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.

Effects of FFT coefficient quantization on sinusoidal signal detection

Abstract: Detection of a sinusoid of unknown frequency in wideband noise is performed efficiently by the FFT (fast Fourier transform). The detector performs a hypothesis test on the magnitude of the FFT output. When the FFT is implemented, error due to arithmetic roundoff coefficient quantization limits the accuracy of the transform and degrades the detection performance. When the FFT is used as a detector of an unknown sinusoidal signal, the coefficient quantization error is significant and increases with the FFT length. The decimation is analyzed in time for a radix-2 FFT. The FFT output error is defined to be the maximum magnitude of the difference between the true FFT and FFT computed with the quantized coefficients. An upper bound on the error is derived by a deterministic analysis and is verified to be close to the actually measured error. Using the functional form of the bound and scaling it to fit the measured error, an empirical formula for the error is derived. The probability of detection of the quantized-coefficient FFT is computed using the empirical error formula. The probability of detection curves is presented as a function of the FFT length. Simulations indicate that when a sufficient number of bits is used to quantize the coefficients, the probability of detection does not significantly degrade. >

A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

Abstract: The discrete Fourier transform (DFT) is the base of modern signal processing 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N2 log N) respectively Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm DFT has two properties One property is that DFT is energy conservation transform The other property is that many DFT coefficients are close to zero The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper The quantum algorithm for convolution estimation is also presented in this paper Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible

The Problem of Calculating the Fast-Fourier Transform of a Step-Like Sampled Function

Abstract: The calculation of the fast fourier transform (FFT) for a step-like bounded function with unequal values at boundaries may be performed by using a convenient decomposition of the total curve into two elementary ones, one of them being a linear ramp. The method may be generalized to functions having asymptotic tails which may be approximated by simple analytic functions, the theoretical FFT of which is known.

Roundoff Error Analysis of the Recursive Moving Window Discrete Fourier Transform

Abstract: This paper presents both worst case and average case analysis of roundoff errors occuring in the floating point computation of the recursive moving window discrete Fourier transform (DFT) with precomputed twiddle factors. We show the strong influence of precomputation errors – both within the initial fast Fourier transform (FFT) and the recursion – on the numerical stability. Numerical simulations confirm the theoretical results.