Topic
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.
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08 Dec 2003TL;DR: Use of simple FFT model greatly reduces the size of the hardware to be used to implement the OFDM technique, and demonstrates how a simple 64-point FFT has a performance comparable to that of a complex floating point arithmetic format.
Abstract: In this paper, the architecture of a 64-point FFT for the OFDM technique used in WLAN standards is proposed. FFT is a complex function whose computational accuracy, hardware size and processing speed depends on the type of arithmetic format used to implement it. Due to the non-linearity of FFT, its computational accuracy is not easy to calculate theoretically. Therefore statistical or simulation methods are used. A simulation method to calculate the performance (hardware size, computational accuracy) of the FFT, based on fixed-point and floating-point formats, has been used. The paper demonstrates how a simple 64-point FFT, based on the fixed point arithmetic format has a performance comparable to that of a complex floating point arithmetic format. Comparison has been made between a fixed point FFT simulation model and a floating point reference model. The results deduced from comparison have shown that both the approaches provide similar results. However, use of simple FFT model greatly reduces the size of the hardware to be used to implement the OFDM technique
2 citations
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TL;DR: A variable order method for the fast and accurate computation of the Fourier transform is presented and the increase in accuracy is achieved by applying corrections to the trapezoidal sum approximations obtained by the FFT method.
Abstract: In this paper, a variable order method for the fast and accurate computation of the Fourier transform is presented. The increase in accuracy is achieved by applying corrections to the trapezoidal sum approximations obtained by the FFT method. It is shown that the additional computational work involved is of orderK(2m+2), wherem is a small integer andK≤n. Analytical expressions for the associated error is also given.
2 citations
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02 May 2004TL;DR: By reformulating the existing radix-2 decimation-in-time (DIT) FHT and complex-valued FFT algorithms using an efficient index mapping, a close relationship between the two algorithms is established and it should be possible to use a single software or hardware module to compute the DHT as well as the forward and inversecomplex-valued DFTs.
Abstract: By reformulating the existing radix-2 decimation-in-time (DIT) FHT and complex-valued FFT algorithms using an efficient index mapping, a close relationship between the two algorithms is established. A detailed comparison between the two algorithms is carried out. It is shown that these algorithms have similar structures and can be implemented using the same butterfly. In view of this relationship and the fact that the DHT is an efficient alternative to the DFT for real data, it should be possible to use a single software or hardware module to compute the DHT as well as the forward and inverse complex-valued DFTs.
2 citations
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TL;DR: This thesis mainly studies data acquisition, controlling and FFT based on FPGA which adopts the algorithm of radix-4,5-step cascading processing and uses CORDIC pipeline structure which is easier than multiplication for the hardware.
Abstract: This thesis mainly studies data acquisition,controlling and FFT based on FPGA.FFT adopts the algorithm of radix-4,5-step cascading processing.The whole system uses pipeline pattern,practicality.The multiplication unit is changed to shift and addi-tion unit by CORDIC pipeline structure which is easier than multiplication for the hardware.Dual-port RAM and ROM are built in-side the system.These methods accelerate the operating and reasonably resolve the mutually restriction of resources and speed.
2 citations
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IBM1
TL;DR: A hybrid of the nested and the prime factor approach is presented to compute DFT using WFTA (Winograd Fourier transform algorithm) and is highly suitable for a two-level memory hierarchy where most of the computing takes place with a very small data set and the accesses to the main memory are minimized.
Abstract: In this paper, a hybrid of the nested and the prime factor approach is presented to compute DFT using WFTA (Winograd Fourier transform algorithm). A one-dimensional DFT is written as a two-dimensional DFT where DFT along each dimension is computed using the nested form of Winograd. Compared to the nested form, the number of multiplications increase only marginally and there is a corresponding decrease in the number of additions. The algorithm is in-place and in-order requiring very little storage other than the data. The coefficient tables required for this approach are very small. The approach suggested is highly suitable for a two-level memory hierarchy where most of the computing takes place with a very small data set and the accesses to the main memory are minimized. This approach is also highly suitable for a vector processor or a hardware implementation. A general-N FORTRAN program has been developed to compute DTFs of lengths up to 5040 (59 different values) using this approach. For this, the computing times are almost proportional to the transform lengths.
2 citations