New Dimensions in Wavelet Analysis
نویسندگان
چکیده
In this paper we propose a new class of signal analysis tools that generalizes the popular wavelet and short-time Fourier transforms. The class allows skews and rotations of the analyzing wavelet in the time-frequency plane, in addition to the time and frequency translations and scalings employed by conventional transforms. In addition to providing a unifying framework for studying existing time-frequency representations , the general class provides a systematic method for designing new representations with properties useful for certain types of signals.
منابع مشابه
A unified theoretical harmonic analysis approach to the cyclic wavelet transform (CWT) for periodic signals of prime dimensions
The article introduces cyclic dilation groups and finite affine groups for prime integers, and as an application of this theory it presents a unified group theoretical approach for the cyclic wavelet transform (CWT) of prime dimensional periodic signals.
متن کاملNumerical solution of optimal control problems by using a new second kind Chebyshev wavelet
The main purpose of this paper is to propose a new numerical method for solving the optimal control problems based on state parameterization. Here, the boundary conditions and the performance index are first converted into an algebraic equation or in other words into an optimization problem. In this case, state variables will be approximated by a new hybrid technique based on new second kind Ch...
متن کاملApplications of Fractal and Wavelet to Feature Extraction
Within this paper a new feature extraction techniques is presented which uses wavelet analysis and fractal theory for image recognition. The proposed method reduces the dimensionality of a twodimensional pattern by way of a central projection approach, and thereafter, performs Daubechies' wavelet transformation on the derived one-dimensional pattern to generate a set of wavelet transformation s...
متن کاملIsogeometric analysis: vibration analysis, Fourier and wavelet spectra
This paper presents the Fourier and wavelet characterization of vibratio...
متن کاملWavelet-based Analysis for Pulse Period of Earthquake Ground-motions
Pulse period of earthquake records has been known as a key parameter in seismology and earthquake engineering. This paper presents a detailed characterization of this parameter for a special class of earthquake records called pulse-like ground motions. This type of motions often resulting from directivity effects is characterized by a strong pulse in the velocity time history of motion, in norm...
متن کاملApplication of Convolution of Daubechies Wavelet in Solving 3D Microscale DPL Problem
In this work, the triple convolution of Daubechies wavelet is used to solve the three dimensional (3D) microscale Dual Phase Lag (DPL) problem. Also, numerical solution of 3D time-dependent initial-boundary value problems of a microscopic heat equation is presented. To generate a 3D wavelet we used the triple convolution of a one dimensional wavelet. Using convolution we get a scaling function ...
متن کامل