problem 5

# problem 5 - ECE 101 Linear Systems Winter 2009 Problem Set...

• Notes
• ProfessorResolvePartridge10091
• 5
• 100% (1) 1 out of 1 people found this document helpful

This preview shows pages 1–2. Sign up to view the full content.

ECE 101 - Linear Systems, Winter 2009 Problem Set # 5 Solutions (send comments/questions to [email protected]) Problem 1 (7.21 (c, d, and f) OW2) 7.21 (c) Here Im { X ( ) } is not specified. Therefore, the Nyquist rate for the signal x ( t ) cannot be determined. This implies that one cannot guarantee that x ( t ) would be recoverable from x p ( t ). 7.21 (d) Since x ( t ) is real, it follows that X ( ) = X * ( - ). Thus, X ( ) = 0 for | ω | > 5000. The Nyquist rate for the given signal is 2 × 5000 π = 10000 π . Therefore, in order to be able to recover x ( t ) from x p ( t ), the sampling period must at most be T max = 2 π/ 10000 π = 2 × 10 - 4 sec. Since the sampling period used is T = 10 - 4 < T max , x ( t ) can be recovered from x p ( t ). 7.21 (f) If X ( ) = 0 for | ω | > ω 1 , then X ( ) * X ( ) = 0 for | ω | > 2 ω 1 . Therefore, in this part, X ( ) = 0 for | ω | > 7500 π . The Nyquist rate for this signal is 2 × 7500 π = 15000 π . Therefore, in order to recover x ( t ) from x p ( t ), the sampling period must at most be T max = 2 π/ 15000 π = 1 . 33 × 10 - 4 sec. Since the sampling period used is T = 10 - 4 < T max , x ( t ) can be recovered from x p ( t ).

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern