Consider the DT LTI system defined by the impulse response h[n]. Please show all

Question

Consider the DT LTI system defined by the impulse response h[n]. Please show all your work on how you got the answer.

Consider the DT LTI system defined by the impulse response h[n] The input to this system is the signal in] a n Suppose we want to use the DFT to find the system output. In other words, we want to compute Ylkj 3HIklXk] and then take the inverse DFT to find yInl. The first step in this process is to compute the DFTs of In] and hIn], i.e. to compute XIk and HIk]. What is the minimum value of N (length of DFT) that can be used? Explain!

Explanation / Answer

h(n) = {1, -1} x(n) = {1, 2, 1}

Length of h(n), n1= 2

Length of x(n), n2 = 3

y(n) = x(n)*h(n)

Maximum possible length of y(n) = n1+n2-1 = 4

Hence, select N = 4

Taking DFT of x(n) and h(n),

X(k)= {0, 1+i , 2, 1-i }

H(k) ={4, -2i , 0, 2i}

Y(k) = {0, 2-2i , 0 2+2i}

Taking inverse DFT of Y(k),

y(n) = {1, 1, -1,-1}

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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