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#1
11-07-2002, 06:00 AM
 Cubsfan Guest Join Date: Jul 2002 Location: Ohio Posts: 5,187
Fourier transform vs Laplace transform. Why use one over the other?

We were discussing this in a comm systems class yesterday and no one could come up with a good explaination as to why we use Laplace transforms over Fourier and vice versa. Both take equations that are in the time domain and transform them into the frequency domain. It seems in Comm we use only Fourier analysis methods and in Circuit analysis and DE we onle use Laplace.

What are the situations that define which one you will use?

On a side note, what are Z transforms typically used for?
#2
11-07-2002, 06:07 AM
 CalMeacham Member Join Date: May 2000 Location: Massachusetts Posts: 42,050
Fourier Transforms and Laplace Transforms are both frequency space transforms, but one has an imaginary argument and the other a real one. They're associated with different physical situations that dictate where they are used. Fourier Transforms are useful if you want to see the frequency spectrum makeup of a signal -- something you don't get from the Laplace Transform. Laplace Transforms, on the other hand, are useful in solving rate equations. They come in useful if you're taking a course in Diffie Q's (Differential Equations).

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#3
11-07-2002, 06:10 AM
 scr4 Member Join Date: Aug 1999 Location: Alabama Posts: 14,239
IIRC, Fourier transforms only work for functions that converge to zero at infinity. Laplace transforms work for functions that diverge exponentially. Many real-world physics problems have exponential solutions.
#4
11-07-2002, 09:05 AM
 David Simmons Charter Member Join Date: Nov 2001 Posts: 12,684
Re: Fourier transform vs Laplace transform. Why use one over the other?

Quote:
 Originally posted by Stinkpalm On a side note, what are Z transforms typically used for?
Z transforms are a method for analyzing sampled data feedback (for example, servomechanism) systems.
#5
11-07-2002, 11:18 AM
 Crafter_Man Guest Join Date: Apr 1999 Location: Ohio Posts: 10,588
In a nutshell,

The Laplace Transform is used for analyzing continuous time signals. It transforms a signal in the time-domain (function of t) to a signal in the “s” domain, where s = s + jw.

The Fourier Transform is a special case of the Laplace Transform in which s = 0, so that s = jw. It is used to analyze “stable” signals (non-exponential, etc.).

The Z-Transform is basically the same thing as the Laplace Transform, except it’s used for discrete (i.e. sampled) signals.

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