Distribution theory and transform analysis: an introduction to generalized functions, with applications
Time-frequency analysis: theory and applications
Time-frequency analysis: theory and applications
Applications of the Wigner distribution function in signal processing
EURASIP Journal on Applied Signal Processing
Nonlinear transformation of differential equations into phase space
EURASIP Journal on Applied Signal Processing
Decomposition of the instantaneous spectrum of a random system
Signal Processing
Optimal kernels for nonstationary spectral estimation
IEEE Transactions on Signal Processing
Minimum-variance time-frequency distribution kernels
IEEE Transactions on Signal Processing
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The frequency spectrum is a fundamental quantity for the analysis and design of a system. When a system is turned on or off, the frequency spectrum of its output changes with time.We define the transient spectrum as the time-frequency spectrum of the system output during the transient phase. We obtain the exact transient spectrum for a wide class of random systems, and we formulate it with respect to the classical power spectrum, which is reached for large times. We apply the developed method to the case of a harmonic oscillator and of a system with two resonances.