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Motivation

ECE 734 Project Implementation of Multiple Constant Multiplication Algorithms for FIR Filters Hamid Shojaei. Motivation.

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Motivation

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  1. ECE 734 ProjectImplementation of Multiple Constant Multiplication Algorithms for FIR FiltersHamid Shojaei

  2. Motivation • Digital filters are widely used in digital communications and audio/video processing. They play a crucial role in digital communication chips such as Ethernet transceivers, cable modems, DSL modems, satellite receivers, mobile phones, etc. • In particular, finite impulse response (FIR) filters are used for their ease of implementation and stability.

  3. Motivation • An FIR filter implements a convolution in the time-domain • Critical path of N-tap filter: • N-1 adds + 1 multiply • Arithmetic complexity of N-tap filter modeled as: • N multiplications+ N-1 adds • Multipliers are expensive both in area and delay • Full flexibility of general purpose multipliers are not required • Implement multipliers by add/sub-shift operation • Minimize adders  multiple constant multiplication

  4. Multiple Constant Multiplication(MCM) Algorithms • Graph based algorithms • BH algorithm • BHM algorithm • RAG-n algorithm • Common Subexpression Elimination (CSE) algorithms • Hybrid Algorithms

  5. Graph based algorithms • Bull Horrocks (BH) Algorithm 9 17x[n] 17 h1 1 2 4 8 1, 9, 16, 26and51 w1 w0 w2 w3 w4 9 26 17 h1 51 1 2 4 8 43 23 operations  8 operations w1 w0 w2 w3 w4 Using shift 9 26 17 h1 51 1 3 43 23 operations  5 operations Figures adapted from Horrocks et. al 1995

  6. MCM Algorithms • BHM Algorithm • In BH, partial sums are generated with values only up to the coefficient. (7 = 8 - 1 rather than 7 = 1+2+4) • The n-dimensional reduced adder graph (RAG-n) algorithm • Similar to dynamic programming • CSE • Matrix splitting

  7. Initial Results # of operations # of coefficients

  8. Initial Results # of operations # of coefficients

  9. Future Works • Applying algorithms on some real FIR filters • A framework for generating coefficients and applying MCM algorithms • Based on the filter we can decide which algorithm or combination of them can applied.

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