Parseval's relationship for nonuniform samples of signals with several variables

Parseval's relationship for nonuniform samples of signals with several variables

The author shows that the Parseval's relationship as described by F.A. Marvasti and L. Chuande (see IEEE Trans. Acoust., Speech, Sign. Processing, vol.38, no.6, p.1061-3, 1990) only holds true for bandlimited signals of finite energy if the irregular sampling sequence is relatively separated, e...

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Veröffentlicht in:IEEE transactions on signal processing 1992-05, Vol.40 (5), p.1262-1263
1. Verfasser: Feichtinger, H.G.
Format: Artikel
Sprache:eng
Schlagworte:
Convergence
Fourier transforms
Frequency
Lattices
Low pass filters
Mathematics
Nonuniform sampling
Sampling methods
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Zusammenfassung:The author shows that the Parseval's relationship as described by F.A. Marvasti and L. Chuande (see IEEE Trans. Acoust., Speech, Sign. Processing, vol.38, no.6, p.1061-3, 1990) only holds true for bandlimited signals of finite energy if the irregular sampling sequence is relatively separated, e.g. if there is a positive minimal distance between two sampling points. The author presents a correct proof of the result for bandlimited functions of any number of variables, if this condition is satisfied.< >
ISSN:1053-587X
1941-0476
DOI:10.1109/78.134489