Title :
Uncertainty and concentration inequalities for nonstationary random processes and time-frequency energy spectra
Author_Institution :
Inst. of Commun. & Radio-Frequency Eng., Vienna Univ. of Technol., Wien, Austria
Abstract :
We provide various sharp uncertainty inequalities for nonstationary random processes. These inequalities relate the temporal and spectral energy concentration of a process to the "effective rank" of its correlation operator. Similar inequalities are established for the time-frequency (TF) concentration of a wide range of TF energy spectra. We further identify TF energy spectra that feature maximum TF concentration and illustrate our results for the practically important class of underspread random processes.
Keywords :
correlation methods; random processes; signal representation; spectral analysis; time-frequency analysis; uncertain systems; TF energy spectra; concentration inequalities; correlation operator; effective rank; nonstationary random processes; signal processing; spectral energy concentration; temporal energy concentration; time-frequency concentration; time-frequency energy spectra; uncertainty; underspread random processes; Eigenvalues and eigenfunctions; Energy measurement; Frequency measurement; Kernel; Radio frequency; Random processes; Spectrogram; Time frequency analysis; Time measurement; Uncertainty;
Conference_Titel :
Signals, Systems and Computers, 2002. Conference Record of the Thirty-Sixth Asilomar Conference on
Conference_Location :
Pacific Grove, CA, USA
Print_ISBN :
0-7803-7576-9
DOI :
10.1109/ACSSC.2002.1197042
