A Signal Harmonic Analysis Method Using Fast Triangular Fourier Transform
A Fourier transform and triangular technology, which is applied in the field of signal harmonic analysis, can solve problems such as unfavorable understanding and complex calculation and reasoning process, and achieve the effects of easy understanding, improved calculation efficiency, and improved real-time performance.
Active Publication Date: 2017-12-19
吕锦柏
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All the above-mentioned calculation methods are performed on the complex exponential form of Fourier transform, and the calculation and reasoning process is relatively complicated, which is not conducive to understanding
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[0049] In order to illustrate the present invention more clearly, the present invention will be further described below in conjunction with preferred embodiments and accompanying drawings. Similar parts in the figures are denoted by the same reference numerals. Those skilled in the art should understand that the content specifically described below is illustrative rather than restrictive, and should not limit the protection scope of the present invention.
[0050] For any continuous signal f(t), its triangular Fourier series can be expressed by formula (1):
[0051]
[0052] In formula (1):
[0053]
[0054] In formula (2), T is the period of the signal f(t), t 0 Indicates the starting point of timing, n indicates the nth harmonic, ω=2π / T. The discrete form of the corresponding Fourier series can be obtained by discretizing formula (2). In the T period, the signal is sampled N times to obtain the N-point sequence corresponding to the signal in the T period. Equation ...
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The invention discloses a signal harmonic analysis method for using fast triangular-form Fourier transform. The signal harmonic analysis method comprises the following steps of sampling a signal, and obtaining an N-point signal sequence, wherein N=2<L>; performing base 2 time extraction on the signal sequence, wherein i is a positive integer which is no larger than L-1, and obtaining 2 2<L-i>-point signal sequences; performing Fourier transform on each 2<L-i>-point signal sequence, and obtaining all self harmonic factors of each 2<L-i>-point signal sequence; converting the harmonic factor of each 2<L-i>-point signal sequence to harmonic process data of the N-point signal sequence from one to 2<L-i-1>; transforming the base from 2i to 2i-1, continuously repeating the transformation process until the base is 2, and calculating each harmonic factor which corresponds with the N-point signal sequence, thereby obtaining a Fourier expression of the signal. The signal harmonic analysis method provided by the technical solution remarkably improves a calculation efficiency for performing Fourier transform on the signal and improves a real-time performance in signal harmonic analysis.
Description
technical field [0001] The invention relates to a method for analyzing signal harmonics. More specifically, it relates to a signal harmonic analysis method using Fast Triangular-form Fourier Transform (FTFT). Background technique [0002] Fourier transform is widely used in physics, electronics, number theory, combinatorics, signal processing, probability theory, statistics, cryptography, acoustics, optics, oceanography, structural dynamics and other fields. However, due to the complex calculation of Fourier transform, the application of Fourier transform is largely restricted. In 1965, Cooley and Tukey published the famous paper "An Algorithm for Machine Computing Fourier Series" in "Computer Science", and the Fast Fourier Transform (FFT) began to be applied on a large scale. The most basic operation of Cooley and Tukey's FFT algorithm is butterfly operation, and each butterfly operation includes two input points, so it is also called base-2 algorithm. After that, some n...
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IPC IPC(8): G01R23/16
Inventor 吕锦柏
Owner 吕锦柏