Efficient Radix-4 and Radix-8 Butterfly Elements

FFT/IFFT has been one of the most important algorithms in digital signal processing. In the recent years, the FFT/IFFT has frequently been applied in the modern communication systems due to its efficiency for OFDM (Orthogonal Frequency Division Multiplex) implementation. Many applications, like xDSL modems, HDTV, mobile radio terminals, use FFT/IFFT processor as a key component. The butterfly elements are one of the basic building blocks in an FFT/IFFT processor. Since FFT/IFFT processors using a radix-4 architecture has fewer multiplications than the processors using radix-2, the radix-4 architectures are often used for FFT/IFFT processors. Higher radix are tend to reduce the memory access rate, arithmetic workload, and, hence, the power consumption [2] [3]. Efficient design of high-radix butterfly elements is therefore important. In the following section, we give a short review on the conventional implementation of butterfly elements. We introduce the carry-save based butterfly in section 3 and the results are presented in section 4.