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.

Design and simulation of a speech analysis-synthesis system based on short-time Fourier analysis

Abstract: This paper discusses the theoretical basis for representation of a speech signal by its short-time Fourier transform. The results of the theoretical studies were used to design a speech analysis-synthesis system which was simulated on a general-purpose laboratory digital computer system. The simulation uses the fast Fourier transform in the analysis stage and specially designed finite duration impulse response filters in the synthesis stage. The results of both the theoretical and computational studies lead to an understanding of the effect of several design parameters and elucidate the design tradeoffs necessary to achieve moderate information rate reductions.

Wavelet Analysis: the effect of varying basic wavelet parameters

Abstract: The most commonly used methods to analyse (observed) quasi-periodic signals are standard techniques such as Fourier and wavelet analysis. Whereas a Fourier transform provides information on the dominant frequencies, wavelet analysis has the added advantage of providing the time localisation of the various frequency components. The usefulness and robustness of wavelet analysis is investigated by varying the different parameters which characterise the `mother' wavelet. We examine the effect of varying these parameters on the temporal and frequency resolution and the damping profile, which can be obtained from the wavelet transform. Additionally, the effect of a changing periodicity on the wavelet transform is investigated. Both simple harmonic functions and intensity oscillations observed by TRACE are used to demonstrate the various advantages and disadvantages of the different methods. In general, using the Paul wavelet or a smaller value of the wavelet parameter k provides a better time resolution, whereas the Morlet wavelet or a larger value of k improves the frequency resolution. Overall, our results indicate that great care is needed when using a wavelet analysis and that all the possible factors that could affect the transform should be taken into consideration.

Image compression using wavelets

Abstract: The discrete wavelet transform (DWT) represents images as a sum of wavelet functions (wavelets) on different resolution levels. The basis for the wavelet transform can be composed of any function that satisfies requirements of multiresolution analysis. It means that there exists a large selection of wavelet families depending on the choice of wavelet function. The choice of wavelet family depends on the application. In image compression application this choice depends on image content. This paper provides fundamentals of wavelet based image compression. The options for wavelet image representations are tested. The results of image quality measurements for different wavelet functions, image contents, compression ratios and resolutions are given.

Spline-Kernelled Chirplet Transform for the Analysis of Signals With Time-Varying Frequency and Its Application

Abstract: The conventional time-frequency analysis (TFA) methods, including continuous wavelet transform, short-time Fourier transform, and Wigner-Ville distribution, have played important roles in analyzing nonstationary signals. However, they often show less capability in dealing with nonstationary signals with time-varying frequency due to the bad energy concentration in the time-frequency plane. On the other hand, by introducing an extra transform kernel that matches the instantaneous frequency of the signal, parameterized TFA methods show powerful ability in characterizing time-frequency patterns of nonstationary signals with time-varying frequency. In this paper, a novel time-frequency transform, called spline-kernelled chirplet transform (SCT), is proposed. By introducing a frequency-rotate operator and a frequency-shift operator constructed with spline kernel function, the SCT is particularly powerful for the strongly nonlinear frequency-modulated signals. In addition, an effective algorithm is developed to estimate the parameters of transform kernel in the SCT. The capabilities of the SCT and parameter estimation algorithm are validated by their applications for numerical signals and a set of vibration signal collected from a rotor test rig.