{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

374bhw12

# 374bhw12 - HW#12 Phys374Spring 2007 Due before class Friday...

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

HW#12 —Phys374—Spring 2007 Prof. Ted Jacobson Due before class, Friday, May 4, 2007 Room 4115, (301)405-6020 www.physics.umd.edu/grt/taj/374b/ [email protected] 1. Sampling Theorem Exact reconstruction of a continuous-time signal from its discrete-time sam- ples is possible if the signal is band-limited and the sampling frequency is greater than twice the signal bandwidth. Consider a signal f ( t ) whose Fourier transform ˜ f ( ω ) is zero for | ω | > Ω, f ( t ) = Ω - Ω ˜ f ( ω ) e - iωt dω. (1) This is called a band-limited signal. Evaluating (1) at the discrete times t = nt s , where the sampling time t s is defined by t s = π/ Ω, yields f ( nt s ) = Ω - Ω ˜ f ( ω ) e - inπω/ Ω dω. (2) The right hand side of (2) is recognized as 2Ω times the n th coefficient in the Fourier series for ˜ f ( ω ). Being limited to the finite range - Ω < ω < Ω, the function ˜ f ( ω ) is determined by its Fourier series coefficients, and therefore by the discrete “samples” f ( nt s ). The sample values thus determine f ( t ) via (1). The sampling frequency 1 /t s = Ω is twice the bandwidth Ω / 2 π .

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