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Wastewater surveillance has emerged as a critical public health tool, enabling early detection of infectious disease outbreaks and providing timely, population-level insights into community health trends. However, variability in sample…

A program WWZ is introduced, which realizes the wavelet analysis using an improved modification of the algorithm of the Morlet wavelet for a general case of irregularly spaced data, which is typical for the databases available in virtual…

This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…

This paper presents an epilepsy detection method based on discrete wavelet transform (DWT) and Machine learning classifiers. Here DWT has been used for feature extraction as it provides a better decomposition of the signals in different…

Continuous wavelet design is the endeavor to construct mother wavelets with desirable properties for the continuous wavelet transform (CWT). One class of methods for choosing a mother wavelet involves minimizing a functional, called the…

Extracting features from the speech is the most critical process in speech signal processing. Mel Frequency Cepstral Coefficients (MFCC) are the most widely used features in the majority of the speaker and speech recognition applications,…

The problem of known signal detection in Additive White Gaussian Noise is considered. In this paper a new detection algorithm based on Discrete Wavelet Transform pre-processing and threshold comparison is introduced. Current approaches…

This note develops the first-ever noise-centric anomaly prediction method for a fused discrete-time signal. A Wavelet Packet Transform (WPT) provides a time--frequency expansion in which structure and residual can be separated via…

Many phenomena are described by bivariate signals or bidimensional vectors in applications ranging from radar to EEG, optics and oceanography. The time-frequency analysis of bivariate signals is usually carried out by analyzing two separate…

We propose a statistical tool to compare the scaling behaviour of turbulence in pairs of molecular cloud maps. Using artificial maps with well defined spatial properties, we calibrate the method and test its limitations to ultimately apply…

We present a construction of isotropic boundary adapted wavelets, which are orthogonal and yield a multi-resolution analysis. We analyze direct numerical simulation data of turbulent channel flow computed at a friction Reynolds number of…

This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…

In nature and engineering world, the acquired signals are usually affected by multiple complicated factors and appear as multicomponent nonstationary modes. In such and many other situations, it is necessary to separate these signals into a…

The dual-tree complex wavelet transform (DTCWT) is an enhancement of the conventional discrete wavelet transform (DWT) due to a higher degree of shift-invariance and a greater directional selectivity, finding its applications in signal and…

In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…

Gravitational wave astronomy relies on the use of multiple detectors, so that coincident detections may distinguish real signals from instrumental artifacts, and also so that relative timing of signals can provide the sky position of…

Both of Wavelet and Fast Fourier Transform are strong signal processing tools in the field of Data Analysis. In this paper fast fourier transform (FFT) and Wavelet Transform are employed to observe some important features of Solar image…

The wavelet transform has been used for numerous studies in astrophysics, including signal--noise periodicity and decomposition as well as the signature of differential rotation in stellar light curves. In the present work, we apply the…

Some recent methods, like the Empirical Mode Decomposition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is…

This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…