MidtermExam2008 - text 4(15 Using the DFT and the IDFT find...

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ECE 158 Fall Quarter 2008 Gibson 11/03/08 Mid-Term Exam Instructions: Do all problems. Show all work. Problems are weighted as shown. 1. (15) Let ( ) x t be an analog signal with a bandwidth of 3,000 Hz. (a) What is the minimum sampling rate for this signal? (b) We wish to use a 2 m N = point DFT to compute the spectrum of the signal with a resolution less than or equal to 50 Hz. What is the minimum number of required samples? 2. (15) Calculate the four point DFT of the sequence {1, 2, 3, 1}. 3. (15) Prove the circular frequency-shifting property in Eq. (5.100) on page 260 of the
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Unformatted text preview: text. 4. (15) Using the DFT and the IDFT, find the four point circular convolution of and the input [ ] {1,2,3,1} h n = { } {4,3,2,2} x n = . 5. (15) Do Problem 5.62 (b) in the text. 6. (15) Let [ ] x n be an N-point real sequence with N-point DFT [ ] X k , N even. If [ ] x n satisfies the property [ ] [ 2 N ], x n x + = − n for 0,1,. ..., 1 2 N n = − , show that for even. [ ] 0, X k = k 7. (5) (a) Show that . / 2 k N k N N W W + = − (5) (b) Show that 2 2 k k N N W W =...
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