Relativistic windowed Fourier transform

• Main Authors: Karim, M.R., Ali, S.T., Bodruzzaman, M.
• Format: Conference or Workshop Item
• Language: English
• Published: IEEE 2000
• Subjects: TA Engineering (General). Civil engineering (General)
• Online Access: http://eprints.um.edu.my/8774/1/Relativistic_windowed_Fourier_transform.pdf; http://eprints.um.edu.my/8774/; http://www.scopus.com/inward/record.url?eid=2-s2.0-0033718350&partnerID=40&md5=c330659b5ecea564f8184b6d78e02b9c http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=00845572

Drawing upon some earlier work on coherent states of the Poincare' group in 1-space and 1-time dimensions, we use these states to define a relativistic windowed Fourier transform, as relativistic extension of the usual windowed Fourier transform. We discretize the resulting transform and obtain conditions under which the discretized transform can be used to reconstruct arbitrary square integrable functions. We present some numerical and graphical exercises to illustrate the theory, as well as to compare the relativistic windowed Fourier transform with the orthodox windowed Fourier transform.