# Lecture 5: System Analysis Using Fourier Transforms

We have seen that we can use Laplace transforms for analysis of LTIC systems. We can do similar things with Fourier transforms, except that we will be able to obtain only steady-state responses, not the transient response. For the differential equation

we can use the time-differentiation property of the F.T.:

so that we can write

or

where

The function is the transfer function of the system, and is related to the transfer function we saw for Laplace transforms.

Analysis with the F.T. is not generally preferable to analysis with
the L.T., because the system must always be asymptotically stable and
we have to lug around
, instead of the more compact
.
However, for systems or signals that are noncausal and Fourier
transformable, the analysis may be easier using F.T.