TAILIEUCHUNG - Lecture VLSI Digital signal processing systems: Chapter 10 - Keshab K. Parhi

Chapter 10 introduce the pipelined and parallel pecursive and adaptive filters. This chapter includes content: Pipelining in 1st-Order IIR Digital Filters, Pipelining in Higher-Order IIR Digital Filters, Parallel Processing for IIR Filters, Combined Pipelining and Parallel Processing for IIR Filters. | Chapter 10: Pipelined and Parallel Recursive and Adaptive Filters Keshab K. Parhi Outline • • • • • Introduction Pipelining in 1st-Order IIR Digital Filters Pipelining in Higher-Order IIR Digital Filters Parallel Processing for IIR Filters Combined Pipelining and Parallel Processing for IIR Filters Chapter 10 2 Look-Ahead Computation First-Order IIR Filter • Consider a 1st-order linear time-invariant recursion (see Fig. 1) () y(n +1) = a ⋅ y(n) + b ⋅ u(n) • The iteration period of this filter is { m +Ta}, where { m,Ta} represent T T word-level multiplication time and addition time • In look-ahead transformation, the linear recursion is first iterated a few times to create additional concurrency. • By recasting this recursion, we can express y(n+2) as a function of y(n) to obtain the following expression (see Fig. 2(a)) () y(n + 2) = a[ay(n) + bu(n)] + bu(n + 1) • The iteration bound of this recursion is 2 (Tm + Ta ) 2 , the same as the original version, because the amount of computation and the number of logical delays inside the recursive loop have both doubled Chapter 10 3 • Another recursion equivalent to () is (). Shown on (b), its iteration bound is (Tm + Ta ) 2 , a factor of 2 lower than before. () y(n + 2) = a2 ⋅ y(n) + ab⋅ u(n) + b ⋅ u(n + 1) • Applying (M-1) steps of look-ahead to the iteration of (), we can obtain an equivalent implementation described by (see Fig. 3) M −1 y ( n + M ) = a M ⋅ y ( n) + ∑ a i ⋅ b ⋅ u ( n + M − 1 − i) () −M i=0 – Note: the loop delay is z instead of z −1 , which means that the loop computation must be completed in M clock cycles (not 1 clock cycle). The iteration bound of this computation is Tm + Ta M , which corresponds to a sample rate M times higher than that of the original filter – The terms ab , a 2 b ,⋅ ⋅ ⋅, a M −1b , a M in () can be pre-computed (referred to as pre-computation terms). The second term in RHS of () is the look-ahead computation term (referred to as

• Điện - Điện tử
• VLSI Digital signal processing systems
• Digital signal
• Digital signal processing
• DSP systems
• Adaptive filters
• Parallel pecursive
• FIR Digital Filters
• Parallel processing
• Loop bound
• DSP programs
• Retiming formulation
• Applications of retiming
• Algorithm for unfolding
• Applications of unfolding
• Retiming for folding
• Systolic architecture design
• Projection vector
• Cook toom algorithm
• Fast convolution
• Algorithmic strength reduction
• Parallel FIR filters
• Round off noise
• State variable description
• Bit level arithmetic architectures
• Parallel multipliers
• Redundant arithmetic
• Redundant number representations
• Numerical strength reduction
• Multiple constant multiplication
• Low power design
• Programmable DSPs
• DSP applications