Power Spectral Density (PSD) of quasi-stationary processes can be efficiently estimated using the short time Fourier series (STFT). In this paper, an algorithm has been proposed that computes the PSD of quasi-stationary process efficiently using offline autoregressive model order estimation algorithm, recursive parameter estimation technique and modified sliding window discrete Fourier Transfor...

Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are “multidimensional” and have directional characteristics along each factor graph. However, the existing graph Fourier transform does not distinguish these directions, and assigns 1-D spectra to signals on product graphs. Furthe...

Harmonic analysis studies the representation of functions as the linear combination of basic wave-like functions. It plays a fundamental role in the processing of time-series signals and images. Recent years have witnessed many efforts to adapt the Fourier and wavelet analysis to the domain of 3D shapes. The manifold Fourier analysis relies on the eigenfunctions of the Laplace-Beltrami operator...

the s-transform has widely been used in the analysis of non-stationary time series. a simple method to obtain depth estimates of gravity field sources is introduced in this study. we have developed a new method based on the spectral characteristics of downward continuation to estimate depth of structures. this calculation procedure is based on replacement of the fourier transform with the s-tra...

In addition to their inestimable importance in mathematics and its applications, Fourier series also serve as the entry point into the wonderful world of Fourier analysis and its wide-ranging extensions and generalizations. An entire industry is devoted to developing the theory and enlarging the scope of applications of Fourier–inspired methods. New directions in Fourier analysis continue to be...

In this paper, a new mathematical model of a Kelvin-Voigt type thermo-visco-elastic, infinite thermally conducting medium has been considered in the context of a new consideration of heat conduction having a non-local fractional order due to the presence of periodically varying heat sources. Three-phase-lag thermoelastic model, Green Naghdi models II and III (i.e., the models which predicts the...

In this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi mod...

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...

– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...

– Fourier transform used to analyze signals by converting signals into a continuous series of sine and cosine functions, each with a constant frequency and amplitude, and of infinite duration – Real world signals (images) have a finite duration and exhibit abrupt changes in frequency – Wavelet transform converts a signal into a series of wavelets – In theory, signals processed by wavelets can b...