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Before I dropped the plank there was nothing,

... breaking something down into component parts that can be put together to create the object but that does not mean that the parts have any relationship to the real components that made the object in the first place.For example if I mage a loud bang by dropping a plank on a hard floor in a quiet room and record the waveform and include say a second of silence before the bang and a few seconds after the bang as the sound dies away I can break this noise down into fourier components using continuous sine waves and it will be recreated with as much accuracy as I desire but all the sine waves will continue for the entire period of the window over which I have decided to reproduce the recording ...

Perfectly true, of course.However the whole concept of Fourier transforms assumes you're working with a periodic or repetitive waveform (like a continuous tone, trumpet sound, violin etc) - not a one-off crash.

What are they? What are they used for?...they seem to pop up a lot in physics.ww.thenakedscientists.com/forum/index.php?topic=11068.0 .

Quote from: Soul Surfer on 11/11/2007 10:28:48... breaking something down into component parts that can be put together to create the object but that does not mean that the parts have any relationship to the real components that made the object in the first place.For example if I mage a loud bang by dropping a plank on a hard floor in a quiet room and record the waveform and include say a second of silence before the bang and a few seconds after the bang as the sound dies away I can break this noise down into fourier components using continuous sine waves and it will be recreated with as much accuracy as I desire but all the sine waves will continue for the entire period of the window over which I have decided to reproduce the recording ...Perfectly true, of course.However the whole concept of Fourier transforms assumes you're working with a periodic or repetitive waveform (like a continuous tone, trumpet sound, violin etc) - not a one-off crash. Furthermore the waveform should be periodic within the timeslice you analyse - there should be an exact whole-number of wavecycles in the analysis interval (otherwise you get some spurious results).For analysing arbitrary (non-strictly periodic) signals, you use a "Short Term Fourier transform" which uses a "window function" to gracefully fade out the signal towards the ends of the sampling interval. It's a fudge, but very useful in practice.I've got a bit of graphical and mathematical info on Fourier transforms etc on my DSP webpage at ...sorry, you cannot view external links. To see them, please REGISTER or LOGINThe concept of deconvolution had an early application in reflection seismology. In 1950, Enders Robinson was a graduate student at MIT. He worked with others at MIT, such as Wiener, Norman Levinson, and economist Paul Samuelson, to develop the "convolutional model" of a reflection seismogram. This model assumes that the recorded seismogram s(t) is the convolution of an Earth-reflectivity function e(t) and a seismic wavelet w(t) from a point source, where t represents recording time. Thus, our convolution equation is s(t) = e(t) * w(t).The seismologist is interested in e, which contains information about the Earth's structure. By the convolution theorem, this equation may be Fourier transformed to S(ω) = E(ω)W(ω)in the frequency domain. - end of Wiki quote.I may be wrong but isn't this the use of Fourier transforms to analyze non-coherent data?(please note - I pulled out my first, undergraduate seismic reflection geophysics book and it didn't even mention deconvolution. My graduate book did. God, I'm a fossil!)

Can I just throw the word "apodization" in here?

Actually techmind, your explanation made perfect sense......Ah, I see where this fits in with black-body radiation now! "I can see clearly now...."Wait, so, to find a function of frequency for the light emitted from a black body at a constant temperature, could you measure the EM waves across a point in space and take E(t) and apply a Fourier Transform to it? If you do this at varying temperatures you could empirically derive Planck's Law! Oh Man! Is there a function relating light intensity to the amplitude of electromagnetic waves? Planck's Law is Intensity or Energy Density, right?