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Split-radix FFT algorithm
About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.
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TL;DR: Using complex numbers of the form a + b μ (where μ is a complex cube root of unity), a radix-6 FFT algorithm in which the component six-point DFT's do not require any multiplication is developed.
Abstract: Using complex numbers of the form a + b μ (where μ is a complex cube root of unity), a radix-6 FFT algorithm in which the component six-point DFT's do not require any multiplication is developed. This number system was used by Dubois and Venetsanopoulos to implement radix-3 FFT. The number of arithmetic operations for the new algorithm is compared with those of standard radix-6, radix-2, and radix-4 FFT algorithms.
31 citations
TL;DR: An algorithm is described that performs well on a Convex C4/XA vector supercomputer on large FFTs by using higher-radix kernels and moving the transpose step into the computational steps.
Abstract: Some implementations of a power-of-two one-dimensional fast Fourier transform (FFT) on vector computers use radix-4 Stockham autosort kernels with a separate transpose step. This paper describes an algorithm that performs well on a Convex C4/XA vector supercomputer on large FFTs by using higher-radix kernels and moving the transpose step into the computational steps. For short transforms a different algorithm is used that calculates the FFT without storing any intermediate results to memory. Performance results using these techniques are given.
31 citations
TL;DR: An efficient algorithm for computing the real-valued FFT using radix-2 decimation-in-frequency (DIF) approach has been introduced and a C++ program that implements this algorithm has been included.
Abstract: An efficient algorithm for computing the real-valued FFT (of length N) using radix-2 decimation-in-frequency (DIF) approach has been introduced. The fact that the odd coefficients are the DFT values of an N/2-length linear phase sequence introduces a redundancy in the form of the symmetry X(2k+1)=X/sup */(N-2k-1), which can be exploited to reduce the arithmetic complexity and memory requirements. The arithmetic complexity and, memory requirements of the algorithm presented are exactly the same as the most efficient decimation-in-time (DIT) algorithm for the real-valued FFT that exists to date. A C++ program that implements this algorithm has been included.
31 citations
TL;DR: This paper describes an analog speech scrambler using the FFT technique (FFT scrambler), which provides highly secured scrambled signal by permuting a large number of FFT coefficients.
Abstract: This paper describes an analog speech scrambler using the FFT technique (FFT scrambler). The FFT scrambler provides highly secured scrambled signal by permuting a large number of FFT coefficients. Important items to be considered in the designing of the FFT scrambler are discussed, such as FFT frame length, permutation of FFT coefficients, and frame synchronization, in addition to the configuration of the experimental FFT scrambler. Possible causes for the degradation of the descrambled signal, such as transmission channel group delay and intersymbol interference, are also discussed, together with experimental results.
31 citations
TL;DR: A new algorithm for the fast computation of the discrete Fourier transform (DFT) is introduced, called the conjugate pair FFT (CPFFT), which is used to compute a length-2m DFT.
Abstract: A new algorithm for the fast computation of the discrete Fourier transform is introduced. The algorithm, called the conjugate pair FFT (CPFFT), is used to compute a length-2m DFT. The number of multiplications and additions required by the CPFFT is less than that required by the SRFFT algorithm.
31 citations