Harmonic wavelet transform

About: Harmonic wavelet transform is a research topic. Over the lifetime, 9602 publications have been published within this topic receiving 247336 citations.

A Comparison of the Existence of "Cross Terms" in the Wigner Distribution and the Squared Magnitude of the Wavelet Transform and the Short Time

Abstract: The wavelet transform (WT), a time-scale repre- sentation, is linear by definition. However, the nonlinear en- ergy distribution of this transform is often used to represent the signal; it contains ''cross terms" which could cause prob- lems while analyzing multicomponent signals. In this paper, we show that the cross terms that exist in the energy distribution of the WT are comparable with those found in the Wigner dis- tribution (WD), a quadratic time-frequency representation, and the energy distribution of the short time Fourier transform (STFT), of closely spaced signals. The cross terms of the WT and the STFT energy distributions occur at the intersection of their respective WT and STFT spaces, while for the WD they occur midtime and midfrequency. The parameters of the cross terms are a function of the difference in center frequencies and center times of the perpended signals. The amplitude of these cross terms can be as large as twice the product of the magni- tudes of the transforms of the two signals in question in all three cases. In this paper, we consider the significance of the effect of the cross terms on the analysis of a multicomponent signal in each of these three representations. We also compare the advantages and disadvantages of all of these methods in appli- cations to signal processing.

A comparison of the existence of 'cross terms' in the Wigner distribution and the squared magnitude of the wavelet transform and the short-time Fourier transform

Abstract: It is shown that cross terms comparable to those found in the Wigner distribution (WD) exist for the energy distributions of the wavelet transform (WT) and the short-time Fourier transform (STFT). The geometry of the cross terms is described by deriving mathematical expressions for the energy distributions of the STFT and the WT of a multicomponent signal. From those mathematical expressions it is inferred that the STFT and the WT cross terms: (1) occur at the intersection of the respective transforms of the two signals under consideration, whereas the WD cross terms occur at mid-time-frequency of the two signals; (2) are oscillatory in nature, as are the WD cross terms, and are modulated by a cosine whose argument is a function of the difference in center times and center frequencies of the signals under consideration; and (3) can have a maximum amplitude as large as twice the product of the magnitude of the transforms of the two signals in question, like WD cross terms. It is shown that the presence of these cross terms could lead to problems in analyzing a multicomponent signal. The consequences of this effect with respect to speech applications are discussed. >

Wavelets and their Applications

Abstract: Contributions discuss signal analysis discrete-time signal processing, wavelets for Quincunx pyramid, transform maxima and multiscale edges, among other topics; numerical analysis; other applications the optical wave transform, continuous wavelet transform, quantum mechanics; and theoretical develop

Medical image enhancement algorithm based on wavelet transform

Abstract: Low contrast and poor quality are main problems in the production of medical images. By using the wavelet transform and Haar transform, a novel image enhancement approach is proposed. First, a medical image was decomposed with wavelet transform. Secondly, all high-frequency sub-images were decomposed with Haar transform. Thirdly, noise in the frequency field was reduced by the soft-threshold method. Fourthly, high-frequency coefficients were enhanced by different weight values in different sub-images. Then, the enhanced image was obtained through the inverse wavelet transform and inverse Haar transform. Lastly, the image's histogram was stretched by nonlinear histogram equalisation. Experiments showed that this method can not only enhance an image's details but can also preserve its edge features effectively.