The Z-Transform and Discrete Signals

Abstract

We return to the FT of a bandlimited function as given by (5.9) in Sect. 5.1. Setting ωΔt = θ we have the FS

$$F\left (\omega \right ) = F({e}^{i\theta }) =\displaystyle\sum _{ n=-\infty }^{\infty }f[n]{e}^{-in\theta }$$

(6.1)

with the coefficients f[n] = f(nΔt)Δt computed in the usual way, viz.,

$$f[n] = \frac{1} {2\pi }\displaystyle\int _{-\pi }^{\pi }F({e}^{i\theta }){e}^{in\theta }d\theta .$$

(6.2)