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I'm a SP student and still a beginner in the field.

When we were learning about window functions, my professor said "you're gonna almost always want to window your data but don't window a transient signal." It's a (semi-)online course with lecture videos so I couldn't ask for an explanation.

Can anyone explain what a transient is and why we wouldn't window it?

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  • $\begingroup$ I did the update with a transient signal (ultrasounds) $\endgroup$ Dec 5, 2016 at 14:20

2 Answers 2

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Loosely speaking, a transient denotes a part of a signal with sudden changes. Think of a constant level signal followed by a damped sine, for instance.

Analyzing a transient with windows such as the Hann or Hamming may affect the transient energy a lot, as these windows decay too fast to small values. Thus, it is sometimes said that it is better to use a rectangular window, to have a constant amplitude change across the time interval.

However, I plead guilty of using windows with very short raised power cosine tapers, such as the one below, to allow the windowed signal to fall down to 0 at the edges, to ease FFT calculations for instance.

Raised power cosine

What is happening on a real-world ultrasound signal? On top, a part of a transient ultrasound. On the center, a rectangular window, an Hamming one and the custom one I talked about above. On the bottom, the windowed signals. The one with the custom window looks closer to the original than the Hamming-windowed one.

ultrasound signal

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  • $\begingroup$ Bug in my code: on the center window panel, the rectangular window is black, the Hamming is blue, the custom is green. However the legend is consistent with the plot below $\endgroup$ Dec 4, 2016 at 21:14
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To build on Laurent's answer, here is an example. Top frame shows an example transient signal: a damped sine wave. As the signal decays very quickly, the first 0.1s of the signal is the most interesting. Second frame shows hann window. Hann window is almost zero over that first 0.1s. Third frame shows what happens when you apply hann window to the signal, the most interesting part of it is completely thrown away.

enter image description here

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    $\begingroup$ @DanielKiracofe Thanks for the picture, I should have done the job! $\endgroup$ Dec 4, 2016 at 17:11

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