Distributed Arithmetic to Digital Signal Processing: A Tutorial Review

Stanley A. White, 1989

Fengbo Ren

fren@ee.ucla.edu

Oct. 7th 2011

Literature Review

Distributed Arithmetic (DA) DA is basically a bit-serial computational operation that

forms an inner product of a pair of vectors, where one of the vector is preferred to be constant

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For Example

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Hardware Implementation

One-bit-at-a-time (1BAAT) fashion When K>N, faster than mult.+accum.

– Require 2K words of memory (huge resources)– Take N cycles to get results (Slow)

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Offset Binary Code (OBC)

Reduces 2K words to 2K-1

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Ckn = {-1,1}

OBC Implementation

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Vector Decomposition

Reduces 2K-1 words to P2M words (MxP=K-1)

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Multiple-Bit-at-A-Time

L-bit/clk/virable Reduces computing time from N clk cycles to N/L

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The Best # of Parallelism Relative Cost

When w=1

L-BAAT for best performance/cost

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Application Example Digital Filter

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Other Applications Adaptive Filters

– Coefficients can be time-varying Circular convolution

Sinusoidal transform

– Discrete Hartley transform (DHT)– Discrete Fourier transform (DFT)– Discrete Cosine Transform (DCT)

Matrices computations involves severe inner products comp.11

Conclusion DA is a very efficient means to perform computations

that are dominated by inner products– Coefficients can be time varying – Equations can be non-linear

Whenever the performance/cost ratio is critical, DA should be seriously considered as contender

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