HW10.solutions

# HW10.solutions - ECE 2704 ‐ Homework Number 10 1 Using...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 2704 ‐ Homework Number 10 1. Using Properties of the Fourier transform, show that if where indicates convolution Solution Since convolution in the time‐domain is a product in the frequency‐domain, . You will need to convince yourself that . 2. Suppose is the input to a system and is the output. The output is the same as the input . Suppose , , then show that except delayed by some unknown amount . That is, , for all , and that Solution Since seconds. 3. Problem 7.5‐3 (page 766) (a, b, c) Solution . Cannot be realized since (a) , so if we add a time delay of can be realized. (b) , . Thus and for all . In other words, is the impulse response of a non‐causal system. The impulse response starts at , then the system is causal and . Corresponds to a noncausal system. Time‐delay does not help since the nonzero response extends to . However, most of the energy of the signal is centered near , so with a modest time‐delay, it is possible to approximate the desired response. (c) . Corresponds to a noncausal system, and a time‐delay won’t help at all. 4. Problem 7.7‐4 (page 766) (a, b) Solution (a) At point a the signal is Fourier transform of this signal is . . The ‐10,000 0 10,000 ω At point b, the signal is ‐10,000 ‐5,000 0 5,000 10,000 ω At point c, the signal this shifts the frequency spectrum in part(b) to . Using the same analysis in part(a), . ‐30,000 ‐20,000 0 20,000 30,000 ω (b) The spectrum is from approximately rads/sec. to rads/sec, so the bandwidth is 30,000 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online