22nd International Conference on COMPUTATIONAL STATISTICS (COMPSTAT 2016)

23-26 August 2016, Auditoro Principe Filipe, Oviedo, Spain

23-26 August 2016, Auditoro Principe Filipe, Oviedo, Spain

Tutorial 1: Band pass filtering and Wavelets analysis:

Tools for the analysis of inhomogeneous time series

Tools for the analysis of inhomogeneous time series

by

D. Stephen G. Pollock, University of Leicester, UK.

Email: stephen_pollock@sigmapi.u-net.com

D. Stephen G. Pollock, University of Leicester, UK.

Email: stephen_pollock@sigmapi.u-net.com

Thursday, 25th of August, 2016 19:45-18:35

Room: Sala Camara

Room: Sala Camara

Summary: A wavelets analysis provides a means of analysing non-stationary time series of which the underlying statistical structures are continually evolving. It is an analysis both in the time domain and in the frequency domain.

The tutorial will begin by describing the effects of digital filtering in the time domain and the frequency domain. It will proceed to provide the generalisation of the Shannon sampling theorem that is appropriate to bandpass filtering. This theorem establishes a relationship between continuous signals and their corresponding sampled sequences that is essential to a wavelets analysis. Once this background has been provided, the theories of Dyadic and non-Dyadic wavelets analysis can be described in detail.

Lecture Slides

INTRODUCTION: Bandpass Filtering and Wavelets Analysis

LECTURE 1: Statistical Signal Extraction

LECTURE 2: Two-Channel Filter Banks

LECTURE 3: Dyadic Wavelets Analysis

LECTURE 4: Multi-Channel Filtering

Texts

1. Statistical Signal Extraction and Filtering

2. The Sampling Theorem and the Bandpass Theorem

3. Two-Channel Filter Banks and Dyadic Decompositions

4. Dyadic Wavelets Analysis

5. Filters and Wavelets for Dyadic Analysis

6. Multichannel Filter Banks

Bibliography