Time-frequency scaling property of Discrete Fourier Transform (DFT)

2010 ◽  
Author(s):  
Sumit A. Talwalkar ◽  
S. Lawrence Marple
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Frequency Scaling ◽  
Time Frequency ◽  
Scaling Property

Research on the Existence of Genuine Inter-Harmonic Components Based on the Component Appearance Rate

2014 ◽  
Vol 875-877 ◽  
pp. 1847-1851
Author(s):  
Xiao Dong Yuan ◽  
Qun Li ◽  
Jin Hui ◽  
Bin Chen
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Theoretical Perspective ◽  
Harmonic Spectrum ◽  
Measured Signal ◽  
Time Frequency ◽  
Appearance Rate ◽  
The Matrix ◽  
Analysis Window ◽  
Harmonic Components

The inter-harmonic spectrum of an electrical voltage or current from discrete Fourier transform can not only be caused by genuine inter-harmonic components, but can also be caused by other system disturbances. Therefore, the existence determination of genuine inter-harmonic s from the spectrum becomes the premise for further calculation of inter-harmonic parameters. From the theoretical perspective, this paper firstly analyzes and points out that the waveform difference among each cycle in the analysis window is the cause of the existence of inter-harmonic spectrum, and then presents a method to determine the existence of genuine inter-harmonic components, which is based on inter-harmonic time-frequency contour chart and the component appearance rate. The presented method firstly performs continuous discrete Fourier transform on the captured signal with certain duration and obtains the corresponding absolute time-frequency matrix, and then the genuine inter-harmonics can be distinguished based on the component appearance rate of the matrix and the criterion threshold. The method is easy to implement with clear principle, it can distinguish the genuine inter-harmonic s from the measured signal. The analysis on several data groups from real measurements verifies the effectiveness and the practicability of the method.

scholarly journals Non-Distorted Optimization Spectrum Analysis

Energies ◽  
2018 ◽  
Vol 11 (7) ◽  
pp. 1841
Author(s):  
Rong-Ching Wu ◽  
Li-Ju Huang
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Spectrum Analysis ◽  
Time Frequency ◽  
Frequency Scale ◽  
Signal Parameters ◽  
Signal Characteristics ◽  
Sampled Signal ◽  
Three Stages ◽  
The Ideal

The discrete Fourier transform is extensively applied in spectrum analysis. However, the sampled signal is random, and the discrete Fourier transform has its own specific limitations. Thus, errors will inevitably occur in time–frequency transformation work. The most common are the leakage effects of the spectrum that are caused from the scale of the spectrum not being able to match the characteristics of the signal. The optimal spectrum is proposed to overcome this defect by adjusting the frequency scale to fit signal characteristics. This includes three stages whereby frequency scale can match signal characteristics. Firstly, the signal parameters must be found. Secondly, the frequency scale can be determined from these signal parameters. Finally, the optimal spectrum can be realized using the adjustable spectrum with the new frequency scale. After processing the optimal spectrum, the leakage effects of the signal will be decreased to a minimum. This method preserves signal characteristics in the optimization process, which reaches the ideal of non-distortion.

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