Definition of frequency response

SOLVED: Find the impulse response function, the step response function, the frequency response function, the gain, and the phase shift for the following linear systems (or filters):a) yt = 0.5xt-1 xt 0.5xt 1b) yt = 0.2(xt-2 xt-1 xt xt 1 xt 2)c) yt = ∇xtd) yt = ∇^2xtwhere in each case t is an integer valued. Plot the gain and phase shift for filters a) and c). Which of the filters are low-pass and which are high-pass?If filters a) and b) are joined in series, find the frequency re

Differential Equations and Linear Algebra, 2.3c: Impulse Response and Step Response