Signal Compression: Laplace vs. Fourier

[rebeka]

I had posted a thread on another forum about building a 100GHz oscilloscope which resulted in the signal being chopped up by a bank of comparators and subsequently being fed into a video buffer for processing using currently developed parallel processing techniques. The subject of compression came up and it was suggested to use Fourier Transforms. I disagreed as I thought under the dynamic nature of the waves being represented essentially Fourier Transforms would in the end be bulky and the compression would essentially take too long. I figured it would be best to represent segments of the waves as differential equations where the differential would be acquired through curve fitting. I guess I'm arguing Laplace vs. Fourier with me siding on Laplace? Just curious as to what more knowledgeable individuals might have to say about this? Am I even making sense? I'm kind of nub ...

 

[gtoguy97]

Yes, you are making sense. Both Laplace and Fourier transforms can be used for compression of waveforms, although they work in different ways. Fourier transforms break down a signal into its component sine and cosine waves, while Laplace transforms break down a signal into its component exponentials. Depending on the type of signal, one may be more suitable than the other. For example, Fourier transforms are better suited to periodic signals, while Laplace transforms are better suited to non-periodic signals. Ultimately, the choice of which method to use will depend on the characteristics of the signal that needs to be compressed.