Chapter 12
This chapter considers the hardware mapping of an algorithm to demonstrate application of the techniques outlined in this book. Requirement specifications include requisite sampling rate and circuit clock.Afolding order is established from the sampling rate and circuit clock. To demonstrate different solutions for HW mapping, these requirements are varied and a set of architectures is designed for these different requirements.
The chapter explores architectures for the digital design of a direct digital frequency synthesizer (DDFS). This generates sine and cosine waveforms. The DDFS is based on a CoORDinate Digital Computer (CORDIC) algorithm. The algorithm, through successive rotations of a unit vector, computes sine and cosine of an input angle . Each rotation is implemented by a CORDIC element (CE). An accumulator in the DDFS keeps computing the next angle for the CORDIC to compute the sine and cosine values. An offset to the accumulator in relation with the circuit clock controls the frequency of the waveforms produced.
After describing the algorithm and its implementation in MATLAB, the chapter covers design techniques that can be applied to implement a DDFS in hardware. The selection is based on the system requirements. First, a fully dedicated architecture (FDA) is given that puts all the CEs in cascade. Pipelining is employed to get better performance. This architecture computes new sine and cosine values in each cycle. If more circuit clock cycles are available for this computation then a timeshared architecture is more attractive, so the chapter considers timeshared or folding architectures. The folding factor defines the number of CEs in the design. The folded architecture is also pipelined to give better timings.
Several novel architectures have been proposed in the literature. The chapter gives some alternate architecture designs for the CORDIC. A distributed ROMbased CORDIC uses readonly memory for initial iterations. Similarly, a collapsed CORDIC uses lookahead transformation to merge several iterations to optimize the CORDIC design.
The chapter also presents a novel design that uses a single iteration to compute the values of sine and cosine, to demonstrate the extent to which a designer can creatively optimize a design.
