Question

Consider an input x[n] and a unit impulse response h[n] given by

x[n]=(1/2)ⁿ⁻² μ[n−2]
h[n]=μ[n+2]​
Determine and plot the output
y[n]=x[n]∗h[n]

Answer 1

To find the output y[n] of the given input and unit impulse response, use the convolution formula y[n] = ∑(x[k] * h[n-k]). Substitute the given values and evaluate the convolution for each value of n.

Step-by-step explanation:

To determine the output y[n] = x[n] * h[n], we need to convolve the input x[n] and the unit impulse response h[n]. The convolution of two signals is given by:

y[n] = ∑(x[k] * h[n-k]) where the summation is taken over all values of k.

Substituting the given values, we have:

y[n] = ∑((1/2)^(k-2) * μ[k-2] * μ[n-k+2]) where the summation is taken over all values of k.

To compute the output, we need to evaluate the convolution for each value of n. By considering the range of values for n, we can determine the limits of the summation and solve for y[n].