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A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic…

Classical Analysis and ODEs · Mathematics 2016-03-24 H. M. de Oliveira , L. R. Soares , T. H. Falk

Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.

Functional Analysis · Mathematics 2010-09-01 Wenchang Sun

In this paper we propose spectral tools based on non-decimated complex wavelet transforms implemented by their matrix formulation. This non-decimated complex wavelet spectra utilizes both real and imaginary parts of complex-valued wavelet…

Applications · Statistics 2019-02-05 Taewoon Kong , Brani Vidakovic

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,…

Sound · Computer Science 2025-10-31 Rinku Sebastian , Simon O'Keefe , Martin Trefzer

In this paper we consider the continuous wavelet transform using Gaussian wavelets multiplied by an appropriate rational term. The zeros and poles of this rational modifier act as free parameters and their choice highly influences the shape…

Machine Learning · Statistics 2026-01-30 Attila Miklós Ámon , Kristian Fenech , Péter Kovács , Tamás Dózsa

The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet…

Instrumentation and Methods for Astrophysics · Physics 2021-08-06 Yun Wang , Ping He

This paper describes a method for decomposing steady-state instrument data into excitation and formant filter components. The input data, taken from several series of recordings of acoustical instruments is analyzed in the frequency domain,…

Sound · Computer Science 2007-05-23 Ilia Bisnovatyi , Michael J. O'Donnell

Cochlear wavenumber and impedance are mechanistic variables that encode information regarding how the cochlea works - specifically wave propagation and Organ of Corti dynamics. These mechanistic variables underlie interesting features of…

Quantitative Methods · Quantitative Biology 2024-07-02 Samiya A Alkhairy

In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the…

Functional Analysis · Mathematics 2007-05-23 Ola Bratteli , Palle E. T. Jorgensen

This paper provides new insights into the problem of selecting filter center frequencies for the auditory filterbanks. We propose to use a constant frequency distance and a consistent frequency coverage as the two metrics that motivate the…

Audio and Speech Processing · Electrical Eng. & Systems 2018-01-03 Shoufeng Lin

To date, various speech technology systems have adopted the vocoder approach, a method for synthesizing speech waveform that shows a major role in the performance of statistical parametric speech synthesis. WaveNet one of the best models…

Sound · Computer Science 2021-06-15 Mohammed Salah Al-Radhi , Tamás Gábor Csapó , Csaba Zainkó , Géza Németh

The influence of higher-order wavelet properties on the analytic wavelet transform behavior is investigated, and wavelet functions offering advantageous performance are identified. This is accomplished through detailed investigation of the…

Methodology · Statistics 2011-10-18 J. M. Lilly , S. C. Olhede

We present SoundMorpher, an open-world sound morphing method designed to generate perceptually uniform morphing trajectories. Traditional sound morphing techniques typically assume a linear relationship between the morphing factor and sound…

Sound · Computer Science 2024-12-17 Xinlei Niu , Jing Zhang , Charles Patrick Martin

This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…

Data Analysis, Statistics and Probability · Physics 2016-09-08 Pierre Argoul , Silvano Erlicher

An analysis of the sensitivity of gaussian and mexican hat wavelet family filters to the detection of point sources of ultra-high energy cosmic rays was performed. A source embedded in a background was simulated and the number of events and…

Instrumentation and Methods for Astrophysics · Physics 2012-03-26 Rafael Alves Batista , Ernesto Kemp , Bruno Daniel

In the realm of signal processing, frequency and spectrum detection are fundamental tasks that can be computationally intensive. This project leverages the power of FPGAs to perform wavelet analysis on an input signal. The goal is to detect…

Hardware Architecture · Computer Science 2024-12-31 Caleb Hill , Darshika G. Perera

We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random…

Functional Analysis · Mathematics 2021-11-02 Harry Sevi , Gabriel Rilling , Pierre Borgnat

In recent years, correntropy has been seccessfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two…

Signal Processing · Electrical Eng. & Systems 2021-11-02 Badong Chen , Yuqing Xie , Zhuang Li , Yingsong Li , Pengju Ren

Heart murmurs are abnormal sounds caused by turbulent blood flow in the heart. Several diagnostic methods are available to detect heart murmurs and their severity, including cardiac auscultation, echocardiography, and phonocardiography…

Signal Processing · Electrical Eng. & Systems 2026-05-12 Md Jobayer , Md. Mehedi Hasan Shawon , Md Zakir Hossain , Shreya Ghosh , Imre Rudas , Tom Gedeon , Md Rakibul Hasan

Phase processing has been replaced by group delay processing for the extraction of source and system parameters from speech. Group delay functions are ill-behaved when the transfer function has zeros that are close to unit circle in the…

Sound · Computer Science 2016-03-18 Rajeev Rajan , Hema A. Murthy