Applications of Distributed Arithmetic to Digital Signal Processing:
A Tutorial Review
Ref: Stanley A. White, "Applications of Distributed Arithmetic to Digital Signal Processing: A Tutorial Review," IEEE ASSP Magazine, July, 1989
Outline:
Distributed Arithmetic (DA) Introduction
Technical overview of DA
Increasing the speed of DA multiplication
Application of DA to a biquadratic digital filter
Conclusions
Distributed Arithmetic (DA, 1974) Introduction
The most-often encountered form of computation in DSP:
Sum of product
Dot-product
Inner-product
Executed most efficiently by DA
By careful design one may reduce gate count in a signal processing arithmetic unit by a number seldom smaller then 50% and often as large as 80%
Technical overview of DA
Advantage of DA: efficiency of mechanization
A frequently argued:
slowness because of its inherent bit-serial nature (not true)
Some modifications to increase the speed by employing techniques:
Plus more arithmetic operations
expense of exponentially increased memory
Technique overview -continued I
The sum of product:
where xk is a 2's-complement binary number scaled such that | xk |
(1)
(2)
(3)
Technique overview -continued II
Critical step
where K=No. of taps (inputs), N: Wordlength of Data
(3)
(4)
Technique overview -continued III
Consider the equation (4)
has only 2K possible values
has only 2K possible values
We can store it in a lookup-table(ROM): size=2*2K
Technique overview -continued IV
Example

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