Pipelined Lattice and Wave Digital Recursive Filters

1 Introduction.- 1.1 Background.- 1.2 Iteration Bound and Retiming.- 1.3 Pipelining.- 1.4 Outline.- 2 Pipeline Interleaving in Digital Filters.- 2.1 Inefficient Single/Multi-Channel Interleaving.- 2.2 Efficient Single-Channel Interleaving.- 2.3 Efficient Multi-Channel Interleaving.- 3 Pipelining Direct Form Recursive Digital Filters.- 3.1 Clustered Look-Ahead Pipelining.- 3.2 Stable Clustered Look-Ahead Filter Design.- 3.3 Scattered Look-Ahead Pipelining Without Decomposition.- 3.4 Scattered Look-Ahead Pipelining with Power-of-Two Decomposition.- 3.5 Scattered Look-Ahead Pipelining With General Decomposition.- 3.6 Constrained Filter Design Techniques.- 3.7 Linear Bidirectional Systolic Array Architectures.- 3.8 FIR versus IIR Filters.- 3.9 Pipelining in State Space Filters.- 3.10 Low-Power Direct Form Filters.- 4 Roundoff Noise In Pipelined Recursive Digital Filters.- 4.1 Introduction.- 4.2 Scaling and Roundoff Noise.- 4.3 SVD of IIR Filters.- 4.4 Scaling and Roundoff Noise Computation Using SVD.- 4.5 Roundoff Noise in Pipelined IIR Filters.- 4.6 Roundoff Noise Computation Examples Using SVD.- 5 Schur Algorithm.- 5.1 Introduction.- 5.2 Computation of Schur Polynomials.- 5.3 An Inner Product Formulation.- 5.4 Orthogonality of Schur Polynomials.- 5.5 Orthonormality of Schur Polynomials.- 5.6 (i — j) Orthonormality of Reverse Schur Polynomials.- 5.7 Polynomial Expansion Algorithm.- 5.8 Power Calculation Using Schur Algorithm.- 6 Digital Lattice Filter Structures.- 6.1 Introduction.- 6.2 Derivation of Basic Lattice Filter.- 6.3 Derivation of One-Multiplier Lattice Filter.- 6.4 Derivation of Normalized Lattice Filter.- 6.5 Derivation of Scaled Normalized Lattice Filter.- 6.6 Roundoff Noise Calculation in Lattice Filters.- 7 Pipelining of Lattice IIR Digital Filters.- 7.1Introduction.- 7.2 Pipelining Property of the Schur Algorithm.- 7.3 Pipelining of Lattice IIR Digital Filters.- 7.4 Design Examples of Pipelined Lattice Filters.- 7.5 Pipelining Levels and Output Roundoff Noise.- 7.6 Low-Power CMOS Implementation of Lattice IIR Filters.- 8 Pipelining of Orthogonal Double-Rotation Digital Lattice Filters.- 8.1 Introduction.- 8.2 Synthesis of ODR Digital Lattice Filters.- 8.3 Pipelining of ODR Digital Lattice Filters.- 8.4 Examples of Pipelined ODR Digital Lattice Filters.- 9 Pipelined Lattice WDF Design for Wideband Digital Filters.- 9.1 Introduction.- 9.2 Direct Lattice WDF Synthesis in Digital Domain.- 9.3 Roundoff Noise Characteristics of WDFs.- 9.4 Pipelining by DIFIR Method.- 9.5 MF FIR and Linear Phase IIR Filters.- 9.6 Examples of Pipelined Lattice WDFs.- 10 Synthesis and Pipelining of Ladder WDFs in Digital Domain.- 10.1 Introduction.- 10.2 Classical Doubly-Terminated Lossless Network.- 10.3 WDF Adaptors.- 10.4 Synthesis of Ladder WDFs.- 10.5 Synthesis of Pipelinable Ladder WDFs.- A Appendix A: Derivation of (3.3), (3.5) and (3.23).- A.2 Pipelining with Clustered Look-Ahead.- A.3 Derivation of (3.23).- B Derivation of Case (A) in Section 10.4.- C Derivation of Case (E) in Section 10.4.- C.1 General.- C.2 Computation of 713.- C.3 Computation of 702 and 712.- C.4 Computation of 7n.- References.