On Sampling the Envelope of a Bandlimited Signal

For x(t) a generalized bandpass signal, either deterministic or zero-mean, wide sense stationary Gaussian, bandlimited to the frequency region characterized by 0 ≤ω0 - σ/2 ≤|ω|≤ ω0 +σ/2 < ∞ with positive frequency bandwidth σ > 0, it is shown that the squared envelope of x(t) is lowpass and bandlimited to |ω| ≤ω. This contrasts with earlier results which gave the bandwidth of the squared envelope as 2σ. One consequence of the lower bandwidth is that the squared envelope (and thus the nonnegative envelope itself) can be reconstructed from its samples taken at a rate of σ/w samples/s.