From: "P.G.Hamer" Subject: Re: Fourier Series w. rect. functions Date: Wed, 13 Dec 2000 19:12:45 +0000 Newsgroups: sci.math.num-analysis Summary: [missing] P.G.Hamer wrote: > Michel Simon wrote: > > > Can anybody help me. I get a memory lack > > and I'm no longer able to retrieve the name of this kind > > of Fourier series where rectangular functions are > > used instead of sine / cosine functions ? > > Walsh? Hamard? Assuming that you meant kinds of orthogonal > series rather than kinds of Fourier Series. > > In some contexts you might be looking at wavelets nowadays, in > which case the Haar transform is the one based on rectangular > functions. To the last paragraph. You may have been thinking of the Haar transform. It was around for about 50 years before it was recognised as a primitive form of wavelet. It's now often called the Haar wavelet transform. Peter PS If you are going to use the Haar transform it may be worth looking for old books that talk about the `rational Haar transform'. Pretty much the same thing, but tweaked to remove the many sqrt(2) terms. ============================================================================== From: Benoit Leprettre Subject: Re: Fourier Series w. rect. functions Date: Wed, 13 Dec 2000 17:01:05 +0100 Newsgroups: sci.math.num-analysis Michel Simon wrote: > > Can anybody help me. I get a memory lack > and I'm no longer able to retrieve the name of this kind > of Fourier series where rectangular functions are > used instead of sine / cosine functions ? > > -- > Michel SIMON simon@lorraine.u-strasbg.fr > Géographie 3, rue l'Argonne F-67000 Strasbourg > Tel: 33 (0)3 88 45 65 38 Fax: 33 (0)3 88 45 33 88 Hi, If it is not based on sine and cosine waves, it is certainly not a Fourier series. The only thing I can think of that comes close to that, is the Haar wavelet. However, it's not really a rectangular function : it is an ocillating function that has this shape : ------ | | ------ | |------ | | ------ The Haar wavelet is the simplest wavelet you can use for Discrete Wavelet Transform. Hope this helps anyway... -- --------------------------------------------------- Benoit LEPRETTRE Signal Processing Engineer Schneider Electric SA, Grenoble, France Note : The opinions here are mine, not my company's --------------------------------------------------- ============================================================================== From: Thomas Kragh Subject: Re: Fourier Series w. rect. functions Date: Wed, 13 Dec 2000 12:06:04 -0500 Newsgroups: sci.math.num-analysis Benoit Leprettre wrote: > Michel Simon wrote: > > > > Can anybody help me. I get a memory lack > > and I'm no longer able to retrieve the name of this kind > > of Fourier series where rectangular functions are > > used instead of sine / cosine functions ? Haar basis functions. They are the simplest kind of wavelet, consisting of shifted, scaled and summed rect-functions. > > > If it is not based on sine and cosine waves, it is certainly > not a Fourier series. Not true. Fourier worked it out for the complex exponential case. Well, really sines & cosine, which can be simplified as being complex exponentials. In the general case, all you need is a complete orthonormal sequence in a Hilbert space (i.e orthogonal polynomials, various wavelet bases, etc). However, Hilbert spaces and what-not is all late 19th and early 20th century math which came after Fourier. > The only thing I can think of that comes > close to that, is the Haar wavelet. However, it's not really > a rectangular function : it is an ocillating function that > has this shape : > > ------ > | | > ------ | |------ > | | > ------ > > The Haar wavelet is the simplest wavelet you can use for > Discrete Wavelet Transform. > -- -----BEGIN GEEK CODE BLOCK----- Version: 3.12 GE d-(+) s++: a C++ ULHS+ P L++ E---- W+ N++ o? K? w-- !O M+ V-- PS+ PE+ Y+ PGP !t 5? X R* tv+ b+ DI++ D G e+++> h--- r+++ y+++* ------END GEEK CODE BLOCK------