Differences between laplace transform, z transform and fourier transform

On Tuesday, July 14, 2009 at 11:58:13 PM UTC+12, somanath17 wrote:
> Hi All,
> 
> I have studied three diff kinds of transforms, The laplace transform, the
> z transform and the fourier transform. As per my understanding the usage of
> the above transforms are:
> Laplace Transforms are used primarily in continuous signal studies, more
> so in realizing the analog circuit equivalent and is widely used in the
> study of transient behaviors of systems.
> 
> The Z transform is the digital equivalent of a Laplace transform and is
> used for steady state analysis and is used to realize the digital circuits
> for digital systems.
> 
> The Fourier transform is a particular case of z-transform, i.e z-transform
> evaluated on a unit circle and is also used in digital signals and is more
> so used to in spectrum analysis and calculating the energy density as
> Fourier transforms always result in even signals and are used for
> calculating the energy of the signal.
> 
> Is my understanding correct. What more technical differences exist and
> where do all these differences find their application. Would be really
> helpful if someone can give an understanding of this and provide links
> where i can look up for the same.
> 
> Thanks,
> Soma

Thing to remember is, none of them work for nonlinear systems! Then you need Volterra-series and the like