On the approximate discrete KLT of fractional Brownian motion and applications |
| |
| Authors: | Anubha Gupta Shiv Dutt Joshi Pushpendra Singh |
| |
| Institution: | 1. SBILab, Department of ECE, IIIT-Delhi, India;2. Department of Electrical Engineering, IIT-Delhi, India;3. SEAS, Bennett University, Greater Noida, India |
| |
| Abstract: | This paper establishes connection between discrete cosine transform (DCT) and the discrete-time fractional Brownian motion process (dfBm). It is proved that the eigenvectors of the auto-covariance matrix of a dfBm can be approximated by DCT basis vectors in the asymptotic sense. This shows that DCT basis acts as discrete Karhunen–Loève transform (DKLT) for these processes in the approximate sense. Analytic perturbation theory of linear operators is used to prove this result. This result will be of great practical significance in applications where one is looking for an appropriate basis to work with signals that can perhaps be modeled as belonging to fBm processes. The utility of the proposed work has been illustrated with two real-life data (a) on compressive sampling based reconstruction of financial time-series and (b) in denoising gravitational wave event GW150914 data obtained from a binary black hole merger. |
| |
| Keywords: | Corresponding author |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
