Lect-2_07 - Lecture-2 Review of Signals and Systems...

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Unformatted text preview: Lecture-2 Review of Signals and Systems Classification of signals: 1. Deterministic or Random (Stochastic ) Also Classified as Discrete-time(digital) Continuous time(analog) Further Classified as 1. Periodic 2. Aperiodic Also classified as Energy signal 0<E< infinity, and P=0 Power signal 0<P< infinity, and E is infinity Fourier Series : Every periodic signal can be ex pressed as an Infinite summation of complex exponential Sinusoidal functions i.e., x(t) = c n exp ( jn t). Where c n are called the Fourier Coefficients which have both magnitude as well as phase. c n = = |c n | exp (j n ) x(t) must satisfy the Dirichlets conditions. -- 2 / 2 / ) exp( ) ( 1 T T dt t jn t x T Dirichlets condition: For the Fourier series to exist, a signal x(t) must satisfy three conditions: 1. It must be absolutely integrable ie., that is as t , the function decays to zero. 1. It must have a finite number of maxima and minima in any finite interval. 3. It must have a finite number of discontinuities in any finite time interval. - < dt t x | ) ( | Bandwidth Estimation: Given a periodic signal one would like to know the spectral extent or spectral occupancy of the signal....
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This note was uploaded on 09/24/2010 for the course MATHEMATIC AAOC C222 taught by Professor Prof.dilipkumarsatpathi during the Fall '07 term at Birla Institute of Technology & Science, Pilani - Hyderabad.

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Lect-2_07 - Lecture-2 Review of Signals and Systems...

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