For this problem please use the LCCDE system at initial rest described below: y[

Question

For this problem please use the LCCDE system at initial rest described below: y[n] + ½ y[n - 1] = x[n] Find and plot the impulse response of this LTI system. From the time domain, tell me if this looks like a high-pass or low-pass filter. Find the DTFT of the impulse response. Show your work. Use Matlab to plot the magnitude of the DTFT. Is this system high-pass or low-pass?

Explanation / Answer

sol: To find the impulse response y[n]: we know that y[n] = homogenous solution + particular solution so... we get lamda - (1/2) = 0 => lamda= (1/2) homogenous solution = C1*(1/2)^n For the particular solution, we assume that a x[n] = delta[n]...am i correct? so ... y[n] - (1/2) y[n-1] = delta[n] + 2 delta[n-1] + delta[n-2] so, for n >2, delta[n] = 0

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.