Design of 8-point DFT based on Rademacher Functions

Abstract

This paper presents a new circuit design for 8-point DFT algorithm based on product of Rademacher functions. The designed circuit is basically constructed base on 8-point DFT decimation in time that mainly construct of two 4-point and four 2-point DFTs. However, the operation of the design circuit is different. It utilized the advantages of Rademacher functions simplicity. Therefore, the proposed design is constructed from our previous design 4-point DFT which is based on product of Rademacher functions. Some analysis upon number types, internal connections and complex conjugate of the results to achieve the more efficient circuit have been made. Therefore, instead of four, the proposed design requires only three 2-point DFTs. Again, two output results of the design DFT have been removed since they are equal in terms of magnitude to the other results, but two negative circuit are required as a compensation. Moreover, the previous designed circuit of 4-point DFT has been replaced with the new circuit design. This circuit is special designed for non-standalone used, the circuit must be integrated inside the proposed 8-point DFT.

FPGA Hardware Realization: Addition of Two Digital Signals Based on Walsh Transforms

“…Another efficient method of calculating both DFT and WHT using radix-2 was published [19]. The new idea that utilizes Rademacher functions for generating Discrete Fourier Transforms (DFT) has been carried out [20][21]. This works proved a strong link between DFT and WHT since both of them can be generated by applying the product of Rademacher functions.…”