Common Waveform Analysis

A New And Practical Generalization of Fourier Analysis
2000
ISBN: 978-0-7923-7905-8
Verlag: Springer US

Buch, Englisch, Band 9, 157 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 442 g

Reihe: The International Series on Asian Studies in Computer and Information Science

, which will be of interest to both electrical engineers and mathematicians, applies the classic Fourier analysis to common waveforms. The following questions are answered:

• Can a signal be considered a superposition of common waveforms with different frequencies?
• How can a signal be decomposed into a series of common waveforms?
• How can a signal best be approximated using finite common waveforms?
• How can a combination of common waveforms that equals a given signal at uniform points be found?
• Can common waveforms be used in techniques that have traditionally been based on sine-cosine functions?

represents the most advanced research available to research scientists and scholars working in fields related to the area.

Zielgruppe

Research

Fachgebiete

• Naturwissenschaften Physik Mechanik Akustik, Schwingungsanalyse
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Mikroprozessoren
• Technische Wissenschaften Elektronik | Nachrichtentechnik Elektronik Bauelemente, Schaltkreise

Inhaltsverzeichnis

1 ABC of Number Theory.- 1.1 Divisibility.- 1.2 Arithmetical Functions.- 1.3 Dirichlet Multiplication.- 1.4 Dirichlet Series.- 2 Square Wave Analysis.- 2.1 Square Wave System and its Basic Properties.- 2.2 Biorthogonal Functions and Square Wave Series.- 2.3 Orthogonalization and the Best Approximation.- 2.4 An Example of Applications.- 3 Triangular Wave Analysis and Trapezoidal Wave Analysis.- 3.1 WASCMFC Functions and Practical Examples.- 3.2 WASCMFC Function Basis, Biorthogonal Basis and Or thonormalized Basis.- 3.3 Basis and Coordinate Transforms.- 3.4 Discrete Triangular Wave Transform and Trapezoidal Wave Transform.- 4 Frequency Analysis Based on General Periodic Functionds.- 4.1 A Frequency System in L2[??,?].- 4.2 A Frequency System in L2odd[??, +?].- 4.3 A Complete System in L2odd[??, +?].- 4.4 An Unconditional Basis in L2odd[??, +?].- 4.5 A Combinative Frequency System in L2[??,?].- 4.6 A Frequency Transform in L2(R).- 5 Main Relations and Basic Techniques.- 5.1 Dirichlet Multiplication and a Related Formula.- 5.2 Relations between Sine Waves and Common Waveforms.- 5.3 Relations between Two Waveforms.- 5.4 Common Waveform Series.- 5.5 Common Waveform Transform.- 5.6 Discrete Transform for Common Waveform.- 5.7 Techniques of Common Waveform Analysis.