# Translations:Appendix L: Design of Hilbert transforms/23/en

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It is important to remember that both signals and are real. The new signal will be created in a special way to meet the requirements that the complex signal be an *analytic signal*. All the information we need is contained in the real and imaginary parts for positive angular frequencies . Because the new signal is also real, we need only to know its spectrum for the same positive angular frequencies. Let us represent its spectrum by . Let us do the simplest thing. For a given positive angular frequency , treat as a complex vector and rotate it by -90°. We call the result . That is, we let