Radix-2α/4β Building Blocks for Efficient VLSI’s Higher Radices Butterflies Implementation
This paper describes an embedded FFT processor where the higher radices butterflies maintain one complex multiplier in its critical path. Based on the concept of a radix-r fast Fourier factorization and based on the FFT parallel processing, we introduce a new concept of a radix-r Fast Fourier Transform in which the concept of the radix-r butterfly computation has been formulated as the combination of radix-2α/4β butterflies implemented in parallel. By doing so, the VLSI butterfly implementation for higher radices would be feasible since it maintains approximately the same complexity of the radix-2/4 butterfly which is obtained by block building of the radix-2/4 modules. The block building process is achieved by duplicating the block circuit diagram of the radix-2/4 module that is materialized by means of a feed-back network which will reuse the block circuit diagram of the radix-2/4 module.