Laplace transform: Difference between revisions
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The '''Laplace transform''' of a [[function]] ''f''(''t'') defined for all [[real number|real numbers]] ''t'' ≥ 0 is the function ''F''(''s''), defined by: |
The '''Laplace transform''' of a [[function]] ''f''(''t'') defined for all [[real number|real numbers]] ''t'' ≥ 0 is the function ''F''(''s''), defined by: |
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: ''F''(''s'') = ∫<sub>0</sub><sup>∞</sup> ''e''<sup>-''st''</sup> ''f''(''t'') d''t'' |
: ''F''(''s'') = ∫<sub>0</sub><sup>∞</sup> ''e''<sup>-''st''</sup> ''f''(''t'') d''t'' |
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The Laplace transform ''F''(''s'') typically exists for all real numbers ''s'' > ''a'', where ''a'' is a constant which depends on the growth behavior of ''f''(''t''). |
The Laplace transform ''F''(''s'') typically exists for all real numbers ''s'' > ''a'', where ''a'' is a constant which depends on the growth behavior of ''f''(''t''). |
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Revision as of 01:53, 29 January 2002
The Laplace transform of a function f(t) defined for all real numbers t ≥ 0 is the function F(s), defined by:
- F(s) = ∫0∞ e-st f(t) dt
The Laplace transform F(s) typically exists for all real numbers s > a, where a is a constant which depends on the growth behavior of f(t).
See also: Fourier transform, transfer function, linear dynamic system.