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This makes sense. A DC offset will shift the envelope just as demonstrated here. The analytic signal of a constant alone is the same constant since the Hilbert Transform will not pass a mean (or "DC offset"), and the process of transforming a signal to the analytic signal is linear. Therefore $$f_a\{K+x(t)\} = f_a\{K\} + f_a{x(t)}$$ where here $f_a\...


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There are a few problems here. Now when I try to obtain the result numerically: In order to do this you have to translate a problem from continuous time to discrete time. This requires sampling and choosing a sampling rate. According to the Nyquist criteria the sample rate needs to be at least twice the highest frequency in the signal. Since a Hilbert ...


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