1. Introduction 2. Fundamentals of Fourier Analysis 3. Fourier Analysis in Systems Theory 4. Fourier Transforms in Probability, Random Variables and Stochastic Processes 5. The Sampling Theory 6. Generalizations of the Sampling Theorem 7. Noise and Error Effects 8. Multidimensional Signal Analysis 9. Time-Frequency Representations 10. Signal Recovery 11. Signal and Image Synthesis: Alternating Projections Onto Convex Sets 12. Mathematical Morphology and Fourier Analysis on Time Sales 13. Applications 14. Appendices 15. Reference

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Handbook of Fourier Analysis & Its Applications

A Generalized Sampling Theorem for Causal Signals

A band-limited part x 0 (t) of a non-band-limited causal signal x(t) is used to completely restore x(t) by using analytic continuation. As a consequence, a generalized sampling theorem for causal signals is derived; the total causal signal x(t) can be completely restored by sampling the band-limited part x 0 (t) with finite sampling frequency.

https://ieeexplore.ieee.org/iel6/29/26179/01164189.pdf

Restoring causal signals by analytic continuation: A generalized sampling theorem for causal signals

Some comments and elaborations are made with reference to a recent contribution by Erteza and Lin [1] on sampling low-pass deterministic signals. It is shown that the expansion theorem of the Erteza-Lin paper involves an incomplete set of orthogonal functions and consequently lacks the generality claimed for it.

Note on the transform property of band-limited functions

Sampling and reconstruction of band-limited functions are fundamental problems in communications and signal processing. This correspondence introduces a new transform pair for any well behaved but arbitrary function f(t) and, thereafter, establishes two transform relationships between a band-limited function and its sample values. This work can be viewed as yet another comment and extension on the sampling theorem.

http://ieeexplore.ieee.org/iel5/5/31295/01456155.pdf

A. Erteza

Papers

On the transform property of a band-limited function and its samples