Determine a mathematical expression for y[n] and sketch y[n] for n = 0,1,2,3 for each of...

  

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Determine a mathematical expression for y[n] and sketch y[n] for n = 0,1,2,3 for each of the following systems given by their input-output relationships and the particular inputs: (a) y[n] = x[n](x[n-1] where x[n] = u[n] n (b) y[n] = x[n]y[n-1], where x[n] = (2)" u[n]. n (c) y[n] = ) y[n-1]+x[n], where x[n] = (-)" u[n]. (x[n], n even 0, n odd |x[n]| 0 (d) y[n] = (e) y[n] = 0, else n where x[n] = ()" u[n]. where x[n] = ()" u[n]. (ii) In each of the above systems, indicate if the system is linear. (iii) In each of the above systems, indicate if the system is time-variant. Determine a mathematical expression for y[n] and sketch y[n] for n = 0,1,2,3 for each of the following systems given by their input-output relationships and the particular inputs: (a) y[n] = x[n](x[n-1] where x[n] = u[n] n (b) y[n] = x[n]y[n-1], where x[n] = (2)" u[n]. n (c) y[n] = ) y[n-1]+x[n], where x[n] = (-)" u[n]. (x[n], n even 0, n odd |x[n]| 0 (d) y[n] = (e) y[n] = 0, else n where x[n] = ()" u[n]. where x[n] = ()" u[n]. (ii) In each of the above systems, indicate if the system is linear. (iii) In each of the above systems, indicate if the system is time-variant.