a) i) The convolution operator is defined as: h[n] x [n] = [h[i]x[n-i] Eq(1). 00 Simplify...

  

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a) i) The convolution operator is defined as: h[n] x [n] = [h[i]x[n-i] Eq(1). 00 Simplify y[n] = h[n] x[n] to a closed-form expression given that, i=0 72 n x[n] = (1) u[n] and h[n] = (-) u[n]. N Σ n=0 Do not use the z-transform method; use the summation formula for the simplification: an 1-a N+1 1-a ,n ≥ 0,a < 1 (4 marks) ii) From the closed-form expression obtained above, evaluate y[n] for 0 ≤ n ≤ 3. (2 marks) b) i) Write a MATLAB program to implement the convolution operation > as defined in a) i). Your program must compute y[n] according to the mathematical algorithm in Eq. (1). Explain the algorithm by adding comments in the program code. (6 marks) ii) Using the values of x[n] and h[n] as given in a), run your program to calculate y [n] for 0 <n ≤20. Present the result of y[n] by the stem- plot function. (2 marks) A a) i) The convolution operator is defined as: h[n] x [n] = [h[i]x[n-i] Eq(1). 00 Simplify y[n] = h[n] x[n] to a closed-form expression given that, i=0 72 n x[n] = (1) u[n] and h[n] = (-) u[n]. N Σ n=0 Do not use the z-transform method; use the summation formula for the simplification: an 1-a N+1 1-a ,n ≥ 0,a < 1 (4 marks) ii) From the closed-form expression obtained above, evaluate y[n] for 0 ≤ n ≤ 3. (2 marks) b) i) Write a MATLAB program to implement the convolution operation > as defined in a) i). Your program must compute y[n] according to the mathematical algorithm in Eq. (1). Explain the algorithm by adding comments in the program code. (6 marks) ii) Using the values of x[n] and h[n] as given in a), run your program to calculate y [n] for 0 <n ≤20. Present the result of y[n] by the stem- plot function. (2 marks) A

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