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Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/8 1- e-sT

Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/8 1- e-sT

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 48E
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Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/s 1- e-sT
Transcribed Image Text:Show that for all T> 0 and the unit step function u (t) that ∞ f (t) = Σu (t-kT) k=0 converges pointwise at each t = [0, ∞) (indeed, is only a finite sum at each t > 0). What does the graph of f (t) look like? Then show that for all Re (s) > 0. £ (f) = 1/s 1- e-sT
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