Common Waveform Analysis
A New And Practical Generalization of Fourier Analysis
Published on 31. August 2000
Book
Hardback
XI, 157 pages
978-0-7923-7905-8 (ISBN)
Description
Common Waveform Analysis
, 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 N uniform points be found?
- Can common waveforms be used in techniques that have traditionally been based on sine-cosine functions?
Reviews / Votes
From the reviews:
"In the book . Wei and Zhang have selected and presented the analysis of square, triangular, and trapezoidal waves with sufficient details and the related mathematical theories behind the subjects. . the work is impressive in a mathematical sense. . Square, triangular, and trapezoidal waveform analysis can be useful in many practical engineering and scientific environments, and this 160-page work is a good reference source for such a specific area." (Nihal Kularatna, IEEE Circuits & Devices Magazine, Vol. 21 (2), 2005)
More details
Series
Edition
2000 ed.
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XI, 157 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 15 mm
Weight
442 gr
ISBN-13
978-0-7923-7905-8 (9780792379058)
DOI
10.1007/978-1-4615-4547-7
Schweitzer Classification
Other editions
Additional editions
Yuchuan Wei | Qishan Zhang
Common Waveform Analysis
A New And Practical Generalization of Fourier Analysis
Book
10/2012
Springer
€106.99
Shipment within 7-9 days
Content
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.