Prof Abul Hasan Siddiqi

1
Applications of Wavelets in Real World Problems
By Prof Abul Hasan Siddiqi ahasan_at_kfupm.edu.sa
Department of Mathematical Sciences King Fahd
University of Petroleum and Minerals Dhahran,
Saudi Arabia
2
The name wavelets means small waves, in contrast,
big waves (sinusoids) occur in Fourier analysis.
Wavelet analysis dealing with properties of
wavelets is a refinement of Fourier analysis.
The theory and applications of wavelets have
been vigorously studied by physicists,
mathematicians and engineers alike in the last
decade. Some of these developments are reported
in the Special Issue on Wavelets and Fractals of
the Arabian Journal for Science and Engineering
last month.
3
The goal of this talk is to discuss some other
emerging areas of applications of wavelets which
are pursued by researchers in North America and
Europe, particularly in France, led by Alain
Arneodo and Yves Meyer.
4

• Some of these themes are wavelet-based
  multifractal formalism and applications to
• Medical sciences such as abnormalities in heart
  functioning, detection of abnormalities in
  mammogram to diagnose breast cancer,
• Bioinformatics and computational biology such as
  DNA sequences, protein structure and microdata
  analysis,
• Environmental studies like climate, clouds,
  rainfall, river levels
• Finance like stock market data and Black-Scholes
  model of option pricing
• Nonlinear Schrödinger equation, and
• Maxwell equations.

5
Time series analysis approach for analyzing
real-world problems is adapted. Wavelet-based
fractal formalisms are focused to detect
singularities, seasonalities, de-noising and long
time trends. Feature detection of
electrocardiogram signal and rainfall data are
taken for illustration of applications of the
methodology. Comprehensive and updated
references are given for further reading.
6
I have divided the lecture into following
headings

• What is wavelet and why wavelet?
• Wavelet Methods for Time Series Representing Real
  World Problems
• Scanning of Singularities with Continuous Wavelet
  Transform
• Diagnosis of Heart Disease
• Wavelet Analysis of Rainfall Data Yearly Data
• Wavelet Analysis using Matlab Toolbox
• Important References and software websites