Abstract
In this letter, closed-form expressions for the discrete Fourier transform (DFT) of a finite chirp are derived. It is shown that when the normalized chirp rate is coprime with the chirp length, then the DFT of a finite chirp is again a finite chirp with magnitude, chirp rate, and carrier frequency appropriately scaled. In particular, when the normalized chirp rate is of unit value, then the DFT of a finite chirp is the same chirp, up to a complex scaling factor. Conversely, when the normalized chirp rate has a common factor with the chirp length, then the support of the DFT of a finite chirp is equal to the ratio of chirp length and the common factor. Among other things, results given here complement certain results, obtained by Janssen, on the computation of time-continuous chirps with rational sweep rates
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 callDisclaimer: 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.
