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Math Help - Projecting on orthonormal basis

  1. #1
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    Projecting on orthonormal basis

    Hello everyone!
    I have a couple of questions, but first if this is not the right forum to post, please redirect me to the correct forum.





    (1) For a periodic function f(t) with period T, we can decompose this function over the the fourier basis where the coefficients of the projections are given by \int _{-T/2} ^{T/2} f(t)e^{-i2\pi nf_0 t} dt Now we say that the basis is infinite but countable. Now when the functions is a periodic, this Fourier series approaches a Fourier transform, but is calculating the Fourier transform projecting on a basis? If so, is this basis uncountable (because we have a continuous frequency spectrum?)

    (2) Suppose \displaystyle f(t) = \Sigma _{i=0} ^{N} \alpha _i \psi _i (t) i.e. we're projecting f on some basis, now, are two sides of the equation really equal for e.g. when the set \{\psi _i\} _{i=0} ^N is the Haar basis.
    Last edited by rebghb; March 1st 2012 at 12:51 AM.
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