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A signal X(t) is a real valued time domain signal and Y(t) is a signal that only contains the non-negative spectral components of X(t). How do I determine whether Y(t) is real-valued or complex?

I know that a time domain signal can be real or complex based on its Fourier transform nature (i.e. even or odd). But how to determine this in such a general case? How to make use of the input- non-negative spectral components, what is its significance?

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    $\begingroup$ Hi! Welcome here! However: This question appears to be homework. Complete answers to homework are off-topic, but specific questions about homework are acceptable if they include enough detail. Please edit the question to include more background about what you don't understand. It certainly helps if you could show all your calculations up to this point and why you can't progress to an answer yourself! $\endgroup$ Commented Oct 2, 2023 at 12:08
  • $\begingroup$ @MarcusMüller thank you, I made some changes that I thought were appropriate. $\endgroup$ Commented Oct 2, 2023 at 12:18
  • $\begingroup$ Honestly, I think then you already know the answer? Relate "even" or "odd" to "only negative frequencies", and there you have your answer. $\endgroup$ Commented Oct 2, 2023 at 12:20

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A real signal in time domain always presents a frequency spectrum with Hermitian symmetry, as you can easily find here. On the other hand, a signal that does not have the negative spectrum portion is called analytic signal, and its time domain counterpart is complex-valued, as specified here.

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