Double series representation of bounded signals

@article{Jensen1988DoubleSR,
  title={Double series representation of bounded signals},
  author={Helge Elbr\ond Jensen and Tom H\oholdt and J\orn Justesen},
  journal={IEEE Trans. Information Theory},
  year={1988},
  volume={34},
  pages={613-624}
}
Series representations of the form f(f)-IE 2 a,,kv(t-n)e2n'k' for bounded signals f(t) are studied, as are conditions on the unit function v(r), such that the coefficients a,, k reveal the energy content of f(t) in the time interval n-(l/2) < t I n +(1/2) and frequency interval 2m(k-(l/2)) I w I 2n(k +(1/2)). These conditions turn out to he 1) orthogonal&y, i.e., if n=k=O otherwise and 2) integrability, v(r) EL!(R) V(w) E L'(R). Based on these conditions a number of properties of the expansion… CONTINUE READING

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