By Panos Z. Marmarelis M.D., Ph.D., Vasilis Z. Marmarelis (auth.)
In learning physiological structures bioscientists are regularly confronted with the matter of supplying descriptions of cause-effect relationships. This activity is mostly conducted in the course of the functionality of stimulus-response experiments. some time past, the layout of such experiments has been advert hoc, incomplete, and positively inefficient. Worse but, bioscientists have didn't benefit from advances in fields without delay on the topic of their difficulties (specifically, advances within the region of platforms analysis). The raison d'etre of this ebook is to rectify this deficiency by means of delivering the physiologist with methodological instruments that would be valuable to her or him in daily labora tory encounters with physiological structures. The e-book was once written in order that it'd be functional, beneficial, and up-to date. With this in brain, elements of it supply step by step descriptions of within the laboratory. it's was hoping that this systematic approaches to be increases the usefulness of the ebook to the common examine physiologist and, possibly, lessen the necessity for in-depth wisdom of a few of the linked arithmetic. even supposing the fabric bargains with state-of-the artwork concepts in structures and sign research, the mathematical point has been saved low that allows you to be understandable to the typical physiologist with out vast education in arithmetic. To this finish, mathematical rigor is frequently sacrificed simply to intuitive easy arguments.
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Extra info for Analysis of Physiological Systems: The White-Noise Approach
106) it is seen that the variance of x(t) is equal to the total power of the signal. For a random process we may consider also a quantity related to the autocorrelation function in the same manner that the variance is related to the second moment. 108) Obviously, these quantities are the same as the corresponding correlation functions except that the mean has been subtracted from the signals. 110) -00 where X1=y(t) and X2=X(t-T). 112) that is, if x(t) and yet) are uncorrelated, then they are independent, provided they are Gaussian signals.
With these basic notions in mind we proceed to examine the case of orthogonal expansion of a signal. Assume that the signal x(t) is represented by a series of orthogonal signals, such as the sines and cosines of the Fourier series. 81) Incidentally, properly normalized sines and cosines have exactly this property. 82) This is easily seen by substituting x(t) from Eq. 80) into Eq. k(t)} as manifested by Eq. 81). Of course, in practice, we can only compute a finite number of coefficients. 84) and ask the question: For which coefficients ak, k = 1, ...
8C) in which the forward and feedback paths have delays d l and d 2 respectively. Then the crosscorrelogram is expected to exhibit peaks at db 2d l + d 2 , 3d l + 2d 2 , etc. In fact, if the feedback is negative then we would expect the peak at 2d l + d z to be negative, the one at 3d l + 2d2 to be positive, the next peak to be negative, and so on. If, on the other hand, the feedback is positive, then all the peaks would be of the same polarity (all positive or all negative). Another use of the crosscorrelogram is in detecting a signal that is buried in noise when the waveform of this signal is known.
Analysis of Physiological Systems: The White-Noise Approach by Panos Z. Marmarelis M.D., Ph.D., Vasilis Z. Marmarelis (auth.)