in exploration seismology quality factor is widely used as a seismic attribute to identify anomalies related to attenuation, especially those caused by hydrocarbon. previous studies have indicated that seismic energy loss known as attenuation is greater for high frequency components of seismic data compared to the low frequency components. here the continuous wavelet transform is used to study ...

In this paper we present a new form of wavelet transform. Unlike the continuous wavelet transform (CWT) or discrete wavelet transform (DWT), the mother wavelet is chosen to be a discrete-time signal and wavelet coefficients are computed by correlating a given discrete-time signal with continuous dilations of the mother wavelet. The results developed are based on the definition of a discrete-tim...

In this paper, formulas relating the Radon transform and Radon transform inversion to various wavelet and multiscale transformations, including the continuous wavelet transform, the semi{continuous wavelet transform of Mallat, steerable multiscale lters of Freeman and Adelson, and separable orthogonal and non{orthogonal wavelet bases, are given. The use of wavelets as a valuable tool in the loc...

Discrete wavelet transform (DWT) is computed by subband lters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of the improper initialized discretization of the continuous-time signal. In this paper, the problem is analyzed and two simple algorithms for the initialization are introduced. Finally, numeric...

Discrete wavelet transform (DWT) is computed by subband lters bank and often used to approximate wavelet series (WS) and continuous wavelet transform (CWT). The approximation is often inaccurate because of the improper initialized discretization of the continuous-time signal. In this paper, the problem is analyzed and two simple algorithms for the initialization are introduced. Finally, numeric...

In 1992 Unser and colleagues proved that the sequence of normalized and scaled B-splines Bm tends to the Gaussian function as the order m increases, [1]. In this article the result of Unser et al. is extended to the derivatives of the B-splines. As a consequence, a certain sequence of wavelets defined by B-splines, tends to the famous Mexican hat wavelet. Another consequence can be observed in ...

The analysis of EEG signals plays a vital role in the detection of Seizure. The EEG signal of a normal person varies when compared to that of a seizure affected person. A new wavelet is created which closely represents a normal EEG wave. The discrete wavelet transform using the new wavelet family is applied to the input EEG signals. Since the new wavelet represents the normal EEG wave pattern t...

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) x J&, embedded into the Lorentz group S00(3, 1) via the Iwasawa decomposition, and X Y SO,(3,1)/C. The space L2(S2, a!~) carries a unitary irreduci...

In this paper we present an overview of wavelet based multiresolution analyses. First, we brie y discuss the continuous wavelet transform in its simplest form. Then, we give the de nition of a multiresolution analysis and show how wavelets t into it. We take a closer look at orthogonal, biorthogonal and semiorthogonal wavelets. The fast wavelet transform, wavelets on an interval, multidimension...

We present a computational method for pattern discovery based on the application of the wavelet transform to symbolic representations of melodies or monophonic voices. We model the importance of a discovered pattern in terms of the compression ratio that can be achieved by using it to describe that part of the melody covered by its occurrences. The proposed method resembles that of paradigmatic...