SP 2005 CH1 Signals Part 1

# SP 2005 CH1 Signals Part 1 - EE 3120 Chapter 1 Lecture 2...

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Unformatted text preview: EE 3120 Chapter 1 Lecture 2 Elementary Continuous Time Signals Elementary continuous time functions : Constant f(t) : = 1 , for all t unit step u(t) : = 1, for t ≥ 0 0, for t < 0 Elementary continuous time functions : unit ramp r(t) : = t for t ≥ 0 0 for t < 0 Elementary continuous time functions : unit impulse = 1 for t ≠ 0 1 Also known as the Dirac delta, or simply delta function. It can be visualized as a tall, narrow rectangular pulse with an area of 1. The width is very small, approaching zero. The height then must be very large, (inverse of width). Therefore we simply draw a line with a height of 1 with an arrow. Multiplying the unit impulse by any continuous function at t = 0, the result is simply the function evaluated at t = 0, since the impulse has a weight of 1 at t=0. ( ) ( ) (0) ( ) ( ) ( ) ( ) ( ) t t t t t T T t T φ δ φ δ φ δ φ δ =- =- ( ) t dt δ- ( ) t δ = Elementary continuous time functions : From this we have the Sampling or sifting property of the unit impulse function:...
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SP 2005 CH1 Signals Part 1 - EE 3120 Chapter 1 Lecture 2...

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