Fe b 20 07 New physical wavelet ’ Gaussian Wave Packet
نویسندگان
چکیده
An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother wavelet for the CWA. Both the wavelet and its Fourier transform are given by explicit formulas and are exponentially localized. The wavelet is directional. The widths of the wavelet and the uncertainty relation are investigated numerically. If a certain parameter is large, the wavelet behaves asymptotically as the Morlet wavelet. The solution is a new physical wavelet in the definition of Kaiser, it may be interpreted as a sum of two parts: an advanced and a retarded part, both being fields of a pulsed point source moving at a speed of wave propagation along a straight line in complex space-time.
منابع مشابه
New physical wavelet ’ Gaussian Wave Packet ’
An exact solution of the homogeneous wave equation which was found previously is treated from the point of view of the continuous wavelet analysis (CWA). Time being a fixed parameter the solution yields a new multidimensional mother wavelet for the CWA. Both the wavelet and its Fourier transform are given with explicit formulas and are exponentially localized. The wavelet is directional. The wi...
متن کاملWavelet-Based Estimation Procedures for Seasonal Long-Memory Models
Motivation • Seasonal long memory is gaining attention as a time series model in econometrics and the physical sciences. { Arteche and Robinson (2000) proposed log-periodogram regression and Gaussian semi-parametric estimation for seasonal long-memory processes. • The discrete wavelet transform (DWT) is a useful alternative to the discrete Fourier transform for the analysis and synthesis of lon...
متن کاملA New Algorithm for Voice Activity Detection Based on Wavelet Packets (RESEARCH NOTE)
Speech constitutes much of the communicated information; most other perceived audio signals do not carry nearly as much information. Indeed, much of the non-speech signals maybe classified as ‘noise’ in human communication. The process of separating conversational speech and noise is termed voice activity detection (VAD). This paper describes a new approach to VAD which is based on the Wavelet ...
متن کاملNecessary Conditions of the Wave Packet Frames with Several Generators
The main goal of this paper is to consider the necessary conditions of wave packet systems to be frames in higher dimensions. The necessary conditions of wave packet frames in higher dimensions with several generators are established, which include the corresponding results of wavelet analysis and Gabor theory as the special cases. The existing results are generalized to the case of several gen...
متن کاملSynchrosqueezed wave packet transforms and diffeomorphism based spectral analysis for 1D general mode decompositions
This paper develops new theory and algorithms for 1D general mode decompositions. First, we introduce the 1D synchrosqueezed wave packet transform and prove that it is able to estimate instantaneous information of well-separated modes from their superposition accurately. The synchrosqueezed wave packet transform has a better resolution than the synchrosqueezed wavelet transform in the time-freq...
متن کامل