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.

Ground-roll suppression using the wavelet transform

Abstract: Low-frequency, high-amplitude ground roll is an old problem in land-based seismic field records. Current processing techniques aimed at ground-roll suppression, such as frequency filtering, f - k filtering, and f - k filtering with time-offset windowing, use the Fourier transform, a technique that assumes that the basic seismic signal is stationary. A new alternative to the Fourier transform is the wavelet transform, which decomposes a function using basis functions that, unlike the Fourier transform, have finite extent in both frequency and time. Application of a filter based on the wavelet transform to land seismic shot records suppresses ground roll in a time-frequency sense; unlike the Fourier filter, this filter does not assume that the signal is stationary. The wavelet transform technique also allows more effective time-frequency analysis and filtering than current processing techniques and can be implemented using an algorithm as computationally efficient as the fast Fourier transform. This new filtering technique leads to the improvement of shot records and considerably improves the final stack quality.

The $S$ -Transform From a Wavelet Point of View

Abstract: The S-transform is becoming popular for time-frequency analysis and data-adaptive filtering thanks to its simplicity. While this transform works well in the continuous domain, its discrete version may fail to achieve accurate results. This paper compares and contrasts this transform with the better known continuous wavelet transform, and defines a relation between both. This connection allows a better understanding of the S-transform, and makes it possible to employ the wavelet reconstruction formula as a new inverse S-transform and to propose several methods to solve some of the main limitations of the discrete S-transform, such as its restriction to linear frequency sampling.

Wavelet transforms: an introduction

Abstract: Wavelets and wavelet transforms are a relatively new topic in signal processing. Their development and, in particular, their application remains an active area of research. This paper presents a tutorial introduction to the theory, implementation and interpretation of the wavelet transform. The paper concentrates on the application of the wavelet transform to the time-scale (time-frequency) analysis of discrete signals. Examples are given of the analysis of basic test signals and of an actual electrocardiographic signal.< >

Fast wave-front reconstruction in large adaptive optics systems with use of the Fourier transform.

Abstract: Wave-front reconstruction with the use of the fast Fourier transform (FFT) and spatial filtering is shown to be computationally tractable and sufficiently accurate for use in large Shack–Hartmann-based adaptive optics systems (up to at least 10,000 actuators). This method is significantly faster than, and can have noise propagation comparable with that of, traditional vector–matrix-multiply reconstructors. The boundary problem that prevented the accurate reconstruction of phase in circular apertures by means of square-grid Fourier transforms (FTs) is identified and solved. The methods are adapted for use on the Fried geometry. Detailed performance analysis of mean squared error and noise propagation for FT methods is presented with the use of both theory and simulation.