Determination of radix numbers of the Booth algorithm for the optimized programmable FIR architecture

The programmable FIR architectures using different radix numbers of the Booth algorithm are explored. Based on the radix-2' Booth algorithm, the modified transposed direct-form FIR architectures with and without programmable dynamic ranges of input data and filter coefficients are formulated. The complexities, throughput rates and complexities per throughput rate of the FIR architecture with and without various programmable dynamic data ranges are analyzed in different radix numbers of the Booth algorithm. According to our analyses: the radix-4 approach would be a good choice to achieve a low hardware complexity. For a high throughput rate, the radix 16 or higher radix number of the Booth algorithm should be considered. But if complexity per throughput rate is important, then the radix-8 and radix-16 approaches may be preferred in the FIR architecture without and with programmable dynamic data ranges: respectively. Therefore, users can apply our results to determine a suitable radix number of the Booth algorithm for designing the optimized FIR architecture with consideration of the chip area, speed, throughput rate, power consumption and so on.