STUDY OF TIME FREQUENCY TRANSFORMS APPLIED TO POWER QUALITY SIGNALS

This work presents a scientific study on Short-Time Frequency Transforms (STFT) with different windows, also called Windowed Fourier Transforms, applied to power quality signals. Additionally, it deals with S transforms, with its frequency-dependent window. The disturbances related to energy quality have non-stationary nature, in which the spectral content varies over time. So, the Fourier Transform is not appropriate for such analysis, because it doesn’t show time locations, only information about existing frequencies in the signal. Therefore, the spectral analysis by windowed transforms helps to identify and detect a series of defects associated to these power signals. The motivation behind this document is to verify which window will provide a more precise identification of the characteristics of the disturbances in time-frequency domain. For this work, synthetic signals were generated for some of these disturbances, and their spectra were compared considering Gaussian, Hann and Blackman windows, as well as the S transform. Based on the obtained results, it was verified that each transform presents different behaviours acording to the input signal, except for the ones with Hann and Blackman windows, that showed similar spectra. For all of them, there is always a tradeoff between time and frequency resolutions. Therefore, the choice of the window must be done according to the desired outputs. The Dev-C ++ ® IDE was used for C ++ programming, and the Gnuplot ® program for graphics generation.

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Time-Frequency Analysis Methods for Power Quality Disturbances Feature Representation

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.298 ◽

2010 ◽

Vol 439-440 ◽

pp. 298-303

Author(s):

Lin Lin ◽

Jia Jin Qi ◽

Nan Tian Huang ◽

Shi Guang Luo

Keyword(s):

Power Quality ◽

Frequency Analysis ◽

Time Instant ◽

Feature Representation ◽

Quality Analysis ◽

Status Report ◽

Time Frequency Analysis ◽

Time Frequency ◽

S Transform ◽

Short Time

Power quality (PQ) analysis is the foundation of power system automation. The premise of power quality analysis is feature representation of power quality events. Time-frequency analysis (TFA) is very suitable for nonstationary signals analysis. The TFA of a PQ signal is to determine the energy distribution along the frequency axis at each time instant. This paper provides a status report of feature representation for PQ events by TFA methods, including short time Fourier transform (STFT), wavelet transform (WT) and S-transform (ST), overview the basic TFA theories for PQ analysis and compare the effectiveness of different TFA methodology. The expectation is that further research and applications of these TFA algorithms will flourish for PQ feature representation in the near future. The analysis direction and emphasis of studying are also put forward.

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The S‐transform with windows of arbitrary and varying shape

Geophysics ◽

10.1190/1.1543223 ◽

2003 ◽

Vol 68 (1) ◽

pp. 381-385 ◽

Cited By ~ 300

Author(s):

C. Robert Pinnegar ◽

Lalu Mansinha

Keyword(s):

Wavelet Transforms ◽

Arrival Time ◽

Fourier Transforms ◽

Frequency Control ◽

P Wave ◽

Time Frequency ◽

S Transform ◽

Spectral Localization ◽

Generalized S Transform ◽

Short Time

The S‐transform is an invertible time‐frequency spectral localization technique which combines elements of wavelet transforms and short‐time Fourier transforms. In previous usage, the frequency dependence of the analyzing window of the S‐transform has been through horizontal and vertical dilations of a basic functional form, usually a Gaussian. In this paper, we present a generalized S‐transform in which two prescribed functions of frequency control the scale and the shape of the analyzing window, and apply it to determining P‐wave arrival time in a noisy seismogram. The S‐transform is also used as a time‐frequency filter; this helps in determining the sign of the P arrival.

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Design of a Novel High Performance Digital Fault Recorder

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.108-111.470 ◽

2010 ◽

Vol 108-111 ◽

pp. 470-475

Author(s):

Nan Tian Huang ◽

Xiao Sheng Liu ◽

Dian Guo Xu ◽

Jian Sun

Keyword(s):

Power Quality ◽

High Performance ◽

Fourier Transforms ◽

Amplitude Spectrum ◽

Quality Analysis ◽

Fault Recorder ◽

Quality Signals ◽

Stationary Signals ◽

Short Time ◽

Design Proposal

Power quality is the most important problems in power system automation. Aim to analysis and improve the power quality, many types of power quality events, such as voltage unbalanced, harmonic, frequency offset and multiple short time power quality disturbances, should be recorded accurately. This paper proposed a new design proposal of a novel digital fault recorder which could record the power quality waveform signals in 24 hours a day. The original power quality signals are transformed by fast Fourier transforms (FFT) and the waveform distortion is determined by the amplitude spectrum. In order to compression the data of power quality signals, the waveform without distortion is described by the first circle’s waveform. Hence, every power quality events signals and stationary signals will be recorded by one circle signal of each time. Then, the first circle signals of each event are compressed by wavelet transform so as to get higher compression ratio. The signal compressed by DFR will be stored in the Flash or RAM chips and transferred to principal computer. The data will be used for power quality analysis.

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A Kaiser Window-Based S-transform for Time-Frequency Analysis of Power Quality Signals

IEEE Transactions on Industrial Informatics ◽

10.1109/tii.2021.3083240 ◽

2021 ◽

pp. 1-1

Author(s):

Chengbin Liang ◽

Zhaosheng Teng ◽

Jianmin Li ◽

Wenxuan Yao ◽

Shiyan Hu ◽

...

Keyword(s):

Power Quality ◽

Frequency Analysis ◽

Time Frequency Analysis ◽

Time Frequency ◽

Quality Signals ◽

S Transform ◽

Kaiser Window

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Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

Applied Sciences ◽

10.3390/app11062582 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2582

Author(s):

Lucas M. Martinho ◽

Alan C. Kubrusly ◽

Nicolás Pérez ◽

Jean Pierre von der Weid

Keyword(s):

Fourier Transform ◽

Guided Waves ◽

Strain Level ◽

Energy Concentration ◽

Short Time Fourier Transform ◽

Time Frequency ◽

Frequency Representation ◽

The Fourier Transform ◽

Short Time ◽

Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

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A Modified S-Transform for EEG Signals Analysis

International Journal of Computational Methods ◽

10.1142/s0219876215500218 ◽

2015 ◽

Vol 12 (03) ◽

pp. 1550021 ◽

Cited By ~ 2

Author(s):

M. A. Al-Manie ◽

W. J. Wang

Keyword(s):

Image Processing ◽

Fourier Transform ◽

Energy Concentration ◽

Biomedical Data ◽

Short Time Fourier Transform ◽

Phase Information ◽

Eeg Signals ◽

Time Frequency ◽

S Transform ◽

Short Time

Due to the advantages offered by the S-transform (ST) distribution, it has been recently successfully implemented for various applications such as seismic and image processing. The desirable properties of the ST include a globally referenced phase as the case with the short time Fourier transform (STFT) while offering a higher spectral resolution as the wavelet transform (WT). However, this estimator suffers from some inherent disadvantages seen as poor energy concentration with higher frequencies. In order to improve the performance of the distribution, a modification to the existing technique is proposed. Additional parameters are proposed to control the window's width which can greatly enhance the signal representation in the time–frequency plane. The new estimator's performance is evaluated using synthetic signals as well as biomedical data. The required features of the ST which include invertability and phase information are still preserved.

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Time-Frequency Representations

Handbook of Fourier Analysis & Its Applications ◽

10.1093/oso/9780195335927.003.0014 ◽

2009 ◽

Author(s):

Robert J Marks II

Keyword(s):

International Standards ◽

Musical Score ◽

Instantaneous Spectrum ◽

Spectral Content ◽

Time Frequency ◽

Frequency Representation ◽

Musical Scores ◽

Vertical Location ◽

Technical Theory ◽

The Fourier Transform

The Fourier transform is not particularly conducive in the illustration of the evolution of frequency with respect to time. A representation of the temporal evolution of the spectral content of a signal is referred to as a time-frequency representation (TFR). The TFR, in essence, attempts to measure the instantaneous spectrum of a dynamic signal at each point in time. Musical scores, in their most fundamental interpretation, are TFR’s. The fundamental frequency of the note is represented by the vertical location of the note on the staff. Time progresses as we read notes from left to right. The musical score shown in Figure 9.1 is an example. Temporal assignment is given by the note types. The 120 next to the quarter note indicates the piece should be played at 120 beats per minute. Thus, the duration of a quarter note is one half second. The frequency of the A above middle C is, by international standards, 440 Hertz. Adjacent notes notes have a ratio of 21/12. The note, A#, for example, has a frequency of 440 × 21/12 = 466.1637615 Hertz. Middle C, nine half tones (a.k.a. semitones or chromatic steps) below A, has a frequency of 440 × 2−9/12 = 261.6255653 Hertz. The interval of an octave doubles the frequency. The frequency of an octave above A is twelve half tones, or, 440 × 212/12 = 880 Hertz. The frequency spacings in the time-frequency representation of musical scores such as Figure 9.1 are thus logarithmic. This is made more clear in the alternate representation of the musical score in Figure 9.2 where time is on the horizontal axis and frequency on the vertical. At every point in time where there is no rest, a frequency is assigned. To make chords, numerous frequencies can be assigned to a point in time. Further discussion of the technical theory of western harmony is in Section 13.1.

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