Canonic real-valued radix-2n FFT computations

Fast Fourier transform (FFT) is an important digital signal processing (DSP) algorithm for analysis of the phase and frequency components of a time-domain signal. Canonic real-valued FFT (RFFT) approach improves the computation performance by completely eliminating arithmetic redundancies. The major advantage of the canonic RFFTs is that these require the least butterfly operations and only involve real datapath when mapped to architectures. In this paper, we study the performances of canonic RFFT computations for different radix factorizations. We compare various radices RFFTs along with their canonic variants from both arithmetic and architectural perspectives. It is shown that decimation-in-frequency (DIF) RFFT structures require less twiddle factor operations than their decimation-in-time (DIT) counterparts. However, we also show that canonic RFFTs may not be desirable when taking the cost of twiddle factor operations as the major consideration.