Implement overlap-save method of frequency-domain filtering

Filtering / Filter Implementations

`dsparch4`

The Overlap-Save FFT Filter block has been replaced with the Frequency-Domain FIR Filter block. Existing instances of the Overlap-Save FFT Filter block continue to run.

The Overlap-Save FFT Filter block uses an FFT to implement the *overlap-save 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).

Overlapping sections of input `u`

are circularly convolved
with the FIR filter coefficients

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

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 circular convolution of each section is computed by multiplying the FFTs of the input section and filter coefficients, and computing the inverse FFT of the product.

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 first `n`

points of the circular convolution are invalid
and are discarded. The Overlap-Save FFT Filter block outputs the remaining
`nfft-n`

points, which are equivalent to the linear
convolution.

In *single-tasking * operation, the Overlap-Save
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-Save 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`

.

For more information on latency and the Simulink^{®} environment tasking modes, see Excess Algorithmic Delay (Tasking Latency)
and Time-Based Scheduling and Code Generation (Simulink Coder).

**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`

.

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.

Double-precision floating point

Single-precision floating point

Overlap-Add FFT Filter | DSP System Toolbox |