tables2 - Table 1 A Short Table of Transforms f(t F(ω = F...

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Unformatted text preview: Table 1: A Short Table of Transforms f (t ) F (ω) = F [ f (t )]|ω restrictions pulseα (t ) 2α sinc(2π αω) 0<α e−α t step(t ) 1 α + i 2π ω 0<α eα t step(−t ) 1 α − i 2π ω 0<α e−α |t | 2α α 2 + 4π 2 ω 2 0<α π π2 exp − ω2 α α 0<α 1 δ(ω) none e i 2π α t δα (ω) none δα (t ) e−i 2π αω none combα (t ) 1 comb 1 (ω) α α 0<α e−α t 2 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, λ = any complex 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 Tλ [ f ] e−i 2π λω F (ω) none ei 2π λt f (t ) Tλ [ F ] none df dt i 2π ω F (ω) see chap. 22 t f (t ) i dF 2π d ω see chap. 22 Df i 2π ω F (ω) none t f (t ) i DF 2π none fg F ∗G see chap. 24 f ∗g FG see chap. 24 ...
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tables2 - Table 1 A Short Table of Transforms f(t F(ω = F...

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