{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ecen314-fall11-hw4.5

# ecen314-fall11-hw4.5 - a k for the following...

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

ECEN 314: Signals and Systems, Fall ‘11 Homework #4.5 Homework Assignment #4.5 Due date – None. Just for practice. Problem 1. Fourier Series Representation Consider a continuous-time periodic signal x ( t ) , which is real valued and has a fundamental period of T = 8 . The nonzero Fourier series coefficients for x ( t ) are as follows: a 1 = a - 1 = 2 , a 3 = a * - 3 = 4 j Express x ( t ) in the form x ( t ) = k a k cos( ω k t + φ k ) . Problem 2. Fourier Series Representation Consider the following continuous-time periodic signal x ( t ) : x ( t ) = 2 + cos 2 π 3 t + sin 5 π 3 t . (a) What is the fundamental frequency w 0 of x ( t ) ? (b) Find the Fourier series coefficients a k such that x ( t ) = k a k e jkω 0 t . Problem 3. Fourier Series Representation Compute the Fourier series coefficients
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: a k for the following continuous-time periodic signal x ( t ) : x ( t ) = ³ 1 . 5 , ≤ t < 1-1 . 5 , 1 ≤ t < 2 with fundamental frequency ω = π . Problem 4. Fourier Series Representation Let x 1 ( t ) be a continuous-time periodic signal with fundamental frequency ω 1 and Fourier series coefﬁcients a k . Now, deﬁne x 2 ( t ) as follows: x 2 ( t ) = x 1 (1-t ) + x 1 ( t-1) . (a) What is the fundamental frequency ω 2 of the signal x 2 ( t ) ? (b) Find the relationship between the Fourier coefﬁcients b k of x 2 ( t ) and the coefﬁcients a k ....
View Full 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