Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

Frequency Estimation Algorithm of Sine Signal Based on FFT Coefficient

Abstract: Larger frequency estimation error will appear when a peak spectrum line phase is closed to±p/2using frequency interpolation algorithm based on the real part of fast Fourier transform(FFT) coefficient. So an improved sine signal frequency estimation algorithm is proposed. The postion of peak spectrum line is firstly indexed by using the real part and imaginary part sequence of FFT coefficient. And then according to the phase of peak spectrum line, the se quences with larger amplitude in real and imaginary part sequences are selected to participate in frequency interpolation. Simulation results show that at the condition ofSNR=3 dB and sampling numberN=128, the root mean square of normalized frequency estimation error at the whole frequency band is less than 0.02 and closed to Cramer-Rao lower bound(CRB). The total performance of the improved algorithm is better than the frequency interpolation and Rife al gorithm based on the real part of FFT coefficient. The improved algorithm has the characteristics of high frequency estimation precision and few computation amounts and it is easy to implement in hardware.

A new algorithm for the 2-D discrete cosine transform

Abstract: A simple relation between the two-dimensional discrete cosine transform (2D DCT) and two-dimensional discrete W transform (2D DWT) is found for multidimensional signal processing. Using the relation, the 2D type-IV DCT (DCT-IV) can be mapped to a number of one-dimensional type-III DWT (DWT-III) by Ma's (1989) real-valued FFT algorithm and the Wang (1992) mapping. Thus, a fast algorithm for 2D DCT-IV based on 1D DWT-III can be obtained. Computation efficiency of the proposed algorithm is higher than the existing algorithms for 2D DCT-IV.

On the exact recovery of the FFT of noisy signals using a non-subtractively dither-quantized input channel

Abstract: Through several algorithmic changes, the FFT and its variants have not only breathed a new lease of life into an otherwise latent classical DFT algorithm but also led to an explosion of applications in numerous areas. In all these applications of the Fourier transform, the FFT input has always been assumed to be sufficiently highly quantized so as to minimize, to a negligible level, an otherwise adverse effect of all quantization errors involved. A coarse quantization of the FFT input, with all the practical advantages that it entails, and an acceptable FFT estimation accuracy therefore seem to conflict with each other. This paper proposes a new theory that resolves this conflict for any quantization resolution used. This theory, tested with a 1-bit quantization scheme and under very noisy environments is very well supported by our simulation results. This makes the possibility of a hardware implementation of a 1-bit FFT chip a goal worth pursuing.

Method and circuit arrangement for carrying out a fast fourier transformation and the use thereof

Abstract: The invention relates to a method and a circuit arrangement for carrying out a fast Fourier transformation, in particular a complex 64 point fast Fourier transformation on the basis of a complex 8 point fast Fourier transformation, and to the use thereof. The circuit arrangement for carrying out a fast Fourier transformation consists of the following, connected in parallel or series: input buffers (IB), FFT blocks (FFT), which work on the basis of the decomposition of a 64 point fast Fourier transformation into an 8 point fast Fourier transformation and which carry out multiplications using additions, subtractions and shift register operations, the required coefficients forming an implemented part of the FFT block (FFT), a multiplier (M), which only carries out multiplications on the basis of additions, subtractions and shift register operations and buffers (B1/B2), which act both as intermediate memories and as data output memories (OP).

Fast algorithm for discrete cosine transform (DCT)-domain image downsampling using Winograd DCTs

Abstract: A fast algorithm for discrete cosine transform (DCT)-domain image resizing is presented. To reduce computations, fast Winograd DCTs are applied to a recently reported image resizing scheme that uses DCT low-pass truncatedapproximation. Our fast algorithm yields significant improvement in computational complexity over the fast algorithm of the reported method.