Main Content

FM Modulator Baseband

Modulate using FM method

expand all in page
  • 库:

  • Communications Toolbox / Modulation / Analog Baseband Modulation

  • FM Modulator Baseband block

Description

TheFM Modulator Basebandblock applies frequency modulation to a real input signal and returns a complex output signal.

Ports

Input

expand all

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

Data Types:double|single

Output

expand all

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

expand all

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

Type of simulation to run, specified asCode generationorInterpreted 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 C code is reused for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster thanInterpreted execution.

  • Interpreted execution–– Simulate the model by using the MATLAB®interpreter. This option requires less startup time than theCode generationmethod, but the speed of subsequent simulations is slower. In this mode, you can debug the source code of the block.

Model Examples

FM Modulation and Demodulation

FM Modulation and Demodulation

The example, shows how the FM Modulator Baseband and FM Demodulator Baseband blocks are used to modulate and demodulate a sinusoidal signal.
Open Model

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 ( 2 π f c t + 2 π f Δ ∫ 0 t x ( τ ) d τ ) ,

where:

  • Ais the carrier amplitude.

  • fcis the carrier frequency.

  • x(τ) is the baseband input signal.

  • fΔis the frequency deviation in Hz.

的频率uency deviation is the maximum shift fromfcin one direction, assuming|x(τ)| ≤ 1.

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

y s ( t ) = Y ( t ) e − j 2 π f c t = A 2 [ e j ( 2 π f c t + 2 π f Δ ∫ 0 t x ( τ ) d τ ) + e − j ( 2 π f c t + 2 π f Δ ∫ 0 t x ( τ ) d τ ) ] e − j 2 π f c t = A 2 [ e j 2 π f Δ ∫ 0 t x ( τ ) d τ + e − j 4 π f c t − j 2 π f Δ ∫ 0 t x ( τ ) d τ ] .

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

y ( t ) = A 2 e j 2 π f Δ ∫ 0 t x ( τ ) d τ .

The expression fory(t) can be rewritten as y ( t ) = A 2 e j ϕ ( t ) , where ϕ ( t ) = 2 π f Δ ∫ 0 t x ( τ ) d τ . Expressingy(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 fromy(t), use a baseband delay demodulator, as this figure shows.

Baseband FM demodulator

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

w ( t ) = A 2 4 e j ϕ ( t ) e − j ϕ ( t − T ) = A 2 4 e j [ ϕ ( t ) − ϕ ( t − T ) ] ,

whereTis the sample period. In discrete terms,

w n = w ( n T ) , w n = A 2 4 e j [ ϕ n − ϕ n − 1 ] , and v n = ϕ n − ϕ n − 1 .

The signalvnis the approximate derivative ofϕnsuch thatvn≈xn.

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.通信系统原理. McGraw-Hill Series in Electrical Engineering. New York: McGraw-Hill, 1971, pp. 142–155..

Extended Capabilities

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

版本历史

Introduced in R2015a

See Also

Blocks

Objects