Abstract
A two-stage representation in terms of preprocessing and postprocessing of DFT is developed by vector transformation of sines and cosines into new basis functions using Mobius inversion of number theory. The preprocessing matrix, with elements 1, -1, and 0, is obtained by replacing \cos 2\pin / N and \sin 2\pin / N by \mu(n / N + 1 / 4) and \mu(n/N) , respectively, where \mu(\cdot) is the bipolar rectangular wave function. The postprocessing matrix is block diagonal where each block is a circular correlation and consists of the new basis functions. The two-stage representation has been found very useful in applications such as parallel implementation of DFT and signal/image recognition.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: IEEE Transactions on Acoustics, Speech, and Signal Processing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
