The culmination of more than twenty years of research, this authoritative resource provides you with a practical understanding of time-frequency signal analysis. The book offers in-depth coverage of critical concepts and principles, along with discussions on key applications in a wide range of signal processing areas, from communications and optics, to radar and biomedicine. Supported with over 140 illustrations and more than 1,700 equations, this detailed reference explores the topics you need to understand for your work in the field, such as Fourier analysis, linear time frequency representations, quadratic time-frequency distributions, higher order time-frequency representations, and analysis of non-stationary noisy signals. This unique book also serves as an excellent text for courses in this area, featuring numerous examples and problems at the end of each chapter.

Time-Frequency Signal Analysis With Applications

Myocardial infarction (MI) is known to elicit activation of the autonomic nervous system. Reperfusion, induced by thrombolysis, is thus expected to bring about a shift in the balance between the sympathetic and vagal systems, according to the infarct location. In this study, we explored the correlation between reperfusion and the spectral components of heart rate (HR) variability (HRV), which are associated with autonomic cardiac control. We analyzed the HR of patients during thrombolysis: nine anterior wall MI (AW-MI) and eight inferoposterior wall MI (IW-MI). Reperfusion was determined from changes in ST levels and reported pain. Reocclusion was detected in four patients. HRV was analyzed using a modified continuous wavelet transform, which provided time-dependent versions of the typically used low-frequency (LF) and high-frequency (HF) peaks and of their ratio, LF/HF. Marked alterations in at least one of the HRV parameters was found in all 18 reperfusion events. Patterns of HRV, compatible with a shift toward relative sympathetic enhancement, were found in all of the nine reperfusion events in IW-MI patients and in three AW-MI patients. Patterns of HRV compatible with relative vagal enhancement were found in six AW-MI patients (P < 0.001). Significant changes in HRV parameters were also found after reocclusion. Time-dependent spectral analysis of HRV using the wavelet transform was found to be valuable for explaining the patterns of cardiac rate control during reperfusion. In addition, examination of the entire record revealed epochs of markedly diminished HRV in two patients, which we attribute to vagal saturation.

Wavelet analysis of instantaneous heart rate: a study of autonomic control during thrombolysis.

Time-frequency analysis of multiple resonances in combustion engine signals

Fast algorithms for the evaluation of running windowed Fourier and continuous wavelet transforms are presented. The analysis functions approximate complex-modulated Gaussians as closely as desired and may be optimally localized in time and frequency. The Gabor filtering is performed indirectly by convolving a premodulated signal with a Gaussian-like window and demodulating the output. The window functions are either B-splines dilated by an integer factor m or quasi-Gaussians of arbitrary size generated from the n-fold convolution of a symmetrical exponential. Both approaches result in a recursive implementation with a complexity independent of the window size (O(N)). >

Fast Gabor-like windowed Fourier and continuous wavelet transforms

An architecture of the system for time-frequency signal analysis is presented. This system is based on the S-method, whose special cases are two the most important distributions: the spectrogram and the Wigner distribution. Systems with constant and signal-dependent window widths are presented.

An architecture for the realization of a system for time-frequency signal analysis

In the recursive Fourier transform, the data window can be chosen such that the number of computations required to update the transform at each frequency upon reception of a new data sample is independent of the transform block length.

http://ieeexplore.ieee.org/iel5/5/31379/01458182.pdf

M.G. Amin

Papers

A new approach to recursive Fourier transform