Re: Stupid question

From: P. Sarma (psarma@seas.upenn.edu)
Date: Fri Dec 07 2001 - 00:27:47 MET

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    Thank you for pointing out the clear and explicit relation between the
    "binary step function" and the Haar functions.

    The Haar functions are a focused set, generating a collection of such
    step-functions, and leading to an extended orthogonal basis. These are
    indeed very similar to the binary-step-functions (bsf). One difference is
    that the bsf has less structure - there is no claim to orthogonality, and in
    that limited sense are more general. Nevertheless, via Cybenko's Theorem,
    the bsf do appear to form a basis set for smooth function approximations.
    The fact that the bsf arises with natural relevance as a simple continuous
    extension of B{0,1}, the numbers of binary logic, was the key to trying them
    out.

    Pramit

    ----- Original Message -----
    From: "Tadeusz Dobrowiecki" <tade@mit.bme.hu>
    To: "Multiple recipients of list" <fuzzy-mail@dbai.tuwien.ac.at>
    Sent: Thursday, December 06, 2001 6:01 AM
    Subject: Re: Stupid question

    >
    > As far as I recall it is a fact (Haar Theorem) that a continuous (i.e.
    > smooth) function can be approximated (pointwise) by step-like functions
    > (the Haar orthogonal function system had been designed to this
    > purpose).
    >
    > Greetings
    >
    > Tadeusz
    >
    >
    >
    >
    >
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