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Method for implementing fractional order Fourier transformation based on multi-sample

A fractional-order Fourier and realization method technology, applied in the field of signal processing, can solve the problems of slow calculation speed, large delay, unfavorable real-time processing, etc., to achieve the effect of removing redundant operations, optimizing algorithm flow, and improving computational efficiency

Inactive Publication Date: 2008-11-12
BEIJING INSTITUTE OF TECHNOLOGYGY
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Problems solved by technology

[0034] The purpose of the present invention is to solve the problems of slow calculation speed, large time delay, and unfavorable real-time processing in the above-mentioned classical implementation method, and proposes a fractional-order Fourier transform implementation method based on multi-sampling, which has a relatively large amount of calculation compared to the original algorithm flow Smaller and more efficient, and due to the parallel structure, it is more suitable for hardware implementation; in addition, the present invention selects a more effective windowed half-band filter in the interpolation filtering part of the input sequence preprocessing, which not only solves the problem of low-order time The problem of edge oscillation occurs, and because the filter length is short, it is conducive to pipeline processing and improves the computational efficiency of implementation

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  • Method for implementing fractional order Fourier transformation based on multi-sample
  • Method for implementing fractional order Fourier transformation based on multi-sample
  • Method for implementing fractional order Fourier transformation based on multi-sample

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[0093] The content of the invention will be described in detail below in conjunction with the accompanying drawings and FPGA embodiments.

[0094] The present invention relates to a kind of efficient realization method of fractional order Fourier transform based on multi-sampling, its principle is shown in formula (7), and the algorithm flow chart of realization method is as follows figure 1 As shown, the whole process is decomposed into the following five steps to complete the operation:

[0095] ① Pass the input signal sequence f(n / Δ) through the polyphase component r of the interpolation filter h(n) i (k) Filter to get the sequence f i (m / Δ), where i=0, 1 represents the number of branches. |n|≤(N-1) / 2, Δ = N Indicates the normalized sampling interval of the input signal sequence, and N indicates the length of the input signal sequence, which is an odd number, where

[0096] h(n)=2·w(n)·sin(πn / 2) / (πn), |n|≤L, 2L+1 is ...

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Abstract

The invention relates to a fractional Fourier transform realizing method based on multi-sampling, belongs to the field of signal processing and can be used for improving the calculation efficiency realized in real time. The method decomposes the original arithmetic into two parallel multi-phase equivalent structures by adopting a multi-sampling signal processing principle based on a discrete sampling arithmetic, thus removing redundant operations, optimizing the arithmetic flows and solves the problems of slow speed, large time lag and not being not beneficial to real time processing of an Ozaktas discrete sampling arithmetic to realize real time calculation; compared with the original arithmetic, the flow calculation load is smaller and the efficiency is higher; besides, the parallel structures are more suitable for the appearance of hardware; moreover, an more effective window-adding semi-band filter is selected at the part of inputting the interpolation filter of the pre-treatment of a sequence, thus not only solving the edge oscillation problem occurred during low orders, but also being beneficial to pipeline processing and improving the calculation efficiency when realizing as the length of the filter is shorter.

Description

technical field [0001] The invention belongs to the field of signal processing, and in particular relates to a multi-sampling-based high-efficiency realization method of fractional-order Fourier transform, which improves the calculation efficiency of real-time realization. Background technique [0002] Fractional Fourier transform was originally widely used in the field of optics. In 1993, Almeida interpreted fractional Fourier transform as the rotation of signals in the time-frequency plane, which was an extension of classical Fourier transform. In 1996, Ozaktas proposed a method with a calculation speed comparable to FFT. After the discrete sampling algorithm, the fractional Fourier transform began to be applied in the field of signal processing. The fractional Fourier transform can be regarded as a unified time-frequency transform, which reflects the information of the signal in the time and frequency domains at the same time. It is different from the commonly used quadra...

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): G06F17/14
Inventor 陶然梁广平黄克武单涛
Owner BEIJING INSTITUTE OF TECHNOLOGYGY
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