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.

Improved fast fractional-Fourier-transform algorithm.

Abstract: Through the optimization of the main interval of the fractional order, an improved fast algorithm for numerical calculation of the fractional Fourier transforms is proposed. With this improved algorithm, the fractional Fourier transforms of a rectangular function and a Gaussian function are calculated. Its calculation errors are compared with those calculated with the previously published algorithm, and the results show that the calculation accuracy of the improved algorithm is much higher.

Metrological characteristics of dual-tree complex wavelet transform for surface analysis

Abstract: The metrological characteristics of a newly developed dual-tree complex wavelet transform (DT-CWT) for surface analysis are investigated, especially on the aspect of transmission characteristics analysis. The property of zero/linear phase by the DT-CWT ensures filtering results with no distortion and good ability for feature localization. Due to the 'steep transmission curve' property of the amplitude transmission characteristic, the DT-CWT can separate different frequency components efficiently. Both computer simulation and experimental results of practical surface 2D/3D filtering prove that the DT-CWT filter is very suitable for the separation and extraction of frequency components such as surface roughness, waviness and form.

The construction of single wavelets in d-dimensions

Abstract: Sets K in d-dimensional Euclidean space are constructed with the property that the inverse Fourier transform of the characteristic function 1 K is a single dyadic orthonormal wavelet. The construction is characterized by its generality in the procedure, by its computational implementation, and by its simplicity. The general case in which the inverse Fourier transforms of the characteristic functions 1K 1, ..., 1K L are a family of orthonormal wavelets is treated in [27].

Wavelet sampling and localization schemes for the Radon transform in two dimensions

Abstract: Two theorems are presented for wavelet decompositions of the two-dimensional Radon transform. The rst theorem establishes an upper error bound in L 2 -norm between the Radon transform and its wavelet approximation whose coecients at dierent scales are estimated from Radon data acquired at corresponding sampling rates. The second theorem gives an estimate of the accuracy of a local image reconstructed from localized Radon data at multiple levels. These results show how to design a multilevel sampling and localization strategy for parallel-beam scanning by using wavelet regularity and vanishing moment characteristics, clarify the interaction between the wavelet structure and the essential bandwidth of an object image, and provide guidelines for wavelet local tomography.

Wavelet-based power quantification approaches

Abstract: This paper presents alternative computing methods for power related quantities using wavelet transforms. First of all, two alternatives for classical reactive power quantities based on real wavelet transform are given, having advantages over the methods published in literature for the calculation of reactive power. They are based on the implementation of a time delay in the wavelet domain and an a method splitting the current in an active and reactive component. Secondly, a totally different method is presented using complex wavelet transforms, allowing the formulation of power definitions in the time-frequency domain itself, similar to Fourier-based power definitions, but theoretically yielding continuously varying power quantities. All approaches are illustrated with examples.