MULTIVARIATE SPECTRAL ANALYSIS USING HILBERT WAVELET PAIRS

2004 ◽  
Vol 02 (04) ◽  
pp. 567-587 ◽  
Author(s):  
BRANDON WHITCHER ◽  
PETER F. CRAIGMILE
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Multivariate Time Series ◽  
Discrete Wavelet ◽  
Pass Filter ◽  
Wavelet Filters ◽  
The Hilbert Transform ◽  
High Pass

We investigate the use of Hilbert wavelet pairs (HWPs) in the non-decimated discrete wavelet transform for the time-varying spectral analysis of multivariate time series. HWPs consist of two high-pass and two low-pass compactly supported filters, such that one high-pass filter is the Hilbert transform (approximately) of the other. Thus, common quantities in the spectral analysis of time series (e.g., power spectrum, coherence, phase) may be estimated in both time and frequency. Compact support of the wavelet filters ensures that the frequency axis will be partitioned dyadically as with the usual discrete wavelet transform. The proposed methodology is used to analyze a bivariate time series of zonal (u) and meridional (v) winds over Truk Island.

Treatment of Noise in Experimental Transport Measurements Plots With Discrete Wavelet Transforms

2009 ◽  
Author(s):  
Rube´n Panta Pazos
Keyword(s):  
Wavelet Transform ◽  
Wavelet Transforms ◽  
Transport Theory ◽  
Discrete Wavelet ◽  
Transform Method ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Thresholding Algorithm ◽  
High Pass

In this work it is applied the wavelet transform method [2] in order to reduce diverse type of noises of experimental measurement plots in transport theory. First, suppose that a problem is governed by the transport equation for neutral particles, and an unknown perturbation occurs. In this case, the perturbation can be associated to the source, or even to the flux inside the domain X. How is the behavior of the perturbed flux in relation to the flux without the perturbation? For that, we employ the wavelet transform method in order to compress the angular flux considered as a 1D, or n-th dimensional signal ψ. The compression of this signal can be performed up to some a convenient order (that depends of the length of the signal). Now, the transport signal is decomposed as [9, 11]: ψ=〈am|dm|dm−1|dm−2|⋯|d2|d1〉 where ak represents the sub signal of k-th level generated by the low-pass filter associated to the discrete wavelet transform (DWT) chosen, and dk the sub signal of k-th level generated by the high-pass filter associated to the same DWT. It is applied basically the Haar, Daub4 and Coiflet wavelets transforms. Indeed, the sub signal am cumulates the energy, for this work of order 96% of the original signal ψ. A thresholding algorithm provides treatment for the noise, with significant reduction in the compressed signal. Then, it is established a comparison with a base of data in order to identify the perturbed signal. After the identification, it is recomposed the signal applying the inverse DWT. Many assumptions can be established: the rate signal-to-noise is properly high, the base of data must contain so many perturbed signals all with the same level of compression. The problem considered is for perturbations in the signal. For measurements the problem is similar, but in this case the unknown perturbations are generated by the apparatus of measurements, problems in experimental techniques, or simply by random noises. With the same above assumptions, the DWT is applied. For the identification, it is used a method evolving statistical and metric techniques. It is given some results obtained with an algebraic computer system.

scholarly journals Technical Vision System for in-Room Access Control

2021 ◽  
Vol 4 (4) ◽  
Author(s):  
Artem Ihorovych Fironov ◽  
Vitaliy Viktorovych Levchenko
Keyword(s):  
Face Recognition ◽  
Wavelet Transform ◽  
Standard Deviation ◽  
Access Control ◽  
Discrete Wavelet Transform ◽  
Output Signal ◽  
Discrete Wavelet ◽  
Pass Filter ◽  
Technical Vision ◽  
Speed Up

Access systems with face recognition is widely used today. They are used in many enterprises and institutes where it is necessary to control the flow of passing people.  Facially recognizable technical vision systems are important because they can be used to store specific individuals faces and use them for access control. As a result of analysis of same modern systems the variant of system there are additional functions is offered. The system consists of ESP-EYE module, with build-in wi-fi and Bluetooth modules, chip sensor camera “ OV2640” and LED display, which dasplays a notification for a person about granting or denying access, notifications are in two collors: geen and red respectively.. Also it has an emergency power supply in case of unforeseen situations. Wi-fi is used as a means of transmiting data from camera to the server. This transmition method of data transmition has several advantages over Bluetooth. It allows to the system to transfer data at a much higher speed and over a grater distance, it is also more secure, provides access to the internet and allows to control the system  remotely. All the listed advantages of this method of transmition give us a great variability in the operation and placement of the system. To recognize people system use a comparison method. It compares the person’s face with a database and, after processing it produces the result. To optimize and speed up this process, the system uses a method of image compression based on discrete wavelet transform. This method is the transmission of a signal through several filtres, usualy two. First, the signal is passed through a low-pass filter whis a pulse response g, resulting in an output signal in the form of a convolutional sum. At the same time the signal is decomposed by a high pass filter. The LPF gives an approximate shape of the output signal, and the HPF – the signal of difference or additional detail. Discrete wavelet transform in an oriented basis makes it possible to construct transformation matrices with a given number of filters ”m”, where “m” is in the general case a prime positive number. The simplest way to compare the two images is by substracting the brightness values of the two matrices and estimating the resulting matrix of differences using standard deviation. The use of standard deviation in combination with fiberboard in OB allows to speed up the process of face recognition in the system by discarding unncessary details, the absence of which minimaly harms the accuracy of the results. The advantages of this system are that it is less expensive, in compareson with existing analogs, less energy-consuming, easy to assemble and install, uses a relatively simple and at the same time quite accurate method of identidying a persons identity.

scholarly journals Wavelet Transform as an Alternative to Power Transformation in Time Series Analysis

2016 ◽  
Vol 17 ◽  
pp. 57-74
Author(s):  
Chukwudi Justin Ogbonna ◽  
C. Jeol Nweke ◽  
Eleazer C. Nwogu ◽  
Iheanyi Sylvester Iwueze
Keyword(s):  
Time Series ◽  
Exchange Rate ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Goodness Of Fit ◽  
Discrete Wavelet ◽  
Power Transformation ◽  
Rate Data ◽  
Forecast Performance ◽  
Constant Variance

This study examines the discrete wavelet transform as a transformation technique in the analysis of non-stationary time series while comparing it with power transformation. A test for constant variance and choice of appropriate transformation is made using Bartlett’s test for constant variance while the Daubechies 4 (D4) Maximal Overlap Discrete Wavelet Transform (DWT) is used for wavelet transform. The stationarity of the transformed (power and wavelet) series is examined with Augmented Dickey-Fuller Unit Root Test (ADF). The stationary series is modeled with Autoregressive Moving Average (ARMA) Model technique. The model precision in terms of goodness of fit is ascertained using information criteria (AIC, BIC and SBC) while the forecast performance is evaluated with RMSE, MAD, and MAPE. The study data are the Nigeria Exchange Rate (2004-2014) and the Nigeria External Reserve (1995-2010). The results of the analysis show that the power transformed series of the exchange rate data admits a random walk (ARIMA (0, 1, 0)) model while its wavelet equivalent is adequately fitted to ARIMA (1,1,0). Similarly, the power transformed version of the External Reserve is adequately fitted to ARIMA (3, 1, 0) while its wavelet transform equivalent is adequately fitted to ARIMA (0, 1, 3). In terms of model precision (goodness - of - fit), the model for the power transformed series is found to have better fit for exchange rate data while model for wavelet transformed series is found to have better fit for external reserve data. In forecast performance, the model for wavelet transformed series outperformed the model for power transformed series. Therefore, we recommend that wavelet transform be used when time series data is non-stationary in variance and our interest is majorly on forecast.

scholarly journals The Shift Invariant Discrete Wavelet Transform (SIDWT) with Inflation Time Series Application

2016 ◽  
Vol 8 (4) ◽  
pp. 14
Author(s):  
Suparti Suparti ◽  
Rezzy Eko Caraka ◽  
Budi Warsito ◽  
Hasbi Yasin
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Well Being ◽  
Discrete Wavelet ◽  
Time Series Modeling ◽  
The Government ◽  
Determining Factor ◽  
Analysis Of Time Series ◽  
Economic Well Being

<p>Analysis of time series used in many areas, one of which is in the field economy. In this research using time series on inflation using Shift Invariant Discrete Wavelet Transform (SIDWT).Time series decomposition using transformation wavelet namely SIDWT with Haar filter and D4. Results of the transformation, coefficient of drag coefficient wavelet and scale that is used for modeling time series. Modeling done by using Multiscale Autoregressive (MAR). In a certain area, inflation to it is an important that he had made the standard-bearer of economic well-being of society, the factors Directors investors in selecting a kind of investment, and the determining factor for the government to formulate policy fiscal, monetary, as well as non-monetary that will be applied. Inflation can be analyzed using methods Shift Invariant Discrete Wavelet Transform (SIDWT) which had been modeled for them to use Mulitiscale Autoregressive (MAR) with the R2 value 93.62%.</p>

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