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Detection of Epileptic Seizures from EEG Data
Published in Narayan Panigrahi, Saraju P. Mohanty, Brain Computer Interface, 2022
Narayan Panigrahi, Saraju P. Mohanty
In the DWT, the frequency axis is divided into dyadic intervals towards the lower frequencies, while the bandwidth length decreases exponentially. The wavelet packet (WP) transform is a generalization of the DWT in which decomposition is undertaken in both directions (lower and higher frequencies). This general decomposition offers a greater range of possibilities for signal analysis than the discrete wavelet decomposition. In the WP tree, each node is recognized by the decomposition level (scale) l with respect to the WP tree root and the frequency band f. The ability of the wavelet transform in adaptive time-scale representation and decomposition of a signal into different frequency sub-bands presents an efficient signal analysis method without introducing a calculation burden. Based on wavelet coefficients obtained after the wavelet transform, the signal can be reconstructed in each of the previously derived sub-bands and its time-domain features in different sub-bands can be studied separately.
Frequency Domain Analysis
Published in Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala, Digital and Statistical Signal Processing, 2018
Anastasia Veloni, Nikolaos I. Miridakis, Erysso Boukouvala
If a time-series is stationary, it is reasonable to assume that its harmonic components can be detected by means of Fourier analysis, e.g., using DFT. Nevertheless, in various practical applications, it became evident that many time-series are not stationary (i.e., their mean statistical properties change in time). The waves of infinite support that form the harmonic components are not adequate in such a case, whereas waves localized not only in frequency but in time are required, as well. These waves are generally known as wavelets and allow a time-scale decomposition of a signal. The Discrete Wavelet Transform (DWT) is used in a variety of signal processing applications, such as video compression, Internet communications compression, and numerical analysis. It can efficiently represent non-stationary signals.
Wavelet and pattern trends based co-occurrence features for age group classification of a facial image
Published in Amir Hussain, Mirjana Ivanovic, Electronics, Communications and Networks IV, 2015
The word wavelet is due to Morlet and Grossmann in the early 1980s. Today wavelets play a significant role in Astronomy, Acoustics, Nuclear Engineering, Subband Coding, Signal and Image Processing (Zhao et al. 2003), Neurophysiology, Music, Magnetic Resonance Imaging, Speech Discrimination, Optics, Turbulence, Earthquake Prediction, Radar, Computer and Human Vision, Data Mining and Pure Mathematics Applications such as Solving Partial Differential Equations etc. The most commonly used transforms are the DCT, DFT, DWT, DLT and DHT. The present paper adopted DWT techniques to achieve better performance. DWT is a powerful tool of signal and image processing that have been successfully used in many scientific fields such as signal processing, image compression, image segmentation, computer graphics, and pattern recognition. The DWT based algorithms, has been emerged as another efficient tool for image processing, mainly due to its ability to display image at different resolutions and to achieve higher compression ratio. Haar wavelet is one of the oldest and simplest wavelet. Therefore, any discussion of wavelets starts with the Haar wavelet. The Haar, Daubechies, Symlets and Coiflets are compactly supported orthogonal wavelets.
An efficient scheme for the detection of defective parts in fabric images using image processing
Published in The Journal of The Textile Institute, 2023
Toqeer Mahmood, Rehan Ashraf, C. M. Nadeem Faisal
Feature extraction from defective and non-defective fabric is the most important factor. It is the preliminary step for feature recognition that directly affects the performance of the automated systems. The dominant features extracted from defective fabric directly affect the results of the systems. Therefore, high-quality features improve the reliability of the automatic fabric defect detection scheme. In the proposed system, the fabric images for defect detection are firstly processed through the discrete wavelet transform (DWT). In computer vision, DWT is applied in many different applications like texture analysis, object detection, remote sensing, and many more (Ashraf et al., 2020; Gangal et al., 2014; Tabassum et al., 2022). In image processing and computer vision schemes, the DWT generates the transformation value called the wavelet coefficients. The DWT algorithm is employed in this proposed research because it is pertinent for non-stationary and varies for spatial ranges. The DWT decomposes digital input image into the low-pass band (L) and the high-pass band (H). The low-pass band (L) is the approximation of the input image, and the high-pass channels (H) are the high-recurrence elements containing the edge information of the input image. The DWT can be applied to digital images by different wavelet types like Haar, Morlet, Daubechies, and many others. However, we employed Daubechies wavelet to apply DWT as described in Figure 2. The three-level decomposition of an image using DWT is shown in Figure 3.
LabView based virtual calorimetric etching solution analyzer (CESA) for the online quantification of hydrogen peroxide for the semiconductor industry
Published in Instrumentation Science & Technology, 2022
Roumen Zlatev, Rogelio Ramos, Margarita Stoytcheva, Benjamín Valdez, Mario Curiel
The main objective of this section is the noise elimination/suppression in the registered temperature versus time curve by the application of the discrete wavelet transform (DWT) applying the denoise function of the LV.[26–29] Noise reduction is needed because of sample dilution which allows reduction of the measuring time and higher sample temperature influence decrease but lowering the analytical response and the signal to noise ratio. However, the digital signal processing based on DWT application facilitates the precise wave slope determination and the precise H2O2 concentration even for low H2O2 concentrations. The main advantages of DWT are maintaining the shape, the slope and the amplitude of the raw (“noisy”) curve as well as the preventing of the curve displacement over the x axis. The maintenance of the real slope is important for the precision in case of its employment as analytical response. Unlike the fast Fourier transform (FFT), where the signal is represented by sine and cosine functions, the signal in DWT is represented as transient functions of short duration, centered on a specific point in time. One of the advantages of DWT is its operation with stationary and non-stationary signals, as well as in time and frequency ranges.[27–29]
Degenerate unmixing estimation technique of speech mixtures in real environments using wavelets
Published in International Journal of Electronics Letters, 2020
Shahin M. Abdulla, J. Jayakumari
Dual-tree complex wavelet transform (DTCWT) (Ivan, Baranuik, & Kingsbury, 2005) was utilised for analysing the signals. DWT is being used as an alternative for short-time Fourier transform to overcome the difficulties encountered with respect to its time and frequency resolution characteristics. The short-time Fourier transform produces uniform resolutions for all frequencies whereas the DWT provides low time resolution for high frequencies and high time resolution for low frequencies (Torkkola, 1996). Complex wavelet transform (CWT) (Ivan et al., 2005) is actually a complex-valued appendage of standard DWT. Real and imaginary parts in the transform domain are obtained by decomposing CWT. We get the amplitude and phase data from the coefficients of real and imaginary parts. With the help of two separate DWT decomposition, Discrete Time Wavelet Transform calculates the complex transforms of the signal. We can find the DTWT of input signal by