An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform

2019 ◽  
Vol 17 (05) ◽  
pp. 1950030
Author(s):  
Hua Yi ◽  
Peichang Ouyang ◽  
Tao Yu ◽  
Tao Zhang
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Discrete Fourier Transform ◽  
Time Domain ◽  
Morlet Wavelet ◽  
Wavelet Function ◽  
Linear Convolution ◽  
Calculation Results ◽  
Morlet Wavelet Transform ◽  
The Time Domain

Continuous wavelet transform (CWT) is a linear convolution of signal and wavelet function for a fixed scale. This paper studies the algorithm of CWT with Morlet wavelet as mother wavelet by using nonzero-padded linear convolution. The time domain filter, which is a non-causal filter, is the sample of wavelet function. By making generalized discrete Fourier transform (GDFT) and inverse transform for this filter, we can get a geometrically weighted periodic extension of the filter when evaluated outside its original support. From this extension of the time domain filter, we can get a causal filter. In this paper, GDFT-based algorithm for CWT, which has a more concise form than that of linear convolution proposed by Jorge Martinez, is constructed by using this causal filter. The analytic expression of the GDFT of this filter, which is essential for GDFT-based algorithm for CWT, is deduced in this paper. The numerical experiments show that the calculation results of GDFT-based algorithm are stable and reliable; the running speed of GDFT-based algorithm is faster than that of the other two algorithms studied in our previous work.

Single-Rate Discrete-Time Signals and Systems

2009 ◽  
pp. 1-22
Author(s):  
Ljiljana Milic
Keyword(s):  
Fourier Transform ◽  
Discrete Fourier Transform ◽  
Discrete Time ◽  
Time Domain ◽  
Transform Domain ◽  
Concise Review ◽  
Discrete Signals ◽  
Time Signals ◽  
The Time Domain

This chapter is a concise review of time-domain and transform-domain representations of single-rate discrete-time signals and systems. We consider first the time-domain representation of discrete-time signals and systems. The representation in transform domain comprises the discrete-time Fourier transform (DTFT), the discrete Fourier transform (DFT), and the z-transform. The basic realization structures for FIR and IIR systems are briefly described. Finally, the relations between continuous and discrete signals are given.

Induction Motor Fault Diagnosis Using Voltage Spectrum of Auxiliary Winding and Lissajous Curve of its Park Components

2013 ◽  
Vol 805-806 ◽  
pp. 963-979 ◽  
Author(s):  
Lamiaâ El Menzhi ◽  
Abdallah Saad
Keyword(s):  
Fourier Transform ◽  
Fault Diagnosis ◽  
Frequency Domain ◽  
Induction Motor ◽  
Discrete Fourier Transform ◽  
Time Domain ◽  
New Method ◽  
Spectrum Simulation ◽  
Simulation Results ◽  
The Time Domain

In this paper, a new method for induction motor fault diagnosis is presented. It is based on the so-called an auxiliary winding voltage and its Park components. The auxiliary winding is a small coil inserted between two of the stator phases. Expressions of the inserted winding voltage and its Park components are presented. After that, discrete Fourier transform analyzer is required for converting the signals from the time domain to the frequency domain. A Lissajous curve formed of the two Park components is associated to the spectrum. Simulation results curried out for non defected and defected motor show the effectiveness of the proposed method.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

339 Morlet wavelet transform in EEG during perceptuo-motor tasks

1998 ◽  
Vol 30 (1-2) ◽  
pp. 131-132
Author(s):  
S. Slobounovl ◽  
R. Tutwiler ◽  
E. Slobounova
Keyword(s):  
Wavelet Transform ◽  
Morlet Wavelet ◽  
Motor Tasks ◽  
Morlet Wavelet Transform

IDENTIFICATION OF INTERHARMONICS BASED ON WAVELET PACKET TRANSFORM

2021 ◽  
Vol 3 (1) ◽  
pp. 031-036
Author(s):  
S. A. GOROVOY ◽  
◽  
V. I. SKOROKHODOV ◽  
D. I. PLOTNIKOV ◽  
◽  
...  
Keyword(s):  
Fourier Transform ◽  
Simulation Model ◽  
Frequency Domain ◽  
Time Domain ◽  
Wavelet Packet ◽  
High Accuracy ◽  
Wavelet Packet Transform ◽  
Mathematical Apparatus ◽  
Nonlinear Load ◽  
The Time Domain

This paper deals with the analysis of interharmonics, which are due to the presence of a nonlinear load. The tool for the analysis was a mathematical apparatus - wavelet packet transform. Which has a number of advantages over the traditional Fourier transform. A simulation model was developed in Simulink to simulate a non-stationary non-sinusoidal mode. The use of the wavelet packet transform will allow to determine the mode parameters with high accuracy from the obtained wavelet coefficients. It also makes it possible to obtain information, both in the frequency domain of the signal and in the time domain.

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