Figures of merit for VLSI implementations of digital signal processing algorithms

The advent of digital VLSI technology demands a reappraisal of the most suitable algorithms for a given processing function. A cost function is developed for making quantitative comparisons between digital algorithm implementations including control and overheads. This provides a tool allowing different implementations of the same algorithm, and also different algorithms for the same function, to be compared. The cost function is chosen to characterise the algorithm and associated logic design independently of the circuit technology that might be used. In this way the techonology options can be introduced separately in designing a practical system. Also, configurations which achieve a higher throughput by using a proportionally larger quantity of hardware or higher logic speed are assessed as having the same effectiveness or cost. As an illustration, the costing is applied to FFT and Winograd Fourier-transform algorithms (WFTA). The results show the advantage gained by minimising the true costs including, particularly, control overheads, instead of just the number of arithmetic operations. Despite its fewer arithmetic operations, the WFTA is shown to be less efficient than the FFT except in the most fully parallel case.