Pipelining, Retiming, Look-ahead Transformation and Polyphase Decomposition - Digital Design of Signal Processing Systems: A Practical Approach - page 301

7
Pipelining, Retiming, Look-ahead
Transformation and Polyphase
Decomposition
7.1 Introduction
The chapter discusses pipelining, retiming and look-ahead techniques for transforming digital
designs to meet the desired objectives. Broadly, signal processing systems can be classified as
feedforward or feedback systems. In feedforward systems the data flows from input to output and
no value in the system is fed back in a recursive loop. Finite impulse response (FIR) filters are
feedforward systems and are fundamental to signal processing. Most of the signal processing
algorithms such as fast Fourier transform (FFT) and discrete cosine transform (DCT) are
feedforward. The timing can be improved by simply adding multiple stages of pipelining in the
hardware design.
Recursive systems such as infinite impulse response (IIR) filters are also widely used in DSP.
The feedback recursive algorithms are used for timing, symbol and frequency recovery in digital
communication receivers. In speech processing and signal modeling, autoregressive moving
average (ARMA) and autoregressive (AR) processes involve IIR systems. These systems are
characterized by a difference equation. To compute an output sample, the equation directly or
indirectly involves previous values of the output samples along with the current and previous values
of input samples. As the previous output samples are required in the computation, adding pipeline
registers to improve timing is not directly available to the designer. The chapter discusses cut-set
retiming and node transfer theorem techniques for systematically adding pipelining registers in
feedforward systems. These techniques are explained with examples. This chapter also discusses
techniques that help in meeting timings in implementing fully dedicated architectures (FDAs) for
feedback systems.
The chapter also defines some of the terms relating to digital design of feedback systems. Iteration,
the iteration period, loop, loop bound and iteration period bound are explainedwith examples. While
designing a feedback system, the designer applies mathematical transformations to bring the critical
path of the design equal to the iteration period bound (IPB), which is defined as the loop bound of the