The discrete fractional Fourier transform (DFRFT) is the generalization of discrete Fourier transform. Many types of DFRFT have been derived and are useful for signal processing applications. In this paper, we will introduce a new type of DFRFT, which are unitary, reversible, and flexible; in addition, the closed-form analytic expression can be obtained. It works in performance similar to the c...

We introduce a fast simple method for computing the real continuous wavelet transform (CWT). The approach achieves O N ( ) complexity per scale and the filter coefficients can be analytically obtained by a simple integration. Our method is to use P wavelets per octave and to approximate them with their oblique projection onto a space defined by a compact scaling function. The wavelet templates ...

The multiscale analysis of potential fields is a valid tool to study the source properties. Among multiscale methods, the Continuous Wavelet Transform (CWT) is well established due to its natural filtering properties. From the beginning the choice of the analyzing wavelet has been the set belonging to the Poisson kernel: within this framework the CWT can be easily performed by upward continuing...

We present a purely group-theoretical derivation of the continuous wavelet transform (CWT) on the (n ? 1)-sphere S n?1 , based on the construction of general coherent states associated to square integrable group representations. The parameter space of the CWT, Y SO(n)R + , is embedded into the generalized Lorentz group SO o (n; 1) via the Iwasawa decomposition, so that X ' SO o (n; 1)=N, where ...

In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWTMOFrFT. Four mod...

The continuous wavelet transform (CWT) can be seen as a filterbank having logarithmic frequency subbands spacing similar to the human auditory system. Thus, to make computers imitate the significant functions of the human auditory system, one promising approach would be to model, analyze and process magnitude spectrograms given by the CWT. To realize this approach, we must be able to convert a ...

An advanced continuous wavelet transform technique has been developed to automatically analyze photomechanics interferograms. This technique utilizes all possible wavelets to match the local interferogram fringes, and it can automatically detect local fringe frequencies and orientations with high accuracies. The advanced wavelet transform technique has the capability to directly determine gradi...

• wavelets are analysis tools for time series and images • as a subject, wavelets are − relatively new (1983 to present) − a synthesis of old/new ideas − keyword in 29, 826+ articles and books since 1989 (4032 more since 2005: an inundation of material!!!) • broadly speaking, there have been two waves of wavelets − continuous wavelet transform (1983 and on) − discrete wavelet transform (1988 an...

We survey the construction of the continuous wavelet transform (CWT) on the two-sphere. Then we discuss the discretization of the spherical CWT, obtaining various types of discrete frames. Finally we give some indications on the construction of a CWT on other conic sections.

Unsupervised boundary detection and classification is both a theoretically interesting question and an important challenge for speech technology. Theoretical interest lies in exploring how and to what extent is the boundary information encoded in purely acoustic material. For technology, automatic boundary detection facilitates cheap and fast labeling of large corpora of speech data. In this wo...