Download PDF by Franz Hlawatsch, Francois Auger: Time-Frequency Analysis

By Franz Hlawatsch, Francois Auger

ISBN-10: 1848210337

ISBN-13: 9781848210332

Masking a interval of approximately 25 years, within which time-frequency has gone through major advancements, this e-book is especially addressed to researchers and engineers attracted to non-stationary sign research and processing. it's written by means of famous specialists within the box.

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FOL 97] F OLLAND G. , “The uncertainty principle: A mathematical survey,” J. Fourier Anal. , vol. 3, pp. 207–238, 1997. , “Theory of communication,” J. IEE, vol. 93, pp. 429–457, 1946. , Foundations of Time-Frequency Analysis, Birkhäuser, Boston, 2001. , O’C ONNELL R. , S CULLY M. , W IGNER E. , “Distribution functions in physics: Fundamentals,” Physics Reports, vol. 106, pp. 121–167, 1984. , B OUDREAUX -BARTELS G. , “Linear and quadratic timefrequency signal representations,” IEEE Signal Process.

To this end, let us associate with a signal x(t) with FT x(f ) and energy Ex the non-negative functions c(t) and d(f ) defined by c(t) = 1 |x(t)|2 , Ex d(f ) = 1 |x(f )|2 . Ex According to the Parseval theorem, the integrals of c(t) and d(f ) are equal to 1. These functions may thus be considered as localization densities of the signal in time and in frequency. By using these densities, we can introduce the moments defined by ∞ mk = tk c(t) dt , −∞ ∞ μl = f l d(f ) df . 12) −∞ In particular, the average time and frequency of x(t) are tx = m1 and fx = μ1 , respectively.

2A, pp. 61–74, 1948. [WIG 32] W IGNER E. , “On the quantum correction for thermodynamic equilibrium,” Phys. , vol. 40, pp. 749–759, 1932. Chapter 2 Instantaneous Frequency of a Signal Abstract: The concepts of instantaneous amplitude and frequency appear quite natural to those who use amplitude or frequency modulations. However, the precise and unambiguous definition of these quantities presents numerous problems that have intrigued researchers for quite some time already and continue to do so. After having presented the problem in a relatively elementary fashion, we show the contradictions that present themselves in most apparently obvious definitions that have been given.

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Time-Frequency Analysis by Franz Hlawatsch, Francois Auger


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