# Documentation

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Implement overlap-add method of frequency-domain filtering

## Library

Filtering / Filter Implementations

`dsparch4`

## Description

The Overlap-Add FFT Filter block uses an FFT to implement the overlap-add method, a technique that combines successive frequency-domain filtered sections of an input sequence.

The block accepts vector or matrix inputs, and treats each column of the input as an individual channel. The block unbuffers the input data into row vectors such that the length of the output vector is equal to the number of channels in the input. The data output rate of the block is M times faster than its data input rate, where M is the length of the columns in the input (frame-size).

The block breaks the scalar input sequence `u`, of length `nu`, into length-`L` nonoverlapping data sections,

which it linearly convolves with the filter's FIR coefficients,

`$H\left(z\right)=B\left(z\right)={b}_{1}+{b}_{2}{z}^{-1}+\dots +{b}_{n+1}{z}^{-n}$`

The numerator coefficients for H(z) are specified as a vector by the FIR coefficients parameter. The coefficient vector, `b = [b(1) b(2) ... b(n+1)]`, can be generated by one of the filter design functions in the Signal Processing Toolbox™ product, such as `fir1`. All filter states are internally initialized to zero.

When either the filter coefficients or the inputs to the block are complex, the Output parameter should be set to `Complex`. Otherwise, the default Output setting, `Real`, instructs the block to take only the real part of the solution.

The block's overlap-add operation is equivalent to

```y = ifft(fft(u(i:i+L-1),nfft) .* fft(b,nfft)) ```

where you specify `nfft` in the FFT size parameter as a power-of-two value greater (typically much greater) than `n+1`. Values for FFT size that are not powers of two are rounded upwards to the nearest power-of-two value to obtain `nfft`.

The block overlaps successive output sections by `n` points and sums them.

The first `L` samples of each summation are output in sequence. The block chooses the parameter `L` based on the filter order and the FFT size.

```L = nfft - n ```

### Latency

In single-tasking operation, the Overlap-Add FFT Filter block has a latency of `nfft-n+1` samples. The first `nfft-n+1` consecutive outputs from the block are zero; the first filtered input value appears at the output as sample `nfft-n+2`.

In multitasking operation, the Overlap-Add FFT Filter block has a latency of `2*(nfft-n)+1` samples. The first `2*(nfft-n)+1` consecutive outputs from the block are zero; the first filtered input value appears at the output as sample `2*(nfft-n)+3`.

## Parameters

FFT size

The size of the FFT, which should be a power-of-two value greater than the length of the specified FIR filter.

FIR coefficients

The filter numerator coefficients.

Output

The complexity of the output; `Real` or `Complex`. When the input signal or the filter coefficients are complex, this should be set to `Complex`.

Treat Mx1 and unoriented sample-based signals as

Specify how the block treats sample-based M-by-1 column vectors and unoriented sample-based vectors of length M. You can select one of the following options:

• `One channel` — When you select this option, the block treats M-by-1 and unoriented sample-based inputs as a column vector (one channel).

• ```M channels (this choice will be removed – see release notes)``` — When you select this option, the block treats M-by-1 and unoriented sample-based inputs as a 1-by-M row vector.

 Note:   This parameter will be removed in a future release. At that time, the block will always treat M-by-1 and unoriented vectors as a single channel.

## References

Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1989.

Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.

## Supported Data Types

• Double-precision floating point

• Single-precision floating point