = x.*cos(2*pi*fc*t)
amdsb-tc— Amplitude modulation, double sideband, transmitted carrier. Subtracts scalaroptfromxand multiplies the result by a sinusoid of frequencyfc.y = (x-opt).*cos(2*pi*fc*t)
If you do not specify the
optparameter,modulateuses a default ofmin(min(x))so that the message signal(x-opt)is entirely nonnegative and has a minimum value of 0.amssb— Amplitude modulation, single sideband. Multipliesxby a sinusoid of frequencyfcand adds the result to the Hilbert transform ofxmultiplied by a phase-shifted sinusoid of frequencyfc.y = x.*cos(2*pi*fc*t)+imag(hilbert(x)).*sin(2*pi*fc*t)
This effectively removes the upper sideband.
fm— Frequency modulation. Creates a sinusoid with instantaneous frequency that varies with the message signalx.y = cos(2*pi*fc*t + opt*c*msum(x))
c*msumis a rectangular approximation of the integral ofx.modulateusesoptas the constant of frequency modulation. If you do not specify theoptparameter,modulateuses a default ofopt=(fc/fs)*2*pi/(max(max(x)))so the maximum frequency excursion fromfcisfcHz.pm— Phase modulation. Creates a sinusoid of frequencyfcwhose phase varies with the message signalx.y = cos(2*pi*fc*t + opt*x)
modulateusesoptas the constant of phase modulation. If you do not specify theoptparameter,modulateuses a default ofopt=pi/(max(max(x)))so the maximum phase excursion is π radians.pwm— Pulse-width modulation. Creates a pulse-width modulated signal from the pulse widths inx. The elements ofxmust be between 0 and 1, specifying the width of each pulse in fractions of a period. The pulses start at the beginning of each period, that is, they are left justified.modulate(x,fc,fs,'pwm','centered')yields pulses centered at the beginning of each period. The length ofyislength(x)*fs/fc.ppm— Pulse-position modulation. Creates a pulse-position modulated signal from the pulse positions inx. The elements ofxmust be between 0 and 1, specifying the left edge of each pulse in fractions of a period.optis a scalar between 0 and 1 that specifies the length of each pulse in fractions of a period. The default foroptis0.1. The length ofyislength(x)*fs/fc.qam— Quadrature amplitude modulation. Creates a quadrature amplitude modulated signal from signalsxandopt.y = x.*cos(2*pi*fc*t) + opt.*sin(2*pi*fc*t)
The input argument
optmust be the same size asx.
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
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y — Modulated signal
real vector | real matrix
Modulated message signal, returned as a real vector or matrix. Except for the methods pwm and ppm, y is the same size as x.
t — Internal time array
real vector
Internal time array used by modulate in its computations, specified as a real vector.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
Version History
Introduced before R2006a
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R2023b: Generate C and C++ code
Generate C and C++ code for the modulate function. You must have MATLAB® Coder™ to use this functionality.
See Also
demod | vco
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