tables1 - Table 1: A Very Short Table of Transforms f (t )...

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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 Near-equivalance: 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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