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Contents outline of a six-chapter book on spectral theory, from a folder of 2003 edits in Phil's book files. It covers the Fourier integral transform, pulse trains and Fourier series, sampled signals (Z, discrete and fast Fourier transforms, Nyquist theorem), practical topics like FIR filters and oversampling, dispersion relations (Hilbert transform, Kramers-Kronig), and spectral densities of line codes such as NRZ, Manchester and AMI.
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Spectral Theory
Chapter 1: The Fourier Integral Transform and Related Topics
Fourier Integral Transform X(), convolution, RC filter, conventions, Laplace Transform,
reflection rule for X(), area rules, Parseval's Theorem, other rules, examples, the square pulse,
exponential sums, delta function technology, sinc function history, meaning of negative
frequencies, Final and Initial Value theorems
Chapter 2: Pulse Trains and the Fourier Series Connection
spectrum of a pulse train, Fourier Series, square wave case,
discrete spectra, biphase case, some Excel graphs
Chapter 3: Sampled Signals
definition of T1, sampled signals and image spectra,
digital filters and their image spectra, the Digital Fourier Transform X'(),
relation between Digital and Analog transforms, the Z Transform,
digital RC filter, poles and flip-flops, digital filter circuits,
amplitude modulated pulse trains, aperture correction,
Discrete Fourier Transform and comparison to Analog
the Fast Fourier Transform, the Nyquist Sampling Theorem
Chapter 4: Some Practical Topics
digital FIR and linear phase, origins of image spectra,
oversampling and decimation
Chapter 5: Some Theoretical Topics
dispersion relations for X() and (), Hilbert Transform,
Kramers-Kronig, filter implications, dispersion and
attenuation, implication for coaxial cable
Chapter 6: Statistical Pulse Trains
autocorrelation, relation to spectral energy density, examples,
application to pulse trains, statistics, coefficients,
spectral densities of various line codes: NRZ, RZ, Manchester, AMI
spectral densities of NRZ, MPSK, QAM, bipolar NRZ, MSK