In Section 2.5, we stated that the solution to the homogeneous difference equation
is of the form
with the Am’s arbitrary and the zm’s the N roots of the polynomial
(a) Determine the general form of the homogeneous solution to the difference equation
(b) Determine the coefficients Am in the homogeneous solution if y[−1] = 1 and y[0] = 0.
(c) Now consider the difference equation
If the homogeneous solution contains only terms of the form of Eq. (P2.50-1), show that the initial conditions y[−1] = 1 and y[0] = 0 cannot be satisfied.
(d) If Eq. (P2.50-2) has two roots that are identical, then, in place of Eq. (P2.50-1), yh[n] will take the form
where we have assumed that the double root is z1. Using Eq. (P2.50-4), determine the general form of yh[n] for Eq. (P2.50-3). Verify explicitly that your answer satisfies Eq. (P2.50-3) with x[n] = 0.
(e) Determine the coefficientsA1 andB1 in the homogeneous solution obtained in part (d) if y[−1] = 1 and y[0] = 0.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.