New PDF release: Funktionentheorie

By Knopp K.

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2 Temporal and Spedral Analysis: Some General Principles Extracting information about the physical properties of sounds usually involves visual representations either in the temporal or spectral domains. In a temporal analysis, usually accomplished with an oscilloscope or its digital equivalent, the amplitude of the signal is displayed as a function of time. The acoustic properties to be measured from such a display indude: duration, rise-fall characteristics (shapes, times), patterns of amplitude modulation (if any), and repetition rate.

Probably, these numbers are written down on a list somewhere, or reside in a form accessible to a computer. An important point is that there is usually some regular spacing between consecutive entries in such a sequence (in this case, 1 day). We can therefore call such a list a discrete-time signal. Another critical point is that the entries are of only finite precision, meaning that the written list or a comparable computer file uses only a certain number of digits for each number. " Signals without time-dependency, such as digital images, are no less useful.

To interpret these components as three harmonics, it would be necessary to assume that the fundamental frequency of this sound is 50 Hz (the largest common denominator of 850, 1000, and 1150 Hz) and that all other harmonics of the 50-Hz fundamental frequency have been eliminated by some filtering mechanism. Such filtering of the fundamental and lower harmonics occurs in some songbirds (Greenwalt 1968). , the percentage difference between the amplitude peaks and troughs in the overall temporal waveform.

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Funktionentheorie by Knopp K.

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