Abstract
A method is proposed for estimating the system function of a time-invariant linear system without simultaneous recording of input and output waveforms, i.e., without using a cross-spectrum. Observed input and output of the system studied are contaminated with Gaussian noise, and the input and output noises are correlated. The input to the system is supposed to be composed of a periodic signal and Gussian noise.
The auto-bispectrum of the observed input waveform and the auto-bispectrum of the observed output waveform are used to identify the phase characteristics of the system. In the identification the term corresponding to the system's transportation lag is elimianted and only the term expressing the phase dispersion among the frequency components is identified. The amplitude term can be estimated, but this term is interfered by the noise.
The merit of this method is that data can be obtained quickly under the optimum measuring conditions since no simultaneous measurement at two points and neither trigger nor synchronization of any type to process the signal are necessary.
This method may be useful, for example, for clinical studies, such as the diagnosis of arteriosclerosis, for which a catheter is too dangerous to use and instead a pressure sensitive transducer should be used externally at the sacrifice of accuracy, and the measurement should be done easily and quickly to diminish the pain of the patient.
The bispectra of arterial pressure waves at two points along an artery were calculated to determine the phase characteristics of the arterial-blood-pressure transfer function. A preliminary experiment showd that the phase characteristics of the artery of the left arm resembled those of the right arm.
The phase characteristics of the arteries of arms are distinctly different from those of the aortas.
