Vol.6, No 1, 2008 pp. 11 - 28
DOI 10.2298/FUPCT0801011V
UDC 621.39;181;618;392
COMPLEX ANALYTIC SIGNALS APPLIED ON TIME DELAY ESTIMATION
Zoran S. Veličković1, Vlastimir D. Pavlović2
1Department of Electronic Engineering, High Technical School, Aleksandra Medvedeva 20, 18000 Niš, Serbia, zorvel@bankerinter.net
2Faculty of Electronic Engineering, Aleksandra Medvedeva 14, 18000 Niš, Serbia, vpavlovic@elfak.ni.ac.yu
Abstract. In this paper, we present the concept of the time delay estimation based on the transformation of real sensor signals into analytic ones. We analyze the differential time delay values obtained using real seismic signals, simulated complex analytic signals and simulated complex analytic signals with real parts coming from real seismic signals. The simulation results indicate that the application of complex analytic signals leads to reliable computation of the differential time delay. The influence of specific signal parameters on spectral coherence threshold in systems for passive localization and proposed methods for lowering the threshold is analyzed. The computation of all differential time delays with respect to the reference sensor (geophone) is based on the application of Generalized Cross-Correlation (GCC) applied on corresponding analytic signals. The difficulties to select a peak of cross-correlation function that corresponds to true differential time delay when dealing with real signals are significantly reduced if GCC is applied on analytic signals. The efficiency of the proposed technique on differential delay estimation is performed on deterministic and real-life signals.
Key words: Array signal processing, complex analytic signal, differential time delay, generalized cross-correlation, source localization, spectral coherence.
PRIMENA KOMPLEKSNIH ANALITIČKIH SIGNALA U IZRAČUNAVANJU VREMENSKOG KAŠNJENJA
U ovom radu je prezentovan koncept izračunavanja diferencijalnog kašnjenja koji je zasnovan na transformaciji realnog senzorskog signala u analitički. Analizirane su vrednosti dobijenih diferencijalnih kašnjenja za realni seizmički signal, simulirani kompleksni analitički signal i simulirani kompleksni analitički signal čiji realni deo odgovara akviziranom realnom signalu. Simulacioni rezultati pokazuju da se primenom kompleksnog analitičkog signala dobijaju pouzdanije vrednosti diferencijalnog kašnjenja. Analiziran je uticaj specifičnih parametara signala na prag koherence u sistemima za pasivnu lokalizaciju i preporučeni su metodi za njeno snižavanje. Diferencijalno vreme kašnjenja je određeno u odnosu na referentni senzor (geofon) primenom GCC metoda nad analitičkim signalima. Poteškoće oko određivanja pika kros-korelacione funkcije kod realnih signala, koji odgovara tačnom diferencijalnom kašnjenju, su znatno redukovane primenom GCC metoda nad analitičkim signalima. Efikasnost predložene tehnike je ispitana na determinističkim i realnim signalima.