Implementing Fast Fourier Transform Algorithms of Real-Valued Sequences With the TMS320 DSP Platform

The Fast Fourier Transform (FFT) is an efficient computation of the Discrete Fourier Transform (DFT) and one of the most important tools used in digital signal processing applications. Because of its well-structured form, the FFT is a benchmark in assessing digital signal processor (DSP) performance. The development of FFT algorithms has assumed an input sequence consisting of complex numbers. This is because complex phase factors, or twiddle factors, result in complex variables. Thus, FFT algorithms are designed to perform complex multiplications and additions. However, the input sequence consists of real numbers in a large number of real applications. This application report discusses the theory and usage of two algorithms used to efficiently compute the DFT of real-valued sequences as implemented on the Texas Instruments TMS320C6000. The first algorithm performs the DFT of two N-point real-valued sequences using one N-point complex DFT and additional computations. The second algorithm performs the DFT of a 2N-point real-valued sequence using one N-point complex DFT and additional computations. Implementations of these additional computations, referred to as the split operation, are presented both in C and C6000 assembly language. For implementation on the C6000, optimization techniques in both C and assembly are covered.