Merge and split of Fourier-tranformed data
Hsieh-Sheng Hou · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
The Cooley-Tukey radix-2 Fast Fourier Transform (FFT) is well known in digital signal processing and has been popularly used in many applications. However, one important function in signal processing is to merge or split of FFT blocks in the Fourier transform domain. The Cooley-Tukey radix-2 decimation-in-frequency FFT algorithm can not be used for this purpose because twiddle factors must be multiplied to the input data before FFT is performed on the resultant. In other words, the existing radix-2 decimation- in-frequency FFT algorithm is not a true radix-2 algorithm. This in turn has prevented it from direct applications to the transform-domain processing, such as merge or split of FFT blocks in the Fourier domain. For real input data one may prefer to use the Fast Hartley Transform (FHT) because it completely deals with real arithmetic calculations. Then the same statements with regard to the radix-2 decimation-in-frequency FFT apply equally well to FHT because the existing FHT algorithms are the real-number equivalence of the complex-number FFT. The true radix-2 Decimation-in-frequency FFT and FHT algorithms presented in this paper have alleviated the above difficulty, and they may provide new techniques for other potential applications.