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comm.FMModulator System object

Modulate using FM method

Description

The FMModulator System object™ applies FM modulation to an input signal.

To FM modulate a signal:

  1. Define and set up the FMModulator object. See Construction.

  2. Call step to apply FM modulation to a signal according to the properties of comm.FMModulator. The behavior of step is specific to each object in the toolbox.

Note

Starting in R2016b, instead of using the step method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Construction

H = comm.FMModulator creates a modulator System object, H, that frequency modulates an input signal.

H = comm.FMModulator(demod) creates an FM modulator object whose properties are determined by the corresponding FM demodulator object, demod.

H = comm.FMModulator(Name,Value) creates an FM modulator object with each specified property Name set to the specified Value. Name must appear inside single quotes. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

Properties

FrequencyDeviation

Peak deviation of the output signal frequency (Hz)

Specify the frequency deviation of the FM modulator in Hz as a positive real scalar. The default value is 75e3. The system bandwidth is equal to twice the sum of the frequency deviation and the message bandwidth. This property is nontunable.

SampleRate

Sample rate of the input signal (Hz)

Specify the sample rate in Hz as a positive real scalar. The default value is 240e3. The output sample rate is equal to the input sample rate. This property is nontunable.

Methods

resetReset states of the FM modulator object
stepApplies FM baseband modulation
Common to All System Objects
clone

Create System object with same property values

getNumInputs

Expected number of inputs to a System object

getNumOutputs

Expected number of outputs of a System object

isLocked

Check locked states of a System object (logical)

release

Allow System object property value changes

Examples

expand all

Apply baseband modulation to a sine wave input signal and plot its response.

Set the example parameters.

fs = 1e3;              % Sample rate (Hz)
ts = 1/fs;             % Sample period (s)
fd = 50;               % 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)])

Apply FM baseband modulation to a white Gaussian noise source and plot its spectrum.

Set the example parameters.

fs = 1e3;              % Sample rate (Hz)
ts = 1/fs;             % Sample period (s)
fd = 10;               % Frequency deviation (Hz)

Create a white Guassian noise source having a duration of 5s.

t = (0:ts:5-ts)';
x = wgn(length(t),1,0);

Create an FM modulator System object™ and modulate the input signal.

MOD1 = comm.FMModulator('SampleRate',fs,'FrequencyDeviation',fd);
y = step(MOD1,x);

Create another modulator object, MOD2, whose frequency deviation is five times larger and apply FM modulation.

MOD2 = comm.FMModulator('SampleRate',fs,'FrequencyDeviation',5*fd);
z = step(MOD2,x);

Plot the spectra of the two modulated signals. The larger frequency deviation associated with channel 2 results in a noise level that is 10 dB higher.

SA = dsp.SpectrumAnalyzer('SampleRate',fs,'ShowLegend',true);
step(SA,[y z])

Algorithms

You can represent a standard frequency modulated passband signal, Y(t), as

Y(t)=Acos(2πfct+2πfΔ0tx(τ)dτ),

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

ys(t)=Y(t)ej2πfct=A2[ej(2πfct+2πfΔ0tx(τ)dτ)+ej(2πfct+2πfΔ0tx(τ)dτ)]ej2πfct=A2[ej2πfΔ0tx(τ)dτ+ej4πfctj2πfΔ0tx(τ)dτ].

Removing the component at -2fc from ys(t) leaves the baseband signal representation, y(t), which is expressed as

y(t)=A2ej2πfΔ0tx(τ)dτ.

The expression for y(t) is rewritten as

y(t)=A2ejϕ(t),

where ϕ(t)=2πfΔ0tx(τ)dτ, 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.

w(t)=A24ejϕ(t)ejϕ(tT)=A24ej[ϕ(t)ϕ(tT)],

where T is the sample period. In discrete terms, wn=w(nT), consequently

wn=A24ej[ϕnϕn1],vn=ϕnϕn1.

The signal vn is the approximate derivative of ϕn such that vnxn.

Selected Bibliography

[1] 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.

[2] Taub, Herbert, and Donald L. Schilling. Principles of Communication Systems. New York: McGraw-Hill, 1971, pp. 142–155.

Extended Capabilities

Introduced in R2015a

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