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.

Low bit rate high quality audio coding with combined harmonic and wavelet representations

Abstract: We describe a novel high quality audio coding method using adaptive signal representation, based on sinusoidal and wavelet analysis of signals. First, we perform a harmonic analysis of the signal to remove strong periodic structures or tones from the signal. Then we carry out wavelet analysis that are useful in tracking the transients of the signal. These transients are then removed from the wavelet coefficients. The remaining coefficients have broadband noise-like structure. Since this method separates out tones (sinusoids), transients, and broadband noise, we may use tonal, noise, and temporal masking information to individually encode the tones and the wavelet coefficients. Our experiments suggest that this method yields a nominal bit rate of 1 bit/sample for high quality audio compression.

Wavelet Analysis and its Application

Abstract: The wavelet analysis is a new subject in the signal processing. It has many good characteristic and applied perspective. The basic principle of the wavelet transform is briefly introduced in this paper. The application of the wavelet transform in the estimation of the signal virtual value is also put forward.

Random fractional Fourier transform

Abstract: We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.

A General Description of Linear Time-Frequency Transforms and Formulation of a Fast, Invertible Transform That Samples the Continuous S-Transform Spectrum Nonredundantly

Abstract: Examining the frequency content of signals is critical in many applications, from neuroscience to astronomy. Many techniques have been proposed to accomplish this. One of these, the S-transform, provides simultaneous time and frequency information similar to the wavelet transform, but uses sinusoidal basis functions to produce frequency and globally referenced phase measurements. It has shown promise in many medical imaging applications but has high computational requirements. This paper presents a general transform that describes Fourier-family transforms, including the Fourier, short-time Fourier, and S- transforms. A discrete, nonredundant formulation of this transform, as well as algorithms for calculating the forward and inverse transforms are also developed. These utilize efficient sampling of the time-frequency plane and have the same computational complexity as the fast Fourier transform. When configured appropriately, this new algorithm samples the continuous S-transform spectrum efficiently and nonredundantly, allowing signals to be transformed in milliseconds rather than days, as compared to the original S-transform algorithm. The new and efficient algorithms make practical many existing signal and image processing techniques, both in biomedical and other applications.