Introduction to Wavelets 16
tang_horse writes "If you're curious about where wavelet theory came from and how it works, but didn't get beyond second semester DQ (or algebra/trig I), there's a lucid review, history, and introduction to wavelet theory on the National Academy of Sciences Beyond Discovery website. It includes some fairly concrete demos of what a wavelet function does to an image."
My thesis was on wavelet compression... (Score:2, Interesting)
Throw a stone into a pool. Those are waves. Take an infinitesimally small arc segment from one of those waves and you have a wavelet, basically.
Totally double-talk that has nothing to do with the soliton basis for Wavelet Theory (WT).
Re:My thesis was on wavelet compression... (Score:1)
thx
-shpoffo
Just how DO you do DSP on a PC? (Score:3, Interesting)
I haven't done any programming with sound files since I tried to play a
And how do these libraries work? Is it basically iterating stuff over a huge array of amplitudes? So that to implement the lowpass filter, you actually have to somehow or other scan the array to look for patterns that need to be smoothed out? (actually, it occurs to me that you might be able to do this by averaging adjacent entries together. Okay, then, how do you do a high-pass filter, keeping the local oscillations but dropping the low-frequency ones?)
Basically, I'm curious about a good primer for DIY sound processing. Not because I want to build my own sound processing stuff, but because I'm really curious how people can do stuff like what Morlet did, especially considering he did it like 20 years ago, with significantly less-powered hardware...
(and, yes, I searched google for this, but it was a year or two ago...didn't find anything really helpful, except an early framework of an open source library that hadn't progessed much).
Re:Just how DO you do DSP on a PC? (Score:4, Interesting)
Re:Just how DO you do DSP on a PC? (Score:4, Informative)
Well, you are getting there... Basically, a lot of the actual processing of discrete sample sequences (such as a .wav file) are based on an operation called a convolution (which is the same as a correlation with one argument reversed in time). Thus, you "convolve" a digital sequence with another, usually much shorter sequence that is known as a filter. The filter sequence is deisgned to be low-pass, high-pass, band-pass, etc.
The key point is that a convolution in the time domain (ie. dealing with discrete samples in time) has an equivalence to operations in the frequency domain (what you get when you do a Fourier Transform on a sequence of time samples). By designing your filter in the frequency domain, you come up with filter sequences in the time domain, and the "convolution" does the rest. It is really some of the most elegant mathematics one can study in an engineering discipline (IMO)
Anyway, this oversimplifies many things, but is a step toward removing the "mystery" of digital filtering. I would suggest a book such as Hamming's "Digital Filters" (which is cheap and good), or checking Google for "Fourier digital filtering", etc. for more info. You were on to something when you talked about averaging; that is indeed a simple low-pass filter, but much better ones can be made almost as simply.
BTW, wavelets are a related topic, but it is probably better to understand the Fourier realm first.
I welcome any corrections or clarifications to these statements by those in the know; or follow up questions if what I said is unclear.
Re:Just how DO you do DSP on a PC? (Score:1)
Probably the best source (ahem) for real-world working signal-processing code, for bit-twiddling type people, is SoX [sourceforge.net], which has been vastly improved by its current maintainer Chris Bagwell who took it over in 1995. It includes a few different filtering algorithms (see band.c, deemphas.c, earwax.c, filter.c, highp.c, lowp.c) among other changes (no more clicking noises when resampling, hooray!).
sound processing (Score:3, Informative)
As far as applications, if you're using windows, there are a number of very advanced audio editor programs, like Cool Edit, Goldwave, etc. Try a search at one of the usual software download places.
Probably the most extensive DSP applications turn to something like Matlab, but that's hardly free.
For a unix-style solution, there's a package of tools here [cf.ac.uk] called pipewave which allows you to do very complicated digital signal processing using unix pipes. It follows the philosophy that you can do very complicated tasks by cascading smaller components using pipelines. Here are some examples from the above site:
JPEG 2000 (Score:2)
David
question... (Score:2, Interesting)
My first impression when they mentioned "transients" and "crappy" was the Gibbs phenomenon. Is this what they were talking about, and more importantly, is the Gibbs phenomenon caused by the H.U.P.?
Re:question... (Score:3)
It's the other way around; HUP (which is physics) is caused by the fact that you can't extrapolate the full shape of a wave from a small piece of it (which is math).
A good general rule of thumb: there are many examples of math causing physics, but there are no known cases of physics causing math.
-- MarkusQ
JPEG-2000 (Score:1)
(Preferably a cheap shareware app. Heh)
intro on wavelets? (Score:1)
Anybody know where you could find a introduction to this subject that actually introduces it?