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Distributed Arithmetic to Digital Signal Processing: A Tutorial Review Stanley A. White, 1989

Literature Review. Distributed Arithmetic to Digital Signal Processing: A Tutorial Review Stanley A. White, 1989. Fengbo Ren fren@ee.ucla.edu. Oct. 7 th 2011. Distributed Arithmetic (DA).

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Distributed Arithmetic to Digital Signal Processing: A Tutorial Review Stanley A. White, 1989

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  1. Literature Review Distributed Arithmetic to Digital Signal Processing: A Tutorial Review Stanley A. White, 1989 Fengbo Ren fren@ee.ucla.edu Oct. 7th 2011

  2. 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

  3. For Example

  4. 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)

  5. Offset Binary Code (OBC) • Reduces 2K words to 2K-1 Ckn = {-1,1}

  6. OBC Implementation

  7. Vector Decomposition • Reduces 2K-1 words to P2M words (MxP=K-1)

  8. Multiple-Bit-at-A-Time • L-bit/clk/virable • Reduces computing time from N clk cycles to N/L

  9. The Best # of Parallelism • Relative Cost • When w=1 • L-BAATfor best performance/cost

  10. Application Example • Digital Filter

  11. 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.

  12. 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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