log fire wrote:> In article <10uo4bedfrdt3a3@corp.supernews.com>, Tim Wescott > <tim@wescottnospamdesign.com> wrote: > > >>Google on "Fourier Transform". Asking here for a book recommendation >>may also be a good idea -- there's a large mass of material to be >>learned, I've always done better with that sort of thing by curling up >>with a book rather than hitting the net. >> >>Rick Lyon's book "Understanding Digital Signal Processing" would be a >>good book, but you may want to get a signal processing book that'll take >>you through continuous-time signal processing first. This stuff is >>generally taught in the second year of a college electronics engineering >>course -- if you can you may want to see if you can take some classes. > > > ok, thanks for the advise. > > can i check this with you/anyone please? i'm having a bit of trouble > seeing why fourier transforms (whatever they really are), particularly > for sound (as opposed to other types of data), should be needed. i'm > wondering why can't i ignore, or why would it be a silly idea to > ignore, fourier transforms and just start analysing sound data just > like i might other types of data such as images or text. (i doubt i'd > be considering fourier transforms for those data types). i'm suggesting > (just in a questioning kind of way) avoiding ft's and directly > accessing audio, sample by sample, and taking my sound analysis > (comparing sounds to see how similar they are etc) from there using my > own dreampt up methods? with images you can easily directly access each > pixel, find out what colour it is, and take it from there with whatever > methods you fancy / can think of. dreampt up methods for image analysis > have the potential to be perfectly successful i think. what's > different, if anything, about sound? (and a further confusion, i > realise that dsp isn't just about sound, but images and other signals > -- any signals i guess). > > is it something like this maybe: single samples from a sound signal are > like single pixels in an image. that is a perfectly reasonable and good > analogy. *but* frequencies are on a higher level than single samples > though. like textures in an image are on a higher level than single > pixels (numerous pixels are needed and some kind of pattern / > relationship goes on to make up a texture -- which needs to be > understood/recognised). and with text, words and meanings are on higher > levels than individual characters. in order to extract/see these higher > level pieces of information, with whatever type of data (sounds, > images, text), you need some kind of logic that almost understands the > data in order to show the higher level information. nobody's forcing me > to use fourier transforms to analyse sound, but if i'm going to analyse > sound i'm going to need to have access to frequencies, and fourier > transforms are the tested and proven way to get at frequencies. i'd be > foolish to attempt to go my own way so far as getting access to > frequencies from sound signals. signals to frequencies, so far as sound > goes, are fourier transform's forte? and i'd be hard pushed to access > the frequencies any other way? is that roughly right? > > another thing: once having used fourier transforms to get access to > frequencies, it'd be ok, and not silly, to then not use fourier > transforms? go on and further analyse the frequencies without ft's?Three reasons: First, because the human ear works more or less like a frequency bank -- your cochlea are little audio filters, and the cilia within them are little pickup devices. In the end what the brain gets is not unlike real-time Fourier transform of what's going on externally. So getting sounds into the frequency domain is getting them closer to the information that's presented to the brain. Second, because many systems in nature are frequency selective, and the Fourier transform allows one to work in that domain. For many such systems the reduction in computation time, and the increased intuitive understanding of what's going on, is profound when you do your work in the frequency domain. Finally, because it's another arrow in your quiver. Because it's so well understood (once you get over that initial hurdle) it's a tool that you can throw at a _lot_ of problems. Even problems where it isn't a good fit may be solved well enough quickly enough that it wouldn't be at all profitable to spend the time necessary to develop a special theory just to solve that one problem. Actually if you're careful with scaling (and time inversion), the Fourier transform of a Flourier transform is your original data. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com
2, i'm sure, very simple questions about signal processing
Started by ●January 15, 2005
Reply by ●January 17, 20052005-01-17
Reply by ●January 17, 20052005-01-17
log fire wrote: ...> ok, thanks for the advise. > > can i check this with you/anyone please? i'm having a bit of trouble > seeing why fourier transforms (whatever they really are), particularly > for sound (as opposed to other types of data), should be needed. i'm > wondering why can't i ignore, or why would it be a silly idea to > ignore, fourier transforms and just start analysing sound data just > like i might other types of data such as images or text.... Sound is about frequencies; that's how your ears work. Fourier analysis is a way to find out what frequencies a sound consists of. There are other ways, but they are equivalent to Fourier analysis. If you can work out a procedure that you like better, go for it. Once you understand the classical Fourier analysis, you'll also understand why it's equivalent to your private method. I once had a private method for doing long division with paper and pencil. I invented it because my teacher couldn't explain why the classical method works. She said "It just does" and I couldn't buy that. After I refined my way to reduce the amount of writing to the absolute minimum, I discovered that I was actually doing the classroom algorithm. But then, I understood why it worked. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●January 18, 20052005-01-18
Tim Wescott wrote:> log fire wrote: > >> Tim Wescott <tim@wescottnospamdesign.com> wrote: >> >> >>> log fire wrote: >>> >>>> but if you have all tones, lasting for ever, that'd be a continual mass >>>> of unchanging sound. can these never ending tones change tone? go very >>>> quiet/silent? change basically? otherwise there wouldn't be any change >>>> in sound ever. just a massive loud countinual din of all possible >>>> tones. everything always. >>>> >>> >>> Not really -- the Fourier transform shows us that the tones will >>> cancel each other everywhere but one spot, if they're organized >>> correctly. >>> >>> The way one is usually expected to gain insight into this is to do >>> the math on a bunch of signals. This will cough up some severely >>> counter-intuitive results indicating that either your math or your >>> intuition needs adjustment. After you verify your math you're left >>> with adjusting your intuition. >> >> >> >> hmm, interesting. what sort of math on signals? what sort of thing >> would be involved? do you know of any webpages that'd explain / help me >> get going with the type of thing you're talking about? >> >> > snip > > Google on "Fourier Transform". Asking here for a book recommendation > may also be a good idea -- there's a large mass of material to be > learned, I've always done better with that sort of thing by curling up > with a book rather than hitting the net. > > Rick Lyon's book "Understanding Digital Signal Processing" would be a > good book, but you may want to get a signal processing book that'll take > you through continuous-time signal processing first. This stuff is > generally taught in the second year of a college electronics engineering > course -- if you can you may want to see if you can take some classes. >When I started asking questions about FFT's, someone posted links to two (related) Java applets that pictorially [ and IIRC aurally ] demonstrated fourier transforms. I've misplaced the link, can anyone supply it. I think it might assist the OP. He might consider downloading Scilab ( http://scilabsoft.inria.fr/ ) It's free ;} He can then create arbitrary functions and then graph the function and its transform.
Reply by ●January 18, 20052005-01-18
In article <10uonvfmuqlml77@corp.supernews.com>, Tim Wescott> > Three reasons: > > First, because the human ear works more or less like a frequency bank -- > your cochlea are little audio filters, and the cilia within them are > little pickup devices. In the end what the brain gets is not unlike > real-time Fourier transform of what's going on externally. So getting > sounds into the frequency domain is getting them closer to the > information that's presented to the brain.right. that's what i was trying to get at with the higher levels of information thing -- a stepup the hierarchical information structure, as you say, closer to to what our brains deal with -- a slightly more consolidated and processed version than the raw input.> > Second, because many systems in nature are frequency selective, and the > Fourier transform allows one to work in that domain. For many such > systems the reduction in computation time, and the increased intuitive > understanding of what's going on, is profound when you do your work in > the frequency domain. > > Finally, because it's another arrow in your quiver. Because it's so > well understood (once you get over that initial hurdle) it's a tool that > you can throw at a _lot_ of problems. Even problems where it isn't a > good fit may be solved well enough quickly enough that it wouldn't be at > all profitable to spend the time necessary to develop a special theory > just to solve that one problem. > > Actually if you're careful with scaling (and time inversion), the > Fourier transform of a Flourier transform is your original data.great. i've now got an idea of the point of, and a feeling of what ft's actually do (roughly). thanks very much.
Reply by ●January 18, 20052005-01-18
In article <353d3uF4hvar3U1@individual.net>, Jerry Avins <jya@ieee.org> wrote:> log fire wrote: > > ... > > > ok, thanks for the advise. > > > > can i check this with you/anyone please? i'm having a bit of trouble > > seeing why fourier transforms (whatever they really are), particularly > > for sound (as opposed to other types of data), should be needed. i'm > > wondering why can't i ignore, or why would it be a silly idea to > > ignore, fourier transforms and just start analysing sound data just > > like i might other types of data such as images or text. > > ... > > Sound is about frequencies; that's how your ears work. Fourier analysis > is a way to find out what frequencies a sound consists of. There are > other ways, but they are equivalent to Fourier analysis. If you can work > out a procedure that you like better, go for it. Once you understand the > classical Fourier analysis, you'll also understand why it's equivalent > to your private method. > > I once had a private method for doing long division with paper and > pencil. I invented it because my teacher couldn't explain why the > classical method works. She said "It just does" and I couldn't buy that. > After I refined my way to reduce the amount of writing to the absolute > minimum, I discovered that I was actually doing the classroom algorithm. > But then, I understood why it worked.right, yes, i see exactly what you mean -- most helpful. thanks.
