Parks, Thomas W.2018-12-182018-12-181978Merchant, Gulamabbas A.. "Fast algorithms for DFT and convolution." (1978) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/104397">https://hdl.handle.net/1911/104397</a>.https://hdl.handle.net/1911/104397Text includes handwritten formulasIn this thesis, a detailed analysis of sufficient conditions for existence of unique multidimensional linear and multidimensional non-linear Index map has been presented, along with a new Index representation. The recent Ideas of converting Discrete Fourier Transform to convolution and Implementing convolution efficiently, have been combined to give two algorithms viz. Nested Fourier Algorithm (NFA -- using linear multidimensional map) and Index Fourier Algorithm (IFA using a non-linear Index map). The two algorithms have been compared for the amount of arithmetic computations required. The algorithms have been Implemented In FORTRAN on IBM 37/155 and their execution timings have been compared.132 ppengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.ThesisRICE2032reformatted digitalTHESIS E.E. 1978 MERCHANT