# Discrete Fourier transform of a finite length signal which saturates at non-zero value

I am performing spectral analysis of a finite length signal that saturates to a non-zero value. The signal ($$s(t)$$) can, practically, be write as $$s(t) = f(t) \big(1-H(t-t_0)\big)$$, where $$t_0$$ is the time at which the signal ends and $$H(t)$$ is the Heaviside step function. The sudden step from a non-zero value to zero at $$t = t_0$$ induces artifacts in the analysis.

I am looking for advice/literature on how to deal with signals of this type.

Question: How does one deal with artifacts cause by signals terminating at a non-zero value when performing spectral analysis.

• What you're looking for is quite literally windowing. I'm not sure how saturation comes into play here? Could you explain what saturation has to do with your rectangularly windowed signal? Commented Dec 21, 2020 at 12:04
• In some sense it is equivalent to windowing I guess. I am not exactly sure what you want me to explain. The saturation comes from the fact that the signal is supposed to represent a signal of infinite length which does not return to zero after some time. It is not a signal which passes and when it ends the signal is zero. However, due to computational constraints, I do not have the infinite length signal. The signal s looks like it does without being windowed. Commented Dec 21, 2020 at 12:12
• I think saturation means something else than you think it does, sorry. What you mean is windowed. Commented Dec 21, 2020 at 12:27
• Maybe the word saturation is not the right one to use. Let me put it this way. How to deal with a signal that has an abrupt end? A signal that does not tend to zero. The end goal is to understand which part of the spectrum is caused by this sudden termination. Commented Dec 21, 2020 at 12:42
• as said, you apply a window, like the Nuttal, Blackman-harris, Hann, or Tschebychev windows. en.wikipedia.org/wiki/Window_function That window doesn't have to be rectangular (i.e. just cutting off), but can be (and should be) tapered at the ends Commented Dec 21, 2020 at 12:44