# Documentation

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# dsp.ChannelSynthesizer System object

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.

Each narrowband signal is stored as a column in the input signal, `x`. The number of columns in `x` corresponds to the number of frequency bands of the filter bank. If `x` is three-dimensional, each matrix corresponds to a separate channel. If M is the number of frequency bands, and `x` is an L-by-M matrix, then the output signal, `y`, has dimensions L×M-by-1. If `x` has more than one channel, that is, it has dimensions L-by-M-by-N, then `y` has dimensions L×M-by-N. The input `x` can be complex and supports single and double data types.

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. This object supports C and C++ code generation.

To merge multiple narrowband signals into a broadband signal:

1. Create a `dsp.ChannelSynthesizer` object and set the properties of the object.

2. Call `step` to synthesize the signal.

### Note

Alternatively, 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

`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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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.

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

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.

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

Coefficients of the prototype lowpass filter, specified as a row vector. 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.

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

This property is tunable. You can change its value even after the object is locked.

## Methods

 coeffs Coefficients of prototype lowpass filter polyphase Polyphase matrix reset Reset internal states of System object step Merge narrowband signals into a broadband signal tf Transfer function
Common to All System Objects
`clone`

Create System object with same property values

`getNumInputs`

Expected number of inputs to a System object

`getNumOutputs`

Expected number of outputs of a System object

`isLocked`

Check locked states of a System object (logical)

`release`

Allow System object property value changes

## 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.