Pipelined Lattice and Wave Digital Recursive Filters

Pipelined Lattice and Wave Digital Recursive Filters uses look-ahead transformation and constrained filter design approaches. It is also shown that pipelining often reduces the roundoff noise in a digital filter. The pipelined recursive lattice and wave digital filters presented are well suited where increasing speed and reducing area or power or roundoff noise are important. Examples are wireless and cellular codec applications, where low power consumption is important, and radar and video applications, where higher speed is important.
The book presents pipelining of direct-form recursive digital filters and demonstrates the usefulness of these topologies in high-speed and low-power applications. It then discusses fundamentals of scaling in the design of lattice and wave digital filters. Approaches to designing four different types of lattice digital filters are discussed, including basic, one-multiplier, normalized, and scaled normalized structures. The roundoff noise in these lattice filters is also studied. The book then presents approaches to the design of pipelined lattice digital filters for the same four types of structures, followed by pipelining of orthogonal double-rotation digital filters, which eliminate limit cycle problems. A discussion of pipelining of lattice wave digital filters follows, showing how linear phase, narrow-band, sharp-transition recursive filters can be implemented using this structure. This example is motivated by a difficult filter design problem in a wireless codec application. Finally, pipelining of ladder wave digital filters is discussed.
Pipelined Lattice and Wave Digital Recursive Filters serves as an excellent reference and may be used as a text for advanced courses on the subject.

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.