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You will understand it better by implementing it on a signal such as x= sin(100t)*sin(t). After using the trigonometric identity that replaces the multiplication by sum, implementation of the Hilbert transform to find the analytic signal, extracting the square absolute value, and using the Pythagorean trigonometric identity, you will be able to extract the ...


3

$\DeclareMathOperator{\sgn}{sgn}$ The modulating signal in AM is $$s(t) = C + a(t)\text,$$ where $a(t)$ is the (audio) amplitude, and $C$ is a constant so that $s(t) \ge 0 \;\forall t$. (Otherwise, your audio amplitude would just frequently "switch" the wave's sign, not really modulate the envelope.) That means, $C > - \min_t(s(t))$. Therefore, the ...


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