exam 2 2010 formulas

exam 2 2010 formulas - Formulas for Exam 2 b a jb = tan1 e...

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Formulas for Exam 2 a + jb = a 2 + b 2 a + jb ( ) = tan 1 b a Λ Ν Μ Ξ Π Ο e j θ = cos ( ) + j sin ( ) e j π 2 = j e j = 1 cos ( ) = 1 2 e j + e j { } sin ( ) = 1 2 j e j e j { } ________________________________________________________________________________________ 1. A CT system’s impulse response h t ( ) is the output when the input is δ t ( ) . 2. The causal LTI CT system having input-output differential equation dy t ( ) dt + a y t ( ) = x t ( ) has impulse response h t ( ) = e at u t ( ) . 3. For a CT LTI system having impulse response h t ( ) and input x t ( ) , the output satisfies y t ( ) = x t ( ) * h t ( ) = x r ( ) −∞ h t r ( ) dr = h t ( ) * r t ( ) = h r ( ) −∞ x t r ( ) dr . 4. A cascade connection of two CT LTI systems having impulse responses h 1 t ( ) and h 2 t ( ) , respectively, has overall impulse response h t ( ) = h 1 t ( ) * h 2 t ( ) . A parallel connection has overall impulse response h t ( ) = h 1 t ( ) + h 2 t ( ) . 5. A CT LTI system with impulse response h t ( ) is causal if h t ( ) = 0 for all t < 0 , and non- causal otherwise; it is stable if h t ( ) dt < −∞ , and unstable otherwise. 6. A CT LTI system with impulse response h t ( ) has transfer function H s ( ) = h t ( ) −∞ e st dt .
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This note was uploaded on 10/27/2011 for the course ECE 313 taught by Professor Muschinski during the Fall '08 term at UMass (Amherst).

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exam 2 2010 formulas - Formulas for Exam 2 b a jb = tan1 e...

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