Find the limit of sin 4 pin8pim as n goes to zero B what is

Find the limit of sin (4 pin)/8pim as n goes to zero. B. what is the minimum frequency that a 10 kHz signal can be sampled to recover the information? C what is g (z) if G (s) = 4/(s +) ? show your work. D. Using synthetic division, find the value of f (t0 at t = 12 second if t = 3 second and f(z0 = 8z/(z^2 + 4z + 2) where t is the sampling time. E. for digital signal processing boards such as the TI TMS320C6713, an analogue lowpass filter (such as a Butterworth filter) is included up front. what is its purpose and what is it called?

Solution

IV.

A. lim _n->0 (sin 4n) / (8n) = lim _n->0 1/2(sin 4n / 4n) = 1/2*1 = 1/2

Using the limit formula lim _x->0 (sin x) / x = 1