Truncated sampling expansions

Author

Papoulis, Anthanasios

Author_Institution

Polytechnic Institute of Brooklyn, Brooklyn, NY, USA

Volume

Issue

fYear

1967

fDate

10/1/1967 12:00:00 AM

Firstpage

604

Lastpage

605

Abstract

Bounds on the output of a linear system are developed and used to reexamine the nature of the truncation error eNin the sampling expansion of a band-limited signal $f(t)$ . It is shown that if $f(t)$ has finite energy, then the maximum of $|e_{N}|$ is bounded by the mean-square value of the error $H(\\omega )$ in the approximation of $e^{\\i\\tau \\omega }$ by a truncated Fourier series. If $f(t)$ has finite power, then the mean-square value of eNis bounded by the maximum of $|H(\\omega )|$ .

Keywords

Band-limited signals; Control systems; Digital-analog conversion; Electrical equipment industry; Error correction; Feedback; Feedforward systems; Linear systems; Quantization; Sampling methods; Upper bound;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1967.1098687

Filename

1098687

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=795283