Analysis of signals with inexact data by using interval-valued functions

Levent H., YILMAZ Y.

JOURNAL OF ANALYSIS, cilt.30, sa.4, ss.1635-1651, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s41478-022-00422-0
  • Dergi Adı: JOURNAL OF ANALYSIS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.1635-1651
  • Anahtar Kelimeler: Inner-product quasilinear space, Integrable selection, Aumann integral, Continuous-time interval signal, Autocorrelation function
  • İnönü Üniversitesi Adresli: Evet

Özet

Mathematically, a signal is a function of an independent variable t and it contains information about the behavior of the physical quantity. In real life, sometimes a signal value in a time t may not be known exactly. This paper presents a new mathematical method for processing of such a non-deterministic signal by using interval-valued functions which is called as its model interval signal. If the properties of a signal are completely unknown then we cannot perform the processing of these signals such as determining the autocorrelation function of the non-deterministic signal. Especially, in this work, we give an application to estimate the autocorrelation function of a signal with inexact data. For this purpose we use some new mathematical methods so called quasilinear functional analysis. Our studies give approximative result, although there are no definite results for such signals. We think that it's better than not having any information.