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Designing a PI filter for a Costas Loop

The low pass filters used must have cutoff frequencies at least 10x higher than the PLL loop bandwidth and of minimum delay so as to not affect loop stability. I recommend using minimum phase filters ...
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Why a demodulated signal can appear at a double frequency?

Assume that we have a signal $$x(t)=\cos(\omega t)$$ with a carrier $$c(t) = \cos(\omega_c t).$$ Than, for the amplitude modulated signal, $$y(t)=x(t)c(t),$$ the analytic signal is $$A(y(t))=x(t)e^{-j\...
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