problem set2

# problem set2 - ELEC 531 STATISTICAL SIGNAL PROCESSING...

• Homework Help
• PresidentHackerCaribou10582
• 3

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

ELEC 531: STATISTICAL SIGNAL PROCESSING Department of Electrical and Computer Engineering Rice University Fall 2007 Problem Set 2 Due: September 13, 2007 Problem 2.1 Determine the mean and correlation function of each of the processes X t defined below. (a) X t is defined by the following equally likely sample functions. X t ( ω 1 ) = 1 X t ( ω 3 ) = sin πt X t ( ω 2 ) = - 2 X t ( ω 4 ) = cos πt (b) X t is defined by X t = cos( At + θ ), where A and θ are statistically independent random variables. θ is uniformly distributed over [0 , 2 π ) and A has the density function p A ( A ) = 1 π (1 + A 2 ) Problem 2.2 (a) Which of the following are valid correlation functions? Indicate your reasoning. (i) R X ( τ ) = e -| τ | - e - 2 | τ | (ii) R X ( τ ) = 5 sin 1000 τ τ (iii) R X ( τ ) = 1 - | τ | T | τ | ≤ T 0 otherwise (iv) R X ( τ ) = 1 | τ | ≤ T 0 otherwise (v) R X ( τ ) = δ ( τ ) + 25 (vi) R X ( τ ) = δ ( τ + 1) + δ ( τ ) + δ ( τ - 1) (b) Which of the following are valid power density spectra? Indicate your reasoning. (i) S X ( f ) = sin πf πf (ii) S X ( f ) = sin πf πf 2 (iii) S X ( f ) = exp - ( f - f 0 ) 2 4 (iv) S X ( f ) = e -| f | - e - 2 | f | (v) S X ( f ) = 1 + 0 . 25 e - j 2 πf (vi) S X ( f ) = 1 | f

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

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