Signals and Systems For Dummies

Chapter 13

The Laplace Transform for Continuous-Time

In This Chapter

Checking out the two-sided and one-sided Laplace transforms

Getting to know the Laplace transform properties

Inversing the Laplace transform

Understanding the system function

The Laplace transform (LT) is a generalization of the Fourier transform (FT) and has a lot of nice features. For starters, the LT exists for a wider class of signals than FT. But the LT really shines when it’s used to solve linear constant coefficient (LCC) differential equations (see Chapter 7) because it enables you to get the total solution (forced and transient) for LCC differential equations and manage nonzero initial conditions automatically with algebraic manipulation alone.

Unlike the frequency domain, which has real frequency variable f or , the LT transforms signals and linear time-invariant (LTI) impulse responses into the s-domain, ...