FM Demodulator Baseband

Demodulate using FM method

• 

Libraries:
Communications Toolbox / Modulation / Analog Baseband Modulation

Description

The FM Demodulator Baseband block demodulates a complex input signal and returns a real output signal.

Examples

Modulate and Demodulate FM Signals in Simulink

Modulate and demodulate a sinusoidal signal using FM Modulator Baseband and FM Demodulator Baseband blocks.

The fmmoddemod model generates a sine wave of frequency 4 Hz and amplitude 1 V. The FM Modulator Baseband block sets the frequency deviation to 50 Hz.

The Modulated Signal scope shows that the frequency of the modulator output, Mod Sig, varies with the amplitude of the input data.

The Demodulated Signal scope demonstrates that the output of the demodulator, Demod Sig, is perfectly aligned with the input data.

Ports

Input

In — Input data signal

scalar | vector | matrix

Input signal, specified as a real scalar, vector, or matrix.

Data Types: double | single

Output

Out — Output data signal

scalar | vector | matrix

Output signal, returned as a real scalar, vector, or matrix. The data at this port has the same data type and size as the input signal.

Data Types: double | single

Parameters

To edit block parameters interactively, use the Property Inspector. From the Simulink^® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Frequency deviation (Hz) — Frequency deviation of demodulator

75e3 (default) | positive scalar

Frequency deviation of the demodulator, in Hz, specified as a positive scalar. The system bandwidth is equal to twice the sum of the frequency deviation and the message bandwidth.

Simulate using — Type of simulation to run

Code generation (default) | Interpreted execution

Type of simulation to run, specified as Code generation or Interpreted execution.

• Code generation — Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with the Interpreted execution option.

• Interpreted execution — Simulate the model by using the MATLAB^® interpreter. This option shortens startup time, but the speed of subsequent simulations is slower than with the Code generation option. In this mode, you can debug the source code of the block.

For more information, see Interpreted Execution vs. Code Generation (Simulink).

Block Characteristics

Data Types	double | single
Multidimensional Signals	no
Variable-Size Signals	no

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.

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 Simulink® Coder™.

Version History

Introduced in R2015a