The Continuous Wavelet Transform and Variable Resolution Time–Frequency Analysis
نویسندگان
چکیده
Wavelet transforms have recently emerged as a mathematical tool for multiresolution decomposition of signals. They have potential applications in many areas of signal processing that require variable time–frequency localization. The continuous wavelet transform is presented here, and its frequency resolution is derived analytically and shown to depend exclusively on one parameter that should be carefully selected in constructing a variable resolution time–frequency distribution for a given signal. Several examples of application to synthetic and real data are shown. (
منابع مشابه
Wavelet Transformation
Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation. Introduction: The...
متن کاملA Variable Resolution transform for music analysis
This paper presents a novel music representation using a Variable Resolution Transform (VRT) which is particularly well adapted for music audio analysis. The VRT is inspired by continuous wavelet transform and it applies different wavelet function at different scale. This method enables a good flexibility of the transform in order to follow log scale of musical note frequencies and at the same ...
متن کاملProposing New Methods to Enhance the Low-Resolution Simulated GPR Responses in the Frequency and Wavelet Domains
To date, a number of numerical methods, including the popular Finite-Difference Time Domain (FDTD) technique, have been proposed to simulate Ground-Penetrating Radar (GPR) responses. Despite having a number of advantages, the finite-difference method also has pitfalls such as being very time consuming in simulating the most common case of media with high dielectric permittivity, causing the for...
متن کاملRobust S-transform based on L-DFT
Introduction: Time-frequency representations (TFRs) indicate variations of the signal spectral characteristics with time, and they are the natural choice as an analysis tool for the non-stationary signals [1]. The main objectives of the various types of time-frequency distribution functions (e.g. Wigner-Ville distribution (WVD) [1], short-time Fourier transform (STFT) [1], the S-transform [2]) ...
متن کاملSynchrosqueezing Transform for High Resolution Time-Frequency Analysis of Shock and Vibration Measurements
This article presents the use of the synchrosqueezing transform (SST) for the timefrequency analysis of shock and vibration measurements. The time-frequency resolution properties of SST is demonstrated by analyzing acceleration measurements from pallets dropped from heights and vibration of pallets acquired in controlled laboratory settings. The article presents results that indicate that SST, ...
متن کامل