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Frequency-Domain Finite Impulse
Response Filter Bank

The finite impulse response (FIR) filter is one of the basic operations in signal processing. This kernel implements a set of M FIR filters. Each FIR filter m, m ∈ {0, 1, ..., M-1 }, has a set of impulse response coefficients wm[k], k ∈ { 0 ... K-1 }. If the length of the input vector is N, the output of filter m, ym, is the convolution of wm with the input xm:
figure
The frequency-domain FIR filter is implemented using fast convolution with the fast Fourier transform (FFT). We define two data sets in Table 1, one for a short filter and one for a long filter. The frequency-domain implementation of the FIR filter has an operation count of (M(10Nlog2N+8N))
Table 1: FIR filter bank input parameters.
Parameter
Name
Description Values
Set 1 Set 2
M Number of filters 64 20
N Length of input and output vectors 4096 1024
K Number of filter coefficients 128 12
W Workload (Mflop) 34 2.21
The operation counts shown in Table 1 assume complex input and output data. In addition, the frequency-domain operation count assumes that an FFT and inverse FFT are implemented using a radix-2 algorithm. Many other implementations of the FFT are possible: see Van Loan for a discussion of algorithms for performing the FFT [1]. Because such a wide variety of FFT implementations exist, and the particular algorithm implemented in a given library may not be known or may change with data size, it is common to use the radix-2 operation count to calculate throughput even when a different algorithm may be in use.

References

1. Charles F. Van Loan. Computational Frameworks for the Fast Fourier Transform. Society for Industrial and Applied Mathematics, 1992.