Laplace Transform Pairs

Laplace Transform - ECE 2 York Table of Laplace Transform Pairs Signal 1 2 3 4 Impulse Step Ramp Power of t Waveform f(t Transform F s 1(t u(t t

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ECE 2 York Table of Laplace Transform Pairs Signal Waveform () f t Transform F s 1 Impulse t δ 1 2 Step ut 1 s 3 Ramp tu t 2 1 s 4 Power of t 1 1 ,2 ,3 1! n t n n = 1 n s 5 Exponential t eu t α 1 s + 6 Damped ramp t te u t 2 1 s + 7 Damped Power of t 1 1 n t t tn n = 1 n s + 8 Sine sin ( ) tut β 22 s + 9 Cosine cos ( ) s s + 10 Sinusoid 1 cos tan ( ) b ab t u t a ⎛⎞ +− ⎜⎟ ⎝⎠ as b s + + 11 Damped Sine sin ( ) t et u t 2 2 s ++ 12 Damped Cosine cos ( ) t u t 2 2 s s + ( ) 2c o s t ke t k ut ( ) +∠ * * where kk sp p j + =− + 13 Damped Sinusoid (Complex Poles) 1 cos tan ( ) t b e t u t a
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This note was uploaded on 10/19/2008 for the course ECE 2B taught by Professor York during the Winter '07 term at UCSB.

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