Overlap-Add FFT Filter (DSP Blockset)

Implement the overlap-add method of frequency-domain filtering.

Library

Filter Realizations, in Filtering

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 breaks the input sequence u, of length nu, into length-L nonoverlapping data sections,

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

The numerator coefficients of the transfer function above are specified as a vector by the FIR coefficients parameter:

B = [b(1) b(2) ... b(n+1)]

The block's overlap-add operation is equivalent to

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

where N_fft is specified by the FFT size parameter. The block overlaps successive output sections by nb-1 points, where nb is the length of the filter (length(B)), and sums them:

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

L = nfft-nb+1

Note that N_fft must be greater (and is typically much greater) than length(B).

Dialog Box

FFT size: The size of the FFT, which must be greater than the length of the specified FIR filter.
FIR coefficients: The filter numerator coefficients.

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.