Fourier transform of a space of holomorphic discrete series

Discrete integer Fourier transform in real space: elliptic Fourier transform

Fourier Series and the Discrete Fourier Transform: Quick Primer

The Fourier Series (FS) and the Discrete Fourier Transform (DFT) should be thought of as playing similar roles for periodic signals in either continuous time (FS) or discrete time (DFT). Both analyze signals into amplitude, phases, and frequencies of complex exponentials; both synthesize signals by linearly combining complex exponentials with appropriate amplitude, phase, and frequency. Finally...

A general construction of Reed-Solomon codes based on generalized discrete Fourier transform

In this paper, we employ the concept of the Generalized Discrete Fourier Transform, which in turn relies on the Hasse derivative of polynomials, to give a general construction of Reed-Solomon codes over Galois fields of characteristic not necessarily co-prime with the length of the code. The constructed linear codes  enjoy nice algebraic properties just as the classic one.

Universality of Holomorphic Discrete Series

The goal here is to recover an apocryphal result on the structure of holomorphic discrete series representations of symplectic groups Spn(R) and unitary groups U(p, q) for sufficiently high highest weight of the lowest K-type. The same sort of argument applies to other groups of hermitian type, for example the classical groups O(n, 2) and O∗(2n). For Sp(n), the maximal compact is isomorphic to ...

Dft : Discrete Fourier Transform

A. Table of contents by sections: 1. Abstract (you’re reading this now) 2. Summary of the DFT (How do I do the homework?) 3. Review of continuous-time Fourier series 4. Bandlimited signals and finite Fourier series 5. Sampling theorem for periodic signals 6. Review of quirks of discrete-time frequency 7. Orthogonality and its significance 8. Discrete Fourier Transform (DFT) 9. Use of DFT to com...