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imagine this signals in the time-domain: green: without a reset; blue: with a reset after each 1000 samples Time domain signals, green: without a reset; blue: with a reset after 1000 samples

Amplitude-Spectrum of the signals from picture 1 in semilogarithmic plot (y-axis is log10, x-axis is linear up to nyquist-frequency) green: without a reset; blue: with a reset after each 1000 samples

FFT of signals in picture 1 in semilogarithmic (y-axis)

Closeup of plot in picture 2

enter image description here

I would like to be able to explain this behaviour.

I looks like the green graph is the envelope-function of the blue graph, but drops at higher frequencies.

To understand why and how the blue and green graph correlate I tried to understand the fourier-transformation of a ramp-function and a saw-tooth-function. But I cannot wrap my head around it.

The ramp-function is a simple example, it would be great if the explanation is generic for other kind of functions ( sin e.g. ) in the "green" graph.

Alex
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  • Maybe it would be easier to analyze if the starting function were $\sin(x)$ and the resets occurred at some time $\tau \in (0,\pi) \cup (\pi,2\pi)$. – Ian Dec 31 '14 at 20:58
  • I rewrote the script to ease it up: http://math.stackexchange.com/questions/1087081/what-happens-to-the-frequency-spectrum-if-this-sine-signal-gets-reset-periodical I hope you meant this – Alex Dec 31 '14 at 22:19

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