Common Waveform Analysis

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.

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)