{"page":"69–92","intvolume":"        32","date_updated":"2023-01-30T11:58:29Z","title":"On the instantaneous frequency of Gaussian stochastic processes","abstract":[{"lang":"eng","text":"We study the instantaneous frequency (IF) of continuous-time, complex-valued, zero-mean, proper, mean-square differentiable, nonstationary Gaussian stochastic processes. We compute the probability density function for the IF for fixed time, which generalizes a result known for wide-sense stationary processes to nonstationary processes. For a fixed point in time, the IF has either zero or infinite variance. For harmonizable processes, we obtain as a consequence the result that the mean of the IF, for fixed time, is the normalized first-order frequency moment of the Wigner spectrum."}],"publication":"Probab.\\ Math.\\ Statist.","status":"public","_id":"40805","date_created":"2023-01-30T11:51:55Z","user_id":"43497","year":"2012","author":[{"full_name":"Wahlberg, Patrik","last_name":"Wahlberg","first_name":"Patrik"},{"full_name":"Schreier, Peter J.","last_name":"Schreier","first_name":"Peter J."}],"citation":{"apa":"Wahlberg, P., &#38; Schreier, P. J. (2012). On the instantaneous frequency of Gaussian stochastic processes. <i>Probab.\\ Math.\\ Statist.</i>, <i>32</i>, 69–92.","mla":"Wahlberg, Patrik, and Peter J. Schreier. “On the Instantaneous Frequency of Gaussian Stochastic Processes.” <i>Probab.\\ Math.\\ Statist.</i>, vol. 32, 2012, pp. 69–92.","chicago":"Wahlberg, Patrik, and Peter J. Schreier. “On the Instantaneous Frequency of Gaussian Stochastic Processes.” <i>Probab.\\ Math.\\ Statist.</i> 32 (2012): 69–92.","ama":"Wahlberg P, Schreier PJ. On the instantaneous frequency of Gaussian stochastic processes. <i>Probab\\ Math\\ Statist</i>. 2012;32:69–92.","bibtex":"@article{Wahlberg_Schreier_2012, title={On the instantaneous frequency of Gaussian stochastic processes}, volume={32}, journal={Probab.\\ Math.\\ Statist.}, author={Wahlberg, Patrik and Schreier, Peter J.}, year={2012}, pages={69–92} }","ieee":"P. Wahlberg and P. J. Schreier, “On the instantaneous frequency of Gaussian stochastic processes,” <i>Probab.\\ Math.\\ Statist.</i>, vol. 32, pp. 69–92, 2012.","short":"P. Wahlberg, P.J. Schreier, Probab.\\ Math.\\ Statist. 32 (2012) 69–92."},"type":"journal_article","volume":32,"department":[{"_id":"263"}]}