comm.FMModulator

Modulate signal using FM method

Description

The comm.FMModulator System object™ applies baseband frequency modulation to a signal. For more information, see Algorithms.

To modulate a signal using the FM method:

1. Create the comm.FMModulator object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

fmmodulator = comm.FMModulator

fmmodulator = comm.FMModulator(Name,Value)

fmmodulator = comm.FMModulator(fmdemodulator)

Description

fmmodulator = comm.FMModulator creates an FM modulator System object.

fmmodulator = comm.FMModulator(Name,Value) sets properties using one or more name-value arguments. For example, 'SampleRate,400e3' specifies a sample rate of 400 kHz.

fmmodulator = comm.FMModulator(fmdemodulator) sets properties based on the configuration of the input comm.FMDemodulator System object, fmdemodulator.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

SampleRate — Sample rate

240e3 (default) | positive scalar

Sample rate of the input signal in Hz, specified as a positive scalar. This property specifies the sample rate at the output of a modulator or at the input of a demodulator. The sample rate must be greater than twice the frequency deviation (that is, SampleRate > 2×FrequencyDeviation).

Data Types: double

FrequencyDeviation — Peak deviation of output signal frequency

75e3 (default) | positive scalar

Peak deviation of the output signal frequency in Hz, specified a positive scalar. The frequency deviation must be less than half the sample rate (that is, FrequencyDeviation < SampleRate/2).

The system bandwidth is B_T = 2×(FrequencyDeviation + B_M), where B_M is the message bandwidth in Hz. For more information, see Algorithms.

Data Types: double

Usage

Syntax

outsig = fmmodulator(insig)

Description

outsig = fmmodulator(insig) modulates the input message signal and outputs a baseband FM signal.

Input Arguments

insig — Input signal

scalar | column vector

Input signal, specified as a scalar or column vector.

This object accepts variable-size inputs. After the object is locked, you can change the size of each input channel, but you cannot change the number of channels. For more information, see Variable-Size Signal Support with System Objects.

Data Types: double | single | fi
Complex Number Support: Yes

Output Arguments

outsig — Modulated baseband FM signal

scalar | column vector

Modulated baseband FM signal, returned as a scalar or column vector with complex values. The output signal has the same data type and size as the input insig.

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

FM-Modulate Sinusoidal Signal

Apply baseband modulation to a sine wave. Plot the sine wave and the modulated signals.

Set parameters for the example.

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

Create a sinusoidal signal with a duration of 0.5 s and frequency of 4 Hz.

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

Create an FM modulator System object™, setting the sample rate and frequency deviation.

fmmodulator = comm.FMModulator( ...
    'SampleRate',fs, ...
    'FrequencyDeviation',fd);

FM-modulate the signal and plot its real part. The frequency of the modulated signal changes with the amplitude of the input signal.

y = fmmodulator(x);
plot(t,[x real(y)])

Plot Spectrum of Baseband FM-Modulated Signal

Apply baseband FM modulation to a white Gaussian noise source and plot the spectrum of the modulated signal.

Initialize parameters for the example.

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

Create a white Gaussian noise source with a duration of 5 seconds.

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

Create two FM modulator System objects, setting the sample rate and frequency deviation. Set the frequency deviation of the second FM modulator object five times higher than the first FM modulator.

fmmod1 = comm.FMModulator( ...
    SampleRate=fs, ...
    FrequencyDeviation=fd);
fmmod2 = comm.FMModulator( ...
    SampleRate=fs, ...
    FrequencyDeviation=5*fd);

Use the FM modulators to apply FM modulation to the signal x.

y1 = fmmod1(x);
y2 = fmmod2(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 than the first channel.

specanalyzer = spectrumAnalyzer(SampleRate=fs,ShowLegend=true);
specanalyzer([y1 y2])
release(specanalyzer)

Modulate and Demodulate Sinusoidal Signal Using FM Method

Modulate and demodulate a sinusoidal signal. Plot the demodulated signal and compare it to the original signal.

Initialize parameters for the example.

fs = 100;  % Sample rate (Hz)
ts = 1/fs; % Sample period (s)
fd = 25;   % Frequency deviation (Hz)

Create a sinusoidal signal with a duration of 0.5 s and frequency of 4 Hz.

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

Create an FM modulator System object™, setting the sample rate and frequency deviation. Then, create an FM demodulator System object, using the FM modulator configuration to set the demodulator properties.

fmmodulator = comm.FMModulator( ...
    'SampleRate',fs, ...
    'FrequencyDeviation',fd);
fmdemodulator = comm.FMDemodulator(fmmodulator);

FM-modulate the signal and plot the real component of the complex signal. The frequency of the modulated signal changes with the amplitude of the input signal.

y = fmmodulator(x);
plot(t,[x real(y)])
title('Input Sinusoid and FM-Modulated Signals')
xlabel('Time (seconds)'); ylabel('Amplitude')
legend('Input signal','Modulated signal (real component)')

Demodulate the FM-modulated signal.

z = fmdemodulator(y);

Plot the original and demodulated signals. The demodulator output signal exactly aligns with the original signal.

plot(t,x,'r',t,z,'ks')
legend('Original signal','Demodulated signal')
xlabel('Time (s)')
ylabel('Amplitude')

Algorithms

A frequency-modulated passband signal, Y(t), is given as

$$Y(t)=A\cos \left(2\pi f_{\text{c}}t+2\pi f_{\text{Δ}}{\displaystyle {\int }_0^{t}x(\text{τ})d\text{τ}}\right),$$

where:

• A is the carrier amplitude.

• f_c is the carrier frequency.

• x(τ) is the baseband input signal.

• f_Δ is the frequency deviation in Hz.

The frequency deviation is the maximum shift from f_c in one direction, assuming |x(τ)| ≤ 1.

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

$$\begin{array}{c}{y}_{\text{s}}(t)=Y(t)e^{-j2\pi f_{\text{c}}t}=\frac{A}{2}\left[e^{j\left(2\text{π}{f}_{\text{c}}t+2\text{π}{f}_{\text{Δ}}{\displaystyle {\int }_0^{t}x(\text{τ})d\text{τ}}\right)}+e^{-j\left(2\text{π}{f}_{\text{c}}t+2\text{π}{f}_{\text{Δ}}{\displaystyle {\int }_0^{t}x(\text{τ})d\text{τ}}\right)}\right]e^{-j2\text{π}{f}_{\text{c}}t}\\ =\frac{A}{2}\left[e^{j2\text{π}{f}_{\text{Δ}}{\displaystyle {\int }_0^{t}x(\text{τ})d\text{τ}}}+e^{-j4\text{π}{f}_{\text{c}}t-j2\text{π}{f}_{\text{Δ}}{\displaystyle {\int }_0^{t}x(\text{τ})d\text{τ}}}\right].\end{array}$$

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

$$y(t)=\frac{A}{2}{e}^{j2\pi f_{\Delta }{\displaystyle {\int }_0^{t}x(\tau )d\tau }}.$$

The expression for y(t) can be rewritten as $$y(t)=\frac{A}{2}{e}^{j\varphi (t)}$$, where $$\varphi (t)=2\text{π}{f}_{\Delta }{\displaystyle {\int }_0^{t}x(\tau )d\tau }$$. Expressing y(t) this way implies that the input signal is a scaled version of the derivative of the phase, ϕ(t).

To recover the input signal from y(t), use a baseband delay demodulator, as this figure shows.

Subtracting a delayed and conjugated copy of the received signal from the signal itself results in this equation.

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

where T is the sample period. In discrete terms,

$$\begin{array}{l}{w}_{\text{n}}=w(\text{n}T),\\ w_{\text{n}}=\frac{A^2}{4}{e}^{j\left[{\varphi }_{\text{n}}-{\varphi }_{\text{n}-1}\right]}\text{, and}\\ v_{\text{n}}={\varphi }_{\text{n}}-{\varphi }_{\text{n}-1}.\end{array}$$

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

References

[1] Hatai, I., and I. Chakrabarti. “A New High-Performance Digital FM Modulator and Demodulator for Software-Defined Radio and Its FPGA Implementation.” International Journal of Reconfigurable Computing (December 25, 2011): 1–10. https://doi.org/10.1155/2011/342532.

[2] Taub, H., and D. Schilling. Principles of Communication Systems. McGraw-Hill Series in Electrical Engineering, 142–55. New York: McGraw-Hill, 1971.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2015a