Signal Processing Blockset™

Overlap-Add FFT Filter - Implement overlap-add method of frequency-domain filtering

Library

Filtering / Filter Designs

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.

Valid inputs to this block are 1-D vectors, sample-based vectors, frame-based vectors, and frame-based full matrices. All outputs are unbuffered into sample-based row vectors. The length of the output vector is equal to the number of channels in the input vector. An M-by-1 sample-based input has M channels, so it would result in a length-M sample-based output vector. An M-by-1 frame-based input has only one channel, so would result in a 1-by-1 (scalar) output.

The block's data output rate is M times faster than its data input rate, where M is the input frame-size. Thus, the block's data input and output rates are the same when the inputs are 1-D vectors, sample-based vectors, or frame-based row vectors. For frame-based column and frame-based full-matrix inputs, the block's data output rate is M times greater than the block's data input rate.

1-D vectors are treated as length-N sample-based vectors, and result in sample-based length-N row vectors.

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,

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.

Note For more information on latency and the Simulink^® software tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Models with Multiple Sample Rates in the Real-Time Workshop^® User's Guide.

Dialog Box

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.

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