FM Broadcast Modulator Baseband

Modulate using broadcast FM method

• 

Libraries:
Communications Toolbox / Modulation / Analog Baseband Modulation

Description

The FM Broadcast Modulator Baseband block creates the FM channel structure for broadcast of an FM signal. For more details, see Algorithms.

This icon shows the block with all ports enabled.

Examples

Modulate and Demodulate Audio Signal

Load an audio input file, and then modulate and demodulate the audio signal by using the FM Broadcast Modulator Baseband and FM Broadcast Demodulator Baseband blocks. Compare the input signal spectrum with the demodulated signal spectrum.

The doc_fmbroadcast model loads the guitar.wav signal, modulates the signal for FM broadcast, demodulates the FM broadcast signal, and then compares the recovered signal to the original audio signal in a spectrum analyzer.

Limitations

• If you select RDS/RBDS modulation, both the audio and RBDS inputs must satisfy this equation:

  $$\frac{audioLength}{audioSampleRate}=\frac{RBDSLength}{RBDSSampleRate}$$

• The input length of the audio signal must be an integer multiple of the audio decimation factor.

• The input length of the RBDS signal must be an integer multiple of the RBDS decimation factor.

Ports

Input

In1 — Audio signal

N-element column vector | 2-by-N matrix

Audio signal, specified as one of these options.

• N-element column vector for mono signals — If you do not select Stereo audio, you must specify the audio signal as a column vector. N is the number of samples in the audio signal.

• 2-by-N matrix for stereo signals — If you select Stereo audio, the audio signal must have two channels and the block performs stereo encoding after pre-emphasis filtering. N is the number of samples in the audio signal per channel.

For information about signal length restrictions, see Limitations.

Data Types: double | single
Complex Number Support: Yes

In2 — RDS (or RBDS) signal

N-element column vector | 2-by-N matrix

RDS (or RBDS) signal, specified as one of these options.

• N-element column vector for mono signals — If you do not select Stereo audio, you must specify the audio signal as a column vector. N is the number of samples in the audio signal.

• 2-by-N matrix for stereo signals — If you select Stereo audio, the audio signal must have two channels and the block performs stereo encoding after pre-emphasis filtering. N is the number of samples in the audio signal per channel.

For information about signal length restrictions, see Limitations.

Data Types: double | single
Complex Number Support: Yes

Output

Out — FM-modulated baseband signal

column vector

FM-modulated baseband signal, returned as a column vector of complex values of the same data type as the input signal. The length of this output is length(Input 1 × Sample rate (Hz) / Sample rate of audio input signal (Hz)).

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.

Sample rate (Hz) — Output signal sample rate

240e3 | positive scalar

Output signal sample rate in Hz, specified as a positive scalar. The sample rate must be greater than twice the frequency deviation. Specifically, Sample rate > 2×Frequency Deviation.

Frequency deviation (Hz) — Peak deviation of modulator output signal frequency

75e3 | positive scalar

Peak deviation of the modulator output signal frequency in Hz, specified as a positive scalar. The frequency deviation must be less than half the sample rate.

The system bandwidth equals two times the sum of the frequency deviation and the message bandwidth. FM broadcast standards specify a value of 75 kHz in the United States and 50 kHz in Europe.

Pre-emphasis filter time constant (s) — Pre-emphasis highpass filter time constant

7.5e-05 (default) | positive scalar

Pre-emphasis highpass filter time constant in seconds, specified as a positive scalar. FM broadcast standards specify a value of 75 μs in the United States and 50 μs in Europe.

Sample rate of audio input signal (Hz) — Sample rate of input audio signal

48000 (default) | positive scalar

Sample rate of the input audio signal in Hz, specified as a positive scalar.

Stereo audio — Option to enable stereo modulation

off (default) | on

Select this check box if the input signal is a stereophonic audio signal. If you do not select, the audio signal is assumed to be monophonic. If you select the Stereo audio check box, the block modulates the stereo audio (L–R) at the 38 kHz band, in addition to the baseband (L+R). For more information, see Multiplexed Stereo and RDS (or RBDS) FM Signal.

RDS/RBDS modulation — Option to enable RDS (or RBDS) waveform modulation

off (default) | on

Select this check box to modulate a baseband RBDS signal at 57 kHz. For more information, see Multiplexed Stereo and RDS (or RBDS) FM Signal.

Oversampling factor of RDS/RBDS input — Oversampling factor of RDS (or RBDS) input signal

10 (default) | positive integer

Oversampling factor of the RDS (or RBDS) input signal, specified as a positive integer. The sample rate of RDS (or RBDS) broadcast data is 1187.5 Hz. The RDS (or RBDS) signal sample rate is (Oversampling factor of RDS/RBDS input × 1187.5) Hz.

Dependencies

To enable this parameter, select RDS/RBDS modulation.

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

The FM Broadcast Modulator Baseband block includes the functionality of the FM Modulator Baseband block, plus de-emphasis filtering and the ability to receive stereophonic signals.

Filtering

FM amplifies high-frequency noise and degrades the overall signal-to-noise ratio. To compensate, FM broadcasters insert a pre-emphasis filter before FM modulation to amplify the high-frequency content. The FM receiver has a reciprocal de-emphasis filter after the FM demodulator to attenuate high-frequency noise and restore a flat signal spectrum. This figure shows the order of processing operations.

The pre-emphasis filter has a highpass characteristic transfer function given by

$$H_{\text{p}}(f)=1+j2\pi f{\tau }_{\text{s}},$$

where τ_s is the filter time constant. The time constant is 75 μs in the United States and 50 μs in Europe. Similarly, the transfer function for the lowpass de-emphasis filter is given by

$$H_{\text{d}}(f)=\frac{1}{1+j2\pi f{\tau }_{\text{s}}}.$$

For an audio sample rate of 44.1 kHz, the de-emphasis filter has the response shown in this figure.

Multiplexed Stereo and RDS (or RBDS) FM Signal

FM broadcast supports stereophonic and monophonic operations. To support stereo transmission:

• The Left + Right channel information is assigned to the mono portion of the spectrum (0 to 15 kHz).

• The Left – Right channel information is amplitude modulated onto the 23 to 53 kHz region of the baseband spectrum using a 38 kHz subcarrier signal.

A pilot tone at 19 kHz in the multiplexed signal enables the FM receiver to coherently demodulate the stereo and RDS (or RBDS) signals.

This figure shows the spectrum of the multiplex baseband signal.

The multiplex message signal m(t) is given by

$$m(t)=C_0\left[L(t)+R(t)\right]+C_1\cos (2\pi \times 19kHz\times t)+C_0\left[L(t)-R(t)\right]\cos (2\pi \times 38kHz\times t)+C_{2}RBDS(t)\cos (2\pi \times 57kHz\times t),$$

where C₀, C₁, and C₂ are gains. To generate the appropriate modulation level, these gains scale the amplitudes of the L(t)±R(t) signals, the 19 kHz pilot tone, and the RDS (or RBDS) subcarrier, respectively.

This figure shows the multiplexing (MPX) encoder block diagram of the FM broadcast modulator, which generates the multiplex baseband signal. L(t) and R(t) are the left and right audio signal components of the time-domain waveforms. RBDS(t) is the time-domain waveform of the RDS (or RBDS) signal.

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.

[3] Der, Lawrence. "Frequency Modulation (FM) Tutorial." Silicon Laboratories Inc.: 4–8.

Extended Capabilities

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

Version History

Introduced in R2015a