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Finding the orthonormal basis for cosine function

  1. Mar 10, 2015 #1
    1. The problem statement, all variables and given/known data
    si(t) = √(((2*E)/T)*cos(2*π*fc*t + i*(π/4))) for 0≤t≤T and 0 otherwise. Where i = 1, 2, 3, 4 and fc = nc/T, for some fixed integer nc.
    What is the dimensionality, N, of the space spanned by this set of signal? Find a set of orthonormal basis functions to represent this set of signals. Plot the locations of si(t) (i = 1, 2, 3, 4) in the signal space.

    2. The attempt at a solution
    Dimensionality N = 4.
    I know how to find the orthonormal basis functions for square waves, because so far we were just given square waves. We used the Gram-Schmidt orthogonalization procedure. My question is how do I find it when the function is a sine wave?

    Just looking for some directions. :)

    Thank You.
     
  2. jcsd
  3. Mar 12, 2015 #2

    BvU

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    What is ##\cos(\alpha + {\pi\over 4})##, what is ##\cos(\alpha + {\pi\over 2})##, ##\cos(\alpha + {3\pi\over 4})## and ##\cos(\alpha + \pi)## when evaluated ?
     
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