By Berti M., Matzeu M., Valdinoci E.

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**Extra resources for On periodic elliptic equations with gradient dependence**

**Example text**

Repeat for the sawtooth signal. Summarize the result. 3 Objective To analyze a real experimental case of a periodic signal via a Fourier series representation. Reminder The Fourier series components are computed at frequencies which are integer multiples of the basic frequency 1/Ttotal ϭ ffundamental For a harmonic signal of frequency f p, spanning exactly p periods in the analyzing window, the location on the frequency scale will be at the index kϭp Description The following information concerns the acquired data (choose the belt option in this exercise).

1). The program responds immediately upon clicking the chosen category. Zooming may be necessary in order to investigate the signal patterns in more detail. e. mean, MS and RMS for periodic and random signals, positive and negative envelope for NB (narrow band) random signals. 1 Instructions This exercise involves mainly inspecting given signals. For some of the signals the parameters MS, RMS are shown. These should be ignored at this stage; they will be considered in the next exercise. For Signals 13 the narrow band (random) signal, the envelope is also shown.

7 Objective Understand the convergence from Fourier transform to Fourier series for periodic signals. Reminder • For a finite duration periodic signal, xT ϭ x(t) w(t) x(t) ϭ x(t ϩ Tp) w(t) ϭ u(t) with u the step function. 5 δ( f ϩ f0 ) Fourier Methods 33 Description Three types of periodic signals can be chosen. A truncated signal can then be chosen, spanning a controllable number of periods. Running the program results in a dynamic display, as one additional period is spanned at each phase, until the preset number of periods has occurred.