Question

Problem 2. Consider the system described by the following difference equation, y[n]=y[n-1]-0.25 y[n-2]+x[n], \quad n \geq 0 with initial conditions y[-1]=1 and y[-2]=3 and input x[n] = 2(0.9)^n u[n]. For

this system: a. Draw a block diagram using multipliers, adders, and shifters that represents the system. b. Determine the initial-condition response, yi[n]. c. Is this system stable? Explain. d. Determine the analytical form of the impulse response function, h[n]. e. Calculate the forced response for the system, yf [n]. f. Finally, determine the analytical form for the total response of the system, y[n].

Fig: 1

Fig: 2

Fig: 3

Fig: 4

Fig: 5

Fig: 6

Fig: 7

Fig: 8

Fig: 9