Gabor and Wavelet Expansions
نویسندگان
چکیده
This paper is an examination of techniques for obtaining Fourier series-like expansions of finite-energy signals using so-called Gabor and wavelet expansions. These expansions decompose a given signal into time and frequency localized components. The theory of frames in Hilbert spaces is used as a criteria for determining when such expansions are good representations of the signals. Some results on the existence of Gabor and wavelet frames in the Hilbert space of all finite-energy signals are presented.
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