ee20-07-Final-Exam-2007-12-19-Formulas-Tables

ee20-07-Final-Exam-2007-12-19-Formulas-Tables - EECS 20N:...

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Unformatted text preview: EECS 20N: Structure and Interpretation of Signals and Systems Department of EECS UNIVERSITY OF CALIFORNIA BERKELEY Final Exam Fall 2007 FORMULAS & TABLES Discrete Fourier Series (DFS) The discrete Fourier series synthesis and analysis equations for a periodic discrete-time signal having period p are x ( n ) = X k = h p i X k e ikω n ←→ X k = 1 p X n = h p i x ( n ) e- ikω n , where ω = 2 π/p is the fundamental frequency and h p i denotes a suitable dis- crete interval of length p (i.e., an interval containing p contiguous integers). For example, X k = h p i may denote p- 1 X k =0 or p X k =1 . Discrete Fourier Transform (DFT) The discrete Fourier transform synthesis and analysis equations for a periodic discrete-time signal having period p are x ( n ) = 1 p X k = h p i X k e ikω n ←→ X k = X n = h p i x ( n ) e- ikω n , where ω = 2 π/p is the fundamental frequency and h p i denotes a suitable dis- crete interval of length p (i.e., an interval containing p contiguous integers). For example, X k = h p i may denote p- 1 X k =0 or p X k =1 . 1 Continuous-Time Complex Exponential Fourier Series The complex exponential Fourier series synthesis and analysis equations for a periodic continuous- time signal having period p are x ( t ) = ∞ X k =-∞ X k e ikω t ←→ X k = 1 p Z h p i x ( t ) e- ikω t dt , where ω = 2 π/p is the fundamental frequency and h p i denotes a suitable continuous interval of length p . For example, Z h p i can denote Z p or Z + p/ 2- p/ 2 ....
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This note was uploaded on 12/24/2011 for the course ELECTRICAL 20 taught by Professor Babak during the Spring '11 term at University of California, Berkeley.

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ee20-07-Final-Exam-2007-12-19-Formulas-Tables - EECS 20N:...

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