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Calculate the linear convolution

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Reference no: EM132050114

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]

Reference no: EM132050114

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