Problem #1
Given x[n] = -3δ[n]+4δ[n-1]+5δ[n-3] and h[n]=2δ[n]+2δ[n-2]
Calculate the linear convolution: y[n] = x[n]*h[n] using any method and give the result, y[n], as a sum of delayed unit samples.
Answer: y[n] =
Problem #2
Given x[n] = [ x[0] x[1] x[2] ] = [ -3 2 1] h[n] = [ h[0] h[1] h[2]] = [ -5 1 4]
Calculate the cyclic or circular convolution modulo-3, between x[n] and h[n], using a 3x3 Circulant Matrix. Give the result, y[n], as a sum of delayed unit samples.
Answer: y[n] =
Problem #3
Given the 4-point DFT of x[n], for k=0,1,2,3, X[k] = DFT{x[n]} = [ 4 1+7j 2 1-7j ]
Find x[n] using any method and write as a sum of delayed unit samples.
Answer: x[n] =
Problem #4
A certain LTI filter has unit-sample response: h[n] = 0.5δ[n] + 0.5δ[n-2] Find the filter steady state response to the input signal x[n] = cos[(π/4)n]u[n]