Approximating signals by fast impulse sampling

Yakar Kannai, George Weiss

Research output: Contribution to journalArticlepeer-review

Abstract

An impulse sampler multiplies an input signal u by a periodic delta impulse train of period Τ. If Τ is small, then the output signal of the sampler (or filtered versions thereof) can be used as an approximation of u. If u belongs to the Sobolev space Hs with s>1/2, then the output is in H-s. Our main result is that as the sampling period Τ becomes small, the impulse sampler approximates the identity in the operator norm from Hs to H-s (we also give the rate of convergence). We obtain related approximation results in the L2 norm, which refer to the situation when filters are connected before and after the impulse sampler (as usually happens in engineering applications). We generalize our results to distributions on ℝn and indicate applications to control theory for distributed parameter systems.

Original languageEnglish
Pages (from-to)166-179
Number of pages14
JournalMathematics of Control, Signals, and Systems
Volume6
Issue number2
DOIs
StatePublished - Jun 1993
Externally publishedYes

Keywords

  • Filter
  • Impulse sampler
  • Sampling theorem
  • Sobolev space

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