22nd International Conference on COMPUTATIONAL STATISTICS (COMPSTAT 2016)
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
D. Stephen G. Pollock, University of Leicester, UK.
Thursday, 25th of August, 2016 19:45-18:35
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.
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
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