Documentation

## Description

The `comm.FMBroadcastDemodulator` System object™ demodulates a complex baseband FM signal and filters the signal with a de-emphasis filter to produce an audio signal. If the `Stereo` property is set to `true`, the object performs stereo decoding. If the `RBDS` property is set to `true`, the object also demodulates the RDS/RBDS waveform. For more details, see Algorithms.

To demodulate a complex baseband FM signal:

1. Define and set up the `comm.FMBroadcastDemodulator` object. See Construction.

2. Call `step` to demodulate the complex baseband FM signal according to the properties of `comm.FMBroadcastDemodulator`.

### 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

`fmbDemod = comm.FMBroadcastDemodulator` creates a demodulator System object, `fmbDemod`, that frequency demodulates an input signal.

`fmbDemod = comm.FMBroadcastDemodulator(Name,Value)` creates an FM demodulator object, `fmbDemod`, with each specified property `Name` set to the specified `Value`. You can specify additional name-value pair arguments in any order as (`Name1`,`Value1`,...,`NameN`,`ValueN`).

`fmbDemod = comm.FMBroadcastDemodulator(MOD)` creates an FM demodulator object, `fmbDemod`, whose properties are determined by the corresponding FM modulator object, `MOD`.

## Properties

 `SampleRate` Input signal sample rate (Hz) Specify the sample rate of the input signal in Hz as a positive real scalar. The default value is `240e3`. This property is nontunable. `FrequencyDeviation` Peak deviation of the output signal frequency (Hz) Specify the frequency deviation of the FM demodulator in Hz as a positive real scalar. The default value is `75e3`. System bandwidth is equal to twice 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. This property is nontunable. `FilterTimeConstant` Time constant of the de-emphasis filter (s) Specify the de-emphasis lowpass filter time constant as a positive real scalar. The default value is `7.5e-05`. FM broadcast standards specify a value of 75 μs in the United States and 50 μs in Europe. This property is nontunable. `AudioSampleRate` Audio sample rate of the output signal (Hz) Specify the output audio sample rate as a positive real scalar. The default value is `48000`. This property is nontunable. `PlaySound` Flag to enable or disable audio playback To playback the output signal on the default audio device, set this property to `true`. The default is `false`. This property is nontunable. `BufferSize` Buffer size of the audio device Specify the size of the buffer (in samples) that the object uses to communicate with an audio device as a positive scalar integer. The default is `4096`. This property is available only when `PlaySound` is `true`. This property is nontunable. `Stereo` Flag to enable or disable stereo audio Set this property to `true` to demodulate a stereophonic audio signal. Set to `false` if the input signal is monophonic. The default is `false`. This property is nontunable. `RBDS` Flag to demodulate RDS/RBDS waveform If `RBDS` is set to `true`, the second output of the `step` method is the baseband RDS/RBDS waveform. The default value is `false`. This property is nontunable. `RBDSSamplesPerSymbol` Oversampling factor of RDS/RBDS output Specify the number of samples of the RDS/RBDS output as a positive integer. The RDS/RBDS sample rate is given by `RBDSSamplesPerSymbol` × `1187.5` Hz. According to the RDS/RBDS standard, the sample rate of each bit is 1187.5 Hz. This property applies only when you set `RBDS` to `true`. The default is 10. `RBDSCostasLoop` Option to recover phase of RDS/RBDS signal Specify whether a Costas loop is used to recover the phase of the RDS/RBDS signal. Set this option to `true` for radio stations that do not lock the `57` kHz RDS/RBDS signal in phase with the third harmonic of the `19` kHz pilot tone. This property applies only when you set `RBDS` to `true`. The default value is `false`.

## Methods

Common to All System Objects
`release`

Allow System object property value changes

## Examples

expand all

Modulate and demodulate a streaming audio signal with the FM broadcast modulator and demodulator objects. Play the audio signal using a default audio device.

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent `step` syntax. For example, myObject(x) becomes step(myObject,x).

Create an audio file reader System object™ and read the file `guitartune.wav`.

`audio = dsp.AudioFileReader('guitartune.wav','SamplesPerFrame',4410);`

Create FM broadcast modulator and demodulator objects. Set the `AudioSampleRate` property to match the sample rate of the input signal. Set the `SampleRate` property of the demodulator to match the specified sample rate of the modulator. Set the `PlaySound` property of the demodulator to `true` to enable audio playback.

```fmbMod = comm.FMBroadcastModulator('AudioSampleRate',audio.SampleRate, ... 'SampleRate',240e3); fmbDemod = comm.FMBroadcastDemodulator( ... 'AudioSampleRate',audio.SampleRate, ... 'SampleRate',240e3,'PlaySound',true);```

Read the audio data in frames of length 4410, apply FM broadcast modulation, demodulate the FM signal and playback the audio input.

```while ~isDone(audio) audioData = audio(); modData = fmbMod(audioData); demodData = fmbDemod(modData); end```

Generate a basic RBDS waveform, FM modulate it with an audio signal, and then demodulate it.

Note: This example runs only in R2017a or later.

Create a RBDS waveform with 19 groups per frame and 10 samples per symbol. The sample rate of the RBDS waveform is given by 1187.5 x 10. Set the audio sample rate to 1187.5 x 40.

```groupLen = 104; sps = 10; groupsPerFrame = 19; rbdsFrameLen = groupLen*sps*groupsPerFrame; afrRate = 40*1187.5; rbdsRate = 1187.5*sps; outRate = 4*57000; afr = dsp.AudioFileReader('rbds_capture_47500.wav','SamplesPerFrame',rbdsFrameLen*afrRate/rbdsRate); rbds = comm.RBDSWaveformGenerator('GroupsPerFrame',groupsPerFrame,'SamplesPerSymbol',sps); fmMod = comm.FMBroadcastModulator('AudioSampleRate',afr.SampleRate,'SampleRate',outRate,... 'Stereo',true,'RBDS',true,'RBDSSamplesPerSymbol',sps); fmDemod = comm.FMBroadcastDemodulator('SampleRate',outRate,... 'Stereo',true,'RBDS',true,'PlaySound',true); scope = dsp.TimeScope('SampleRate',outRate,'YLimits',10^-2*[-1 1]); ```

Get the current audio input. Generate RBDS information at the same configured rate as audio. FM modulate the stereo audio with RBDS information. Add additive white Gaussian noise. FM demodulate the audio and RBDS waveforms. View the waveforms in a time scope.

```for idx = 1:7 input = afr(); rbdsWave = rbds(); yFM = fmMod([input input], rbdsWave); rcv = awgn(yFM, 40); [audioRcv, rbdsRcv] = fmDemod(rcv); scope(rbdsRcv); end ```
```Warning: File: /mathworks/devel/bat/Bdoc19b/build/matlab/toolbox/dsp/dsp/+dsp/FilterCascade.m Line: 562 Column: 92 Unrecognized pragma "%#okgrow". Warning: File: /mathworks/devel/bat/Bdoc19b/build/matlab/toolbox/dsp/dsp/+dsp/FilterCascade.m Line: 949 Column: 124 Unrecognized pragma "%#okgrow". ```

## Algorithms

The FM Broadcast demodulator includes the functionality of the baseband FM demodulator, de-emphasis filtering, and the ability to receive stereophonic signals. The algorithms which govern basic FM modulation and demodulation are covered in `comm.FMDemodulator`.

### Filtering

FM amplifies high-frequency noise and degrades the overall signal-to-noise ratio. To compensate, FM broadcasters insert a pre-emphasis filter prior to 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.

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

`${H}_{p}\left(f\right)=1+j2\pi f{\tau }_{s}\text{\hspace{0.17em}},$`

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

`${H}_{d}\left(f\right)=\frac{1}{1+j2\pi f{\tau }_{s}}\text{\hspace{0.17em}}.$`

For an audio sample rate of 44.1 kHz, the de-emphasis filter has the following response.

### Stereo and RDS/RBDS FM — Multiplex Signal

The FM broadcast demodulator supports stereophonic and monophonic operations. To support stereo transmission, the left (L) and right (R) channel information (L+R) is assigned to the mono portion of the spectrum (0 to 15 kHz). The (L-R) 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/RBDS signals.

Here is the spectrum of the multiplex baseband signal, m(t).

m(t) is given by

`$m\left(t\right)={C}_{0}\left[L\left(t\right)+R\left(t\right)\right]+{C}_{1}\mathrm{cos}\left(2\pi ×19kHz×t\right)+{C}_{0}\left[L\left(t\right)-R\left(t\right)\right]\mathrm{cos}\left(2\pi ×38kHz×t\right)+{C}_{2}RBDS\left(t\right)\mathrm{cos}\left(2\pi ×57kHz×t\right)\text{\hspace{0.17em}},$`

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/RBDS subcarrier, respectively.

The demodulator applies m(t) to three bandpass filters with center frequencies at 19, 38, and 57 kHz, and to a lowpass filter with a 3-dB cutoff frequency of 15 kHz. The 19 kHz bandpass filter extracts the pilot tone from the modulated signal. The recovered pilot tone is doubled and tripled in frequency to produce the 38 kHz and 57 kHz signals, which demodulate the (LR) and RDS/RBDS signals, respectively. To generate a scaled version of the left and right channels that produce the stereo sound, the (L + R) and (LR) signals are added and subtracted. The RDS/RBDS signal is recovered by mixing with the 57 kHz signal.

Here is the block diagram of the FM broadcast demodulator.

## Limitations

The input length must be an integer multiple of the `AudioDecimationFactor` property. If `RBDS` is set to `true`, the input length in addition must be an integer multiple of `RBDSDecimationFactor`. For more information on these two properties, see the `info` method.

## References

[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.

[3] Der, Lawrence. “Frequency Modulation (FM) Tutorial”. FM Tutorial. Silicon Laboratories Inc., pp. 4–8.
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