Intrinsic Integer-Periodic Functions for Discrete Periodicity Detection
Journal
IEEE Signal Processing Letters
Journal Volume
22
Journal Issue
8
Pages
1108-1112
Date Issued
2015-08
Author(s)
KS Lu
Abstract
In this letter we focus on discrete integer-periodic signals, whose periodicity are different from the periodicity of continuous periodic signals in many aspects. We introduce a class of discrete periodic signals called intrinsic integer-periodic function (IIPF). An IIPF contains only a single period in terms of downsampling, which leads to some interesting properties for analyzing periodic components from a discrete signal. We show that one can use Ramanujan sum to decompose discrete periodic signals into IIPF components. Finally, we also propose an integer periodic spectrum rather than frequency spectrum. Our results show that the proposed integer periodic spectrum outperforms the conventional Ramanujan Fourier transform.
Type
journal article