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Is it correct to compute the Hilbert Transform and then the complex envelope, expressed as $v = z~ e^{-j 2\pi f_c t}$, where $z$ represents the analytic signal and $f_c$ represents the carrier frequency, in order to determine the instantaneous attributes (amplitude, phase and freq.) of non-modulated signals? For example, consider a square wave signal with three distinct frequencies (1 kHz, 3 kHz, and 9 kHz). I am aware that the Hilbert function in MATLAB generates the analytic signal, which can be utilized to derive the instantaneous attributes.

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Nothing prevents you from calculating the "complex envelope" of any passband signal (but note that applying the Hilbert transform to wideband signals is tricky). The question is whether that "complex envelope" contains the information you're interested in -- and whether that information is easier to obtain in this way.

I'd recommend working out the math -- write down the expression for the passband signal and its "complex envelope", and see if you can derive the information you need from that expression.

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  • $\begingroup$ but what about the carrier frequency in the exponential part? $\endgroup$
    – Asli
    Jul 13, 2023 at 20:05
  • $\begingroup$ @Asli: If you're using MATLAB software to work on your problem, I can help you. If you are interested, send me a private e-mail at: [email protected] $\endgroup$ Jul 13, 2023 at 23:17
  • $\begingroup$ @Asli just use the center frequency of your passband signal. $\endgroup$
    – MBaz
    Jul 14, 2023 at 0:13

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