Maple

Harmonic Analysis

Intended Audience:

• Researchers and engineers who work with signals
• Financial analysts who model securities prices
• Mathematicians and physicists who apply harmonic analysis or conformal mapping to problems in mathematical physics
• Instructors teaching courses in signal processing, complex variables, or mathematical physics
• Students needing an introduction to harmonic analysis, conformal mappings or harmonic correlation

Product Description:

Harmonic Analysis combines innovative numerical tools for signal processing with rich analytical tools for studying problems of physics and the mathematics of complex variables. Harmonic Analysis provides a Maple package with worked examples in signal filtering, finance, and conformal mapping. The rich documentation includes an in-depth explanation of the theory of harmonic analysis.

The algorithms in Harmonic Analysis are the culmination of new research by the author in the field of harmonic analysis. They have a US Patent pending (#10/856,453), and a paper on the methods behind the technology is published in the September 2004 issue of IEEE Explorer.

Features list:

• Provides tools for filtering signals based on amplitude-frequency characteristics
• Extends the power of Maple’s FFT routines to handle signals with arbitrary data length (e.g. need not be a power of 2 or have small prime divisors), using an innovative algorithm that reduces transforms to vector-to-circulant matrix multiplication
• Greatly extends the power of Maple’s conformal mapping routines
• Computes values of analytic functions from their values on the unit circle
• Computes values of harmonic-conjugate functions
• Provides groundbreaking algorithms for:
  • computing conformal mappings of functions from the unit circle to connected domains
  • computing the ratios of signals by tilde operators and harmonic correlation

Technical Requirements

• Maple 8 or higher

Author Information

• Dr. Vladimir Clue is an independent researcher. After graduating from the elite Kolmogorv school in Moscow and N. Novgorod University, he worked at the Scientific Research Institute of Mechanics. He then piloted a research project on signal processing and conformal mapping for the Russian Academy of Science (RAN) as a scientific colleague in the Institute of Machine Science. During nine years of research in Russia, the author has pioneered many new algorithms and approaches to harmonic analysis. The Harmonic Analysis MapleConnect package is the culmination of the author’s research.

Technical Support

• Terms: Standard support is included for commercial, academic and student purchases. In addition:
• For a period of one year after purchase, if and when any bug fixes and updates are released, they will be made available to the customer.
• For a period of four months after purchase, if and when any feature upgrades are released, will be made available free of charge to the customer.

  Student purchases include 30-day installation support only.

  Email: vclue@earthlink.net