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Mapping iterative algorithm for realizing mixed base FFT (fast fourier transform) final stage reordering

A technology of reordering and mixed bases, which is applied in complex mathematical operations and other directions, and can solve problems that cannot meet general needs.

Inactive Publication Date: 2012-10-03
FUDAN UNIV
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  • Claims
  • Application Information

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Problems solved by technology

This obviously has limitations and cannot meet general needs

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  • Mapping iterative algorithm for realizing mixed base FFT (fast fourier transform) final stage reordering
  • Mapping iterative algorithm for realizing mixed base FFT (fast fourier transform) final stage reordering
  • Mapping iterative algorithm for realizing mixed base FFT (fast fourier transform) final stage reordering

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Embodiment Construction

[0027] The present invention is further described below in conjunction with embodiment.

[0028] According to the mapping iterative algorithm in the present invention, when the number of input points of FFT satisfies is a non-zero natural number in the way of mixed base decomposition, it can be guaranteed that the transformation function Satisfy the following relationship: ;

[0029] by As an example, the initial vector group input to the final FFT reordering module is shown in column (1) in Table 1, which corresponds to the The mixed base decomposition method is the last link of the 32-point FFT: the output of 4 groups of 8-point DFT. Starting from the reference sequence, after 5 rounds of loop iterations, the final vector group is output in natural order, as shown in column (5). After the 6th round of iteration starts, the vector group is read sequentially, and the output returns to The mixed basis decomposition method of , as shown in column (1).

[0030] As sho...

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Abstract

The invention belongs to the technical field of digital integrated circuits and systems, and particularly relates to a mapping iterative algorithm for realizing mixed base FFT (fast fourier transform) final stage reordering. A final stage reordering module of an FFT is a necessary link for guaranteeing the realization of queue order output under the condition of adopting a DIF-FFT (decimation in frequency-fast fourier transform) algorithm. The treatment on this problem in the past commonly adopts a bit-reversal algorithm, but the bit-reversal algorithm is limited by the fact that input point must meet certain requirements, and universality is not achieved. The invention provides the mapping iterative algorithm in view of this situation, so that natural order output of sequence can be achieved when an arbitrary input point is an integer power of 2, and a uniform reordering algorithm to the FFT disintegrated by the way in which the arbitrary input point is a non-zero natural number mixed base is provided.

Description

technical field [0001] The invention belongs to the technical field of digital integrated circuits and systems, and in particular relates to a mapping iteration algorithm for realizing mixed-radix FFT last-stage reordering. Background technique [0002] The final reordering module of FFT (Fast Fourier Transform) is a necessary link to ensure the output of queue order when DIF-FFT (Frequency Domain Fast Fourier Transform) is used. When using DIF-FFT (FFT of frequency domain extraction method), the last-stage reordering module ensures that the final sequence is output in natural order, and realizes FIFO (sequence input, sequence output), which is the read and write of data between the front and rear stages Provides convenience. However, in the past, the design of the last-level reordering module was based on the bit-reversal algorithm. As the name implies, this algorithm is to represent the serial number of the input sequence in binary form, and then only need to perform a "b...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/14
Inventor 叶凡黄佳森任俊彦李宁许俊李巍
Owner FUDAN UNIV
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