20111eeM214A_1_ps411-sol

# 20111eeM214A_1_ps411-sol - k is given by ℜ h k n = e an 2...

This preview shows pages 1–9. Sign up to view the full content.

UCLA Dept. of Electrical Engineering EE M214A, Winter 2011 Problem Set 4 Solution February 7, 2011 1. 7.13 Answer: 1

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

View Full Document
2

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

View Full Document
4
5

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

View Full Document
4. Answer: Omitted. 5. (a) To avoid aliasing in the time domain, the number filters must be at least equal to the length of the window in samples. Thus N min =19. (b) The impulse response of the filter for channel k is given by: h k ( n ) = w k ( n ) e j 2 πnk N (1) h k ( n ) = e an 2 e j 2 πnk N (2) h k ( n ) = e an 2 + j 2 πnk N (3) (c) The spacing between adjacent filters is given by: Δ ω = 2 π N = 2 π 50 . (3) Thus, the spectral resolution in Hz is given by: Δ F = Δ ω 2 π F s = 2 π 50 × 2 π 10kHz = 200Hz . (3) (d) The real part of the impulse response of channel

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.

Unformatted text preview: k is given by: ℜ ( h k ( n )) = e an 2 cos p 2 πnk 50 P . (3) ±or the example channels k = 0 , 5, the real part oF the impulse response reduces to: ℜ ( h ( n )) = e an 2 (4) ℜ ( h 5 ( n )) = e an 2 cos p 2 πn 10 P (5) These Functions are illustrated in ±igure 1. 7 0.2 0.4 0.6 0.8 1 h (n)-1-0.5 0.5 1 5 Figure 1: Real Parts of the Filters h k ( n ) for Channels k =0 and 5. 6. a) 8 b) 3: female; 4: male. c) 3: 210 Hz 4: 140 Hz 9...
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