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.

Comments on Errors of DFT Spectrum

2014 ◽  
Vol 568-570 ◽  
pp. 189-192
Author(s):  
Feng Han ◽  
Yao Lin Liu ◽  
Zhen Liu ◽  
Hai Dong Zeng
Keyword(s):  
Fourier Transform ◽  
Error Analysis ◽  
Energy Loss ◽  
Discrete Fourier Transform ◽  
Spectrum Analysis ◽  
Analytical Error ◽  
Error Estimators ◽  
Asynchronous Sampling ◽  
Parseval’S Theorem ◽  
Further Development

Discrete Fourier transform (DFT/FFT) spectrums contain a variety of inherent errors in asynchronous sampling. Spectrum analysis with the accuracy above 10-3 are generally challenging issues. This work divides the DFT procedure into four signal transforms and exams six spectrum errors originated from these distortions. Besides the review of traditional errors, a so-called energy loss-gain (ELG) error is briefly introduced, which is proved to be a considerable error on the basis of Parseval's theorem. With the help of full error analysis mentioned here and the further development of analytical error estimators, it is expectable to obtain a DFT spectrum with a specified accuracy.

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.

THE FAST FOURIER TRANSFORM AND THE CONTINUOUS WAVELET TRANSFORM ANALYSIS OF THE PHONOCARDIOGRAM SIGNAL

2004 ◽  
Vol 04 (03) ◽  
pp. 257-272 ◽  
Author(s):  
S. M. DEBBAL ◽  
F. BEREKSI-REGUIG ◽  
A. MEZIANE TANI
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Fast Fourier Transform ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Quantitative Measurements ◽  
Signal Characteristics ◽  
Wavelet Transform Analysis ◽  
Pcg Signals

This paper is concerned with a synthesis study of the fast Fourier transform (FFT) and the continuous wavelet transform (CWT) in analysing the phonocardiogram signal (PCG). It is shown that the continuous wavelet transform provides enough features of the PCG signals that will help clinics to obtain qualitative and quantitative measurements of the time-frequency PCG signal characteristics and consequently aid to diagnosis. Similary, it is shown that the frequency content of such a signal can be determined by the FFT without difficulties.

scholarly journals A Fourier based algorithm to estimate the period of a sampled signal

2018 ◽  
Vol 11 (2) ◽  
pp. 152-160
Author(s):  
José Danilo Rairán Antolines
Keyword(s):  
Fourier Transform ◽  
Real Time ◽  
Discrete Fourier Transform ◽  
Upper Bound ◽  
Power Grid ◽  
Noisy Data ◽  
Physiological Signals ◽  
Sampled Signal ◽  
Null Value ◽  
Data Length

Given a sampled signal, in general, is not possible to compute its period, but just an approximation. We propose an algorithm to approximate the period, based on the Discrete Fourier Transform. If that transformation uses data length for multiples of the true period, some of its harmonics have null value. Thus, the best candidate to be a multiple of the period minimizes the value of those harmonics. The validation for noiseless data shows an upper bound in the error equal to a quarter of the time between two consecutive samples, whereas the result for noisy data demonstrates robustness. As application, the algorithm estimates the period of physiological signals, and tracks the frequency of the power grid in real time, which evidence its versatility

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