Convolution and LTI systems: A linear system S has the relationship
y[n] = ∑∞k=-∞s[k]g[n-2k]
between its input x[n] and its output y[n], where
g[n] = u[n] - u[n-4].
a) Determine y[n] when x[n] = δ[n - 1]
b) Determine y[n] when x[n] = δ[n -2]
c) Is S an LTI system?
Hint: Show the system output with input x[n] = δ[n -1] is y[n] = g[n -2]
Convolution
{1 : 0 ≤ t ≤ 1
Suppose that x(t) = { 0 : elsewhere and h(t) = x(t1a), where 0 < a < 1. : elsewhere
1. Determine and sketch y(t) = x(t) * h(t).
2. if dy(t)/dt contains only three discontinuities, what is the value of α?