Optimality of uncertaintyprinciples for joint timefrequencyrepresentations
Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
The study of joint time-frequency representations is a large field of mathematics and physics, especially signal analysis. Based on Heisenberg's cllassical uncertainty principle various inequalities for such time-frequency distributions have been studied. The objective of this thesis is to examine the role that Gaussian functions, including those with a chirp contribution, play in inequalities for the Short-Time Fourier transform and the Wigner distribution. We show that Gröchenig's uncertainty principles for the Short-Time Fourier transform are not optimal with regard to these functions. As for the Wigner distribution we show how an existing uncertainty principle by Janssen can be modied to reach optimality for Chirp Gaussians.
Place, publisher, year, edition, pages
2014. , 37 p.
IdentifiersURN: urn:nbn:se:lnu:diva-35399OAI: oai:DiVA.org:lnu-35399DiVA: diva2:727114
Subject / course
Mathematics and Modelling, Master Programme, 60 credits
Wahlberg, Patrik, Lektor
Toft, Joachim, Professor