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Efficient discrete Fourier transform method

A discrete Fourier, efficient technology, applied in the direction of complex mathematical operations, etc., can solve the problems that have not been widely used, the meaning of real-time problem processing is not great, and the operation efficiency is low

Inactive Publication Date: 2016-02-03
SOUTHWEST CHINA RES INST OF ELECTRONICS EQUIP
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Problems solved by technology

Although the discrete Fourier transform has a clear physical meaning, it is the most direct mathematical process to determine the frequency components of the time-domain sequence, and it is also convenient for computers to process, but its calculation efficiency is very low, and it has little significance for real-time problem processing, so it has been used for a long time. not really widely used

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Embodiment Construction

[0034] In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present invention, not to limit the present invention.

[0035] Any feature disclosed in this specification (including the abstract and drawings), unless specifically stated, can be replaced by other equivalent or similar purpose alternative features. That is, unless expressly stated otherwise, each feature is one example only of a series of equivalent or similar features.

[0036] In this specific embodiment, a 7-point DFT calculation is taken as an example for specific description.

[0037] Suppose the X vector of N=7 points is X=[5311276491]. The specific calculation method steps are:

[0038] 1) Decompose N and determine the number of iterations. ...

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Abstract

The invention provides an efficient discrete Fourier transform method. Reduced DFT (Discrete Fourier Transform) operation and butterfly operation are combined, and the method can realize the DFT operation of any odd point through a way that repeated iteration reduction is combined with a butterfly algorithm; and the method also can realize the DFT operation of any even number point and the odd point obtained after butterfly simplification is carried out through the way that the repeated iteration reduction is combined with the butterfly algorithm. Compared with the traditional DFT algorithm, the efficient discrete Fourier transform method adopts fewer complex multiplication operations so as to greatly lower operation complexity. The algorithm has the advantages of being simple and reasonable in architecture, few in resource expenditure and high in engineering realizability.

Description

technical field [0001] The invention relates to a high-efficiency discrete Fourier transform method, in particular to a high-efficiency discrete Fourier transform method. Background technique [0002] Discrete Fourier Transform (DFT) is one of the most commonly used and powerful processing methods encountered in the field of digital signal processing, and is the core of digital signal processing. Using DFT transformation, the analysis and synthesis of signals and systems can be realized. At the same time, many algorithms, such as correlation, filtering, spectral estimation, etc., can also be transformed into DFT, so DFT has been applied in many engineering fields. [0003] The purpose of discrete Fourier transform is to transform the signal from the time domain to the frequency domain, so that the information can be analyzed and processed in the frequency domain. At the same time, the obtained results can also be inversely transformed to the time domain by the discrete Fou...

Claims

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Application Information

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IPC IPC(8): G06F17/14
Inventor 刘宪军陈俊霖向川云彭艳
Owner SOUTHWEST CHINA RES INST OF ELECTRONICS EQUIP
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