comm.FMModulator

Modulate using FM method

Description

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

To FM modulate a signal:

Define and set up the FMModulator object. See Construction.
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

reset	Reset states of the FM modulator object
step	Applies FM baseband modulation

Common to All System Objects
`release`	Allow System object property value changes

Examples

collapse all

FM Modulate a Sinusoidal Signal

Open Live Script

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)])

Plot Spectrum of FM Modulated Baseband Signal

Open Script

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 Gaussian 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])

FM Modulate and Demodulate a Sinusoidal Signal

Open Live Script

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 0.5 s and frequency 4 Hz.

t = (0:ts:0.5-ts)';
x = sin(2*pi*4*t);

Create FM modulator and demodulator System objects.

fmmod = comm.FMModulator('SampleRate',fs,'FrequencyDeviation',fd);
fmdemod = comm.FMDemodulator('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 = fmmod(x);
plot(t,[x real(y)])

Demodulate the FM modulated signal.

z = fmdemod(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')

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.

Algorithms

Represent a frequency modulated passband signal, Y(t), as

$Y (t) = A \cos (2 π f_{c} t + 2 π f_{Δ} \int_{0}^{t} x (τ) d τ),$

where A is the carrier amplitude, f_c is the carrier frequency, x(τ) is the baseband input signal, and f_Δ is the frequency deviation in Hz. The frequency deviation is the maximum shift from f_c in one direction, assuming |x(t)| ≤ 1.

A baseband FM signal can be derived from the passband representation by downconverting it by f_c such that

$\begin{matrix} y_{s} (t) = Y (t) e^{- j 2 π f_{c} t} = \frac{A}{2} [e^{j (2 π f_{c} t + 2 π f_{Δ} \int_{0}^{t} x (τ) d τ)} + e^{- j (2 π f_{c} t + 2 π f_{Δ} \int_{0}^{t} x (τ) d τ)}] e^{- j 2 π f_{c} t} \\ = \frac{A}{2} [e^{j 2 π f_{Δ} \int_{0}^{t} x (τ) d τ} + e^{- j 4 π f_{c} t - j 2 π f_{Δ} \int_{0}^{t} x (τ) d τ}] . \end{matrix}$

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

$y (t) = \frac{A}{2} e^{j 2 π f_{Δ} \int_{0}^{t} x (τ) d τ} .$

The expression for y(t) is rewritten as

$y (t) = \frac{A}{2} e^{j ϕ (t)},$

where $ϕ (t) = 2 π f_{Δ} \int_{0}^{t} x (τ) d τ$ , 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,

$w (t) = \frac{A^{2}}{4} e^{j ϕ (t)} e^{- j ϕ (t - T)} = \frac{A^{2}}{4} e^{j [ϕ (t) - ϕ (t - T)]},$

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

$\begin{array}{l} w_{n} = \frac{A^{2}}{4} e^{j [ϕ_{n} - ϕ_{n - 1}]}, \\ v_{n} = ϕ_{n} - ϕ_{n - 1} . \end{array}$

The signal v_n is the approximate derivative of ϕ_n, such that v_n ≈ x_n.

Documentation

comm.FMModulator

Description

Construction

Properties

Methods

Examples

FM Modulate a Sinusoidal Signal

Plot Spectrum of FM Modulated Baseband Signal

FM Modulate and Demodulate a Sinusoidal Signal

Selected Bibliography

Algorithms

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

See Also

Communications Toolbox Documentation

Support

Documentation

comm.FMModulator

Description

Construction

Properties

Methods

Examples

FM Modulate a Sinusoidal Signal

Plot Spectrum of FM Modulated Baseband Signal

FM Modulate and Demodulate a Sinusoidal Signal

Selected Bibliography

Algorithms

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Communications Toolbox Documentation

Support

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.