Efficient FFT algorithms for DSP processors using tensor product decompositions

A new class of FFT (fast Fourier transform) algorithms that run very efficiently on digital signal processors (DSPs) is described. The algorithms are based on a tensor product factorization of the DFT (discrete Fourier transform). The tensor product factorization not only controls the breakdown into short-length DFTs but also shows the data flow between the various blocks. This allows a better scheduling of operations, which again gives a better utilization of the DSP pipelining/parallel capabilities, and leads to algorithms with significantly lower overhead than traditional methods. Several different programs have been implemented in assembly code for the TMS320C30 and simulated to find their execution times. The new algorithms are shown to be more than 20% faster than traditional sequential algorithms adapted to the processor, because of lower overhead, and better utilization of the parallel instruction sets and the pipelining is obtained