envelope

The signal $$\cos\;\omega_ct\;+\;0.5\;\cos\;\omega_mt\;s\mathrm{in}\;\omega_ct$$ is

The probability density function of the envelope of narrow band Gaussian noise is

A DSB-SC signal is generated using the carrier $$\cos\left(\omega_ct\;+\;\theta\right)$$ and modulating singal x(t). The envelope of the DSB-SC signal is

For a narrow band noise with Gaussian quadrature and inphase components, the probability density function of its enveolope will be

White Gaussian noise is passed through a linear narrow band filter. The probability density function of the envelope of the noise at the filter output is: