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# dsp.ChannelSynthesizer

Polyphase FFT synthesis filter bank

## Description

The `dsp.ChannelSynthesizer` System object™ merges multiple narrowband signals into a broadband signal by using an FFT based synthesis filter bank. The filter bank uses a prototype lowpass filter and is implemented using a polyphase structure. You can specify the filter coefficients directly or through design parameters.

To merge multiple narrowband signals into a broadband signal:

1. Create the `dsp.ChannelSynthesizer` 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

``synthesizer = dsp.ChannelSynthesizer``
``synthesizer = dsp.ChannelSynthesizer(Name,Value)``

### Description

example

````synthesizer = dsp.ChannelSynthesizer` creates a synthesizer object, using the default properties.`synthesizer = dsp.ChannelSynthesizer(Name,Value)` specifies additional properties using `Name,Value` pairs. Unspecified properties have default values.Example: ```synthesizer = dsp.ChannelSynthesizer('NumTapsPerBand',20,'StopbandAttenuation',140)``````

## Properties

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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.

Filter design parameters or filter coefficients, specified as one of these options:

• `'Number of taps per band and stopband attenuation'` — Specify the filter design parameters through the `NumTapsPerBand` and `StopbandAttenuation` properties.

• `'Coefficients'` — Specify the filter coefficients directly using `LowpassCoefficients`.

Number of filter coefficients each polyphase branch uses, specified as a positive integer. The number of polyphase branches matches the number of frequency bands. The total number of filter coefficients for the prototype lowpass filter is given by product of the number of frequency bands and `NumTapsPerBand`. For a given stopband attenuation, increasing the number of taps per band narrows the transition width of the filter. As a result, there is more usable bandwidth for each frequency band at the expense of increased computation.

#### Dependencies

This property applies when you set `Specification` to `'Number of taps per band and stopband attenuation'`.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

Stopband attenuation of the lowpass filter, specified as a positive real scalar in dB. This value controls the maximum amount of aliasing from one frequency band to the next. Larger is the stopband attenuation, smaller is the passband ripple.

#### Dependencies

This property applies when you set `Specification` to `'Number of taps per band and stopband attenuation'`.

Data Types: `single` | `double`

Coefficients of the prototype lowpass filter, specified as a row vector. The default vector of coefficients is obtained using `rcosdesign(0.25,6,8,'sqrt')`. There must be at least one coefficient per frequency band. If the length of the lowpass filter is less than the number of frequency bands, the object zero-pads the coefficients.

If you specify complex coefficients, the object designs a prototype filter that is centered at a nonzero frequency, also known as a bandpass filter. The modulated versions of the prototype bandpass filter appear with respect to the prototype filter and are wrapped around the frequency range [−Fs Fs].

Tunable: Yes

#### Dependencies

This property applies when you set `Specification` to `'Coefficients'`.

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

## Usage

### Syntax

``synthOut = synthesizer(input)``

### Description

example

````synthOut = synthesizer(input)` merges the narrowband input signals contained as columns in `input` into broadband signal, `synthOut`.```

### Input Arguments

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Narrowband signals, specified as a matrix or a 3-D array. Each narrowband signal is stored as a column in the input signal. The number of columns in `input` corresponds to the number of frequency bands of the filter bank. If `input` is three-dimensional, each matrix corresponds to a separate channel. If M is the number of frequency bands, and `input` is an L-by-M matrix, then the output signal, `synthOut`, has dimensions L×M-by-1. If `input` has more than one channel, that is, it has dimensions L-by-M-by-N, then `synthOut` has dimensions L×M-by-N.

This object also accepts variable-size inputs. That is, once the object is locked, you can change the size of each input channel. The number of channels cannot change.

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

### Output Arguments

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Merged broadband signal, returned as a matrix or a 3-D array. If M is the number of frequency bands, and `input` is an L-by-M matrix, then the output signal, `synthOut`, has dimensions L×M-by-1. If `input` has more than one channel, that is, it has dimensions L-by-M-by-N, then `synthOut` has dimensions L×M-by-N.

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

## 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)`

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 `coeffs` Coefficients of prototype lowpass filter `tf` Return transfer function of overall prototype lowpass filter `polyphase` Return polyphase matrix
 `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

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The quadrature mirror filter bank (QMF) contains an analysis filter bank section and a synthesis filter bank section. `dsp.Channelizer` implements the analysis filter bank. `dsp.ChannelSynthesizer` implements the synthesis filter bank using the efficient polyphase implementation based on a prototype lowpass filter.

Initialization

Initialize the `dsp.Channelizer` and `dsp.ChannelSynthesizer` System objects. Each object is set up with 8 frequency bands, 8 polyphase branches in each filter, 12 coefficients per polyphase branch, and a stopband attenuation of 140 dB. Use a sine wave with multiple frequencies as the input signal. View the input spectrum and the output spectrum using a spectrum analyzer.

```offsets = [-40,-30,-20,10,15,25,35,-15]; sinewave = dsp.SineWave('ComplexOutput',true,'Frequency',... offsets+(-375:125:500),'SamplesPerFrame',800); channelizer = dsp.Channelizer('StopbandAttenuation',140); synthesizer = dsp.ChannelSynthesizer('StopbandAttenuation',140); spectrumAnalyzer = dsp.SpectrumAnalyzer('ShowLegend',true,'NumInputPorts',... 2,'ChannelNames',{'Input','Output'},'Title','Input and Output of QMF'); ```

Streaming

Use the channelizer to split the broadband input signal into multiple narrow bands. Then pass the multiple narrowband signals into the synthesizer, which merges these signals to form the broadband signal. Compare the spectra of the input and output signals. The input and output spectra match very closely.

```for i = 1:5000 x = sum(sinewave(),2); y = channelizer(x); v = synthesizer(y); spectrumAnalyzer(x,v) end ```

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## References

[1] Harris, Fredric J, Multirate Signal Processing for Communication Systems, Prentice Hall PTR, 2004.

[2] Harris, F.J., Chris Dick, Michael Rice. "Digital Receivers and Transmitters Using Polyphase Filter Banks for Wireless Communications." IEEE Transactions on microwave theory and techniques. Vol. 51, Number 4, April 2003.

## Extended Capabilities

Introduced in R2016b

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