Discrete Lissajous Figures and Applications

Karacor D., NAZLIBİLEK S., SAZLI M. H., AKARSU E. S.

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, cilt.63, sa.12, ss.2963-2972, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 63 Sayı: 12
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1109/tim.2014.2318891
  • Dergi Adı: IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.2963-2972
  • Anahtar Kelimeler: Correlation, discrete-time systems, electrocardiography, electroencephalography (EEG), signal processing, signal representations, FREQUENCY
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, an innovative method based on an algorithm utilizing discrete convolutions of discrete-time functions is developed to obtain and represent discrete Lissajous and recton functions. They are actually discrete auto- and cross-correlation functions. The theory of discrete Lissajous figures is developed. The concept of rectons is introduced. The relation between the discrete Lissajous figures and autocorrelation functions is set. Some applications are described including phase, frequency, and period determination of periodic signals, time-domain characteristics (such as damping ratio) of a control system, and abnormality and spike detection within a signal, are described. In addition, an electrocardiogram signal with an abnormality of atrial fibrillation is given for abnormality detection by means of recton functions. An epileptic activity detection within an electroencephalography signal is also given.