Question

1. Apply a recursion approach to solve the folliowing causal LTY system problem (a) Find and sketch the impulse response, hEnl. (b) Is the system FIR or IR? (c) Sketch its step response, sIn). (d) Draw the direct form and direct-form l Implementation of the abon difterence equation.

Answer 1

Given that y(n) - 2y (n - 1) - 3y (n - 2) - 2x(n) + x(n - 1) a find and sketch the pulse response, h(n) In the above equation. y (z) - 24 (z) z^-1 - 3 y (z) z^-2 = 2 times (z) + times (z) z^-1 y(z) [1.2 z^-1 - 37^-2] = times (z) [2 + z^-1] y (z)/x(z) = 2 + z^-1/(1 - 2 z^-1 - 3 z^-2) H(z) = 2 + z^-1/(1.2 z^-1 3 z^-2) H(z) = z + z^-1/1 - 2 z^-1 - 3 z^-2 H(z) = 2 + z^-1/(1 - 3 z^-1)(1 + z^-1) 2 + z^-1/(1 - 3 z^-1)(1 + z^-1) = A/(1 - 37 - 1) + 8/(1 + z^-1) \r\n z^-1 = 1/3 A = 2 + 1/3/1 + 1/3 = 6 + 1/3/4/3 = m 7/4 z^-1 = -1 B = 2 - 1/1 - 3(-1) = 1/1 + 3 = 1/4 /1 - 3 z^-1) (1 + z^-1) = 7/4 1/(1 - 3 z^-1) + 1/4 1/1 + z^-1 = 7/4 1/1 - 3 z^-1 + 1/4 1/1 -