By Panos Z. Marmarelis M.D., Ph.D., Vasilis Z. Marmarelis (auth.)

In learning physiological structures bioscientists are continuously confronted with the matter of offering descriptions of cause-effect relationships. This job is mostly performed throughout the functionality of stimulus-response experiments. long ago, the layout of such experiments has been advert hoc, incomplete, and definitely inefficient. Worse but, bioscientists have didn't reap the benefits of advances in fields without delay on the topic of their difficulties (specifically, advances within the sector of structures analysis). The raison d'etre of this ebook is to rectify this deficiency via supplying the physiologist with methodological instruments that would be precious to her or him in daily labora tory encounters with physiological structures. The e-book used to be written in order that it might be useful, precious, and up-to date. With this in brain, components of it supply step by step descriptions of within the laboratory. it's was hoping that this systematic techniques to be increases the usefulness of the booklet to the typical learn physiologist and, probably, decrease the necessity for in-depth wisdom of a few of the linked arithmetic. although the cloth offers with state-of-the artwork options in structures and sign research, the mathematical point has been saved low so that it will be understandable to the typical physiologist with out broad education in arithmetic. To this finish, mathematical rigor is frequently sacrificed without problems to intuitive easy arguments.

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**Example text**

Now the question arises: Which of the frequencies in the range (0, Ie) are thus aliased by which of the higher frequencies I> Ie? Or, put in another way, given the samples such as in Fig. 16, which ones are the frequencies that can be obtained from the sampled record and thus be indistinguishable from the frequencies actually present in the original record? Obviously there is an infinite number of them. It can easily be shown that for any frequency I in the range (0, Ie) the frequencies that will be indistinguishable from the sampled record are j = (2fc n ± f), n = 1, 2, ...

12B). This follows from Eq. 72). In a similar fashion, if a signal is given over the interval [0, T], as shown in Fig. 12A, we can represent it by a series of cosines: ao 2 x(t)=-+ where Wo = 17"/ T, and ak = -2 T f. 76) k=l 33 Analysis of Physiological Signals B A .... T " ,\. " I T ..... Fig. 12. Even and odd expansions of finite-duration signal. This series represents the signal in [0, T] and also produces copies of it outside this interval-as shown by Fig. 12A. 78) The difference is that in the sine representation the copies of the signal are such as to make the periodic signal an odd function.

10. Periodic electrocardiographic (ECG) signal and its Fourier amplitudes. shown in the figure. A question may arise as to how the very low frequencies (lower than about 1 Hz) were obtained, since the waveform has a periodicity of about 1 Hz. 73), a multiple of the obvious period of about 1 sec. This procedure then permits measurement of frequencies lower than 1 Hz, the lowest being 1I T, for the chosen T. A procedure often used in the case of physiological signals is to (a) choose the period T about 1 sec or longer, (b) then average the signal cycles of period T to obtain a signal of duration T, and (c) perform Fourier analysis on this signal as described in the following paragraphs.