The following two contributions in this volume are highlighting some remarkable recent developments at the interface between precision laser spectroscopy and ultrafast laser physics. After decades of struggle, we have finally found a practical method for measuring the frequency of light with extreme precision [1]. Femtosecond laser optical frequency comb synthesizers are opening exciting new pe...

Chirps (i.e., transient AM-FM waveforms) are ubiquitous in nature and man-made systems, and they may serve as a paradigm for many nonstationary deterministic signals. The time-frequency plane is a natural representation space for chirps, and we will here review a number of questions related to chirps, as addressed from a time-frequency perspective. Global and local approaches will be described ...

This disproves a conjecture of Kinber. (2) We give a transparent proof of a generalization of Kinber's result that there exist arbitrarily complex problems admitting a polynomial time frequency computation. Several corollaries provide more insight into the structure of the hierarchy of polynomial time frequency classes. (3) The relationships between polynomial time frequency classes and selecti...

In time-frequency analysis there are four bilinear domains commonly used: time-frequency, ambiguity, temporal auto-correlation, and spectral auto-correlation. This paper introduces four new domains that are quadralinear in the signal. These four domains are each a function of three of the four variables used in the bilinear domains. Properties of these quantities are developed and an applicatio...

This article presents the RIMO/ELISA speaker veriication system which has been used in the 1999 NIST speaker recognition evaluation. This system is based on a new technique for analyzing speech signals called time-frequency principal component (TFPC) analysis. This technique consists in extracting principal components from the contextual covariance matrix, which is the covariance matrix of a se...

In analyzing a signal, especially a non-stationary signal, it is often necessary the desired signal to be segmented into small epochs. Segmentation can be performed by splitting the signal at time instances where signal amplitude or frequency change. In this paper, the signal is initially decomposed into signals with different frequency bands using wavelet transform. Then, fractal dimension of ...

Wavelet transformation is one of the most practical mathematical transformations in the field of image processing, especially image and signal processing. Depending on the nature of the multiresolution analysis, Wavelet transformation become more accessible and powerful tools. In this paper, we refer to the mathematical foundations of this transformation.   Introduction: The...