ECE 734 Project Implementation of Multiple Constant Multiplication Algorithms for FIR Filters Hamid ShojaeiMotivationSlide 3Multiple Constant Multiplication(MCM) AlgorithmsGraph based algorithmsMCM AlgorithmsInitial ResultsSlide 8Future WorksECE 734 ProjectImplementation of Multiple Constant Multiplication Algorithms for FIR FiltersHamid ShojaeiMotivation•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.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 +xz-1+xz-1+xz-1+xz-1xz-1X [n]y [n]h0hL-1hL-2hL-3h1. . .Multiple Constant Multiplication(MCM) Algorithms•Graph based algorithms–BH algorithm–BHM algorithm–RAG-n algorithm•Common Subexpression Elimination (CSE) algorithms•Hybrid AlgorithmsGraph based algorithms•Bull Horrocks (BH) Algorithm1, 9, 16, 26 and 51w0w1w2 w3Using shiftFigures adapted from Horrocks et. al 19951 2 4 891717x[n]h11 2 4 891726h15143w423 operations 8 operationsw0w1w2 w3191726h15143w4323 operations 5 operationsMCM 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 splittingInitial Results# of coefficients# of operationsInitial Results# of coefficients# of operationsFuture 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
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