Question

1,For the given first-order system in (1), linear difference equation with a = 0.43 and b = 0.47:(a) iteratively evaluate the response, y[k], when y[0] = 0, and u[k] 10 for k= 0, 1, 2, 3, 4, 5.That is, compute numerical values for y[0],y[1]....,y[5]. (b) With u[k] = 0 and y[0]find the number of sample periods, N, needed for an initial condition, e.g., y[0] 1, to decay to 1% of its original value. Or, stated another way, find the integer value N in the 1% settling time expression, T. = NT, where T is the sample period. TT wasn't explicitly given in the problem statement. T is already accounted for in the values of a = 0.43 and b= 0.47. One doesn't need T to find N in this problem. In fact, you are unable to find a numerical value for T., since T has not been given .ANG=H y[k+1]=a y[k]+b u[k]

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