Convolution and lti systems a linear system s has the, Ask an Expert

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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?

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Engineering Mathematics, Engineering

Category:- Engineering Mathematics
Reference No.:- M91981305

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