18. Laplace transform

If Laplace transform is used, the difficult calculation of derivation and integration required in the design of the control circuit can be replaced with the simple multiplication, division calculation of algebra operation. Laplace transform is defined as follows.
Fs defined by on the time function ft defined by t≧0 is called the Laplace transform of f(t). The list of Laplace transform of the fundamental function is shown below.

Function name Time function f(t) Laplace transform F(s)

Unit impulse function

δ(t)

1

Unit step function

1

Unit ramp function

t

Exponential function

Sine function

sin ωt

Cosine function

cos ωt

Hyperbolic sineSineFunction

sinh ωt

Hyperbolic cosineCosineFunction

cosh ωt

sinc Function

Other functions

t sin ωt

t cos ωt