Unformatted text preview: Table 1: A Very Short Table of Transforms
f (t ) F (ω) = F [ f (t )]ω restrictions pulseα (t ) 2α sinc(2π αω) 0<α e−αt step(t ) 1
α + i 2π ω 0<α e−α t 
e−αt α2 2α
+ 4π 2 ω2 π
π2
exp − ω2
α
α 2 0<α 0<α Table 2: A Basic Table of Identities Nearequivalance:
F −1 [φ(x )] y = F [φ(−x )] y = F [φ(x )]− y and
F [φ(x )] y = F −1 [φ(−x )] y = F −1 [φ(x )]− y . In the following:
α = any real number, F (ω) = F [ f (t )]ω , and G (ω) = F [g (t )]ω
h (t ) H (ω) = F [h (t )]ω restrictions ∞ f (t ) e−i 2π ωt dt f in A 1
ω
F
α 
α f (t ) α=0 −∞ f (α t )
f (t − α) e−i 2π αω F (ω) none e i 2 π α t f (t ) F (ω − α) none df
dt i 2π ω F (ω) see chap. 22 t f (t ) i dF
2π d ω see chap. 22 ...
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This note was uploaded on 11/07/2011 for the course MA 460 taught by Professor Staff during the Fall '11 term at University of Alabama in Huntsville.
 Fall '11
 Staff

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