Communication in the presence of noise

Abstract

Recall that the sampling theorem (the Kotel’nikov formula)

$$f(t) = \sum_{-\infty}^{\infty} f \left(\frac {K}{2W}\right)\frac{\rm Sin 2\pi W (t-{k}{2W})}{\rm 2\pi W(t-{k}{2W})}$$

(3.1)

recovers the signal, which is a function $f \in L_2 \mathbb{(R)}$ with compactly supported spectrum of frequencies v not exceeding W Hertz from the set of sample values $f(t_k)$ at the points $t_k = k\Delta,$ where $\Delta = \frac{1}{2W}$ is the sampling time interval (Nyquist interval), which depends on W.