By Katz N.M.

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**Additional resources for A conjecture in arithmetic theory of differential equations (Bull. Soc. Math. Fr. 1982)**

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The Fourier series decomposition can be undertaken manually: when the manual button is pressed, the next harmonic is added to the composite signal. 2). The upper plot shows the amplitude spectrum of the current sum. The current number of harmonics is shown in the box next to the number of component slider, and also in the lower left box. The harmonics can be added automatically, resulting in a dynamic display. Instruction/Tasks • Choose a square signal, set number of components to zero (by overwriting zero in the slider box).

6 Objective To investigate the Fourier transform scaling theorem. 6). A slider enables us to compress or expand the signal, the resulting energy being shown. 6 32 Discover Signal Processing: An Interactive Guide for Engineers The button energy opens a second window, showing the signal (upper plot) and the absolute value of X( f ) (lower plot), with cursors on each plot. Scrolling the cursors will show the area under the plots bounded by it. Noted for the time and frequency domain plots are the location of the cursors, the energies of the bounded areas, the total energies and finally the relative energies in percent.

The response spectrum shows a large peak at 30 Hz, a smaller one around 60 Hz. The response shows a faster oscillation at the beginning, which however decays very fast, and a second slower oscillation, decaying more slowly. The oscillating frequencies can be inspected by zooming in, showing values of 60 and 30 respectively. The fact that the higher frequency oscillations decay faster show that the loss of energy (causing the decay) somehow depends on the number of periods which occurred. 2 Signals Overview Applied signal processing methods must often be geared to the properties of the specific signals encountered.

### A conjecture in arithmetic theory of differential equations (Bull. Soc. Math. Fr. 1982) by Katz N.M.

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