On the Degradation of Hard-Limiting Systems by Sampling

Sampling performed in conjunction with hard-limiting of a narrow band signal in band-limited white Gaussian noise increases the loss in output signal-to-noise ratio over that incurred by hardlimiting the original time-continuous signal. The largest increase in noise is by a factor of
\pi^{2}/8
in both the band-pass and the base-band cases, and occurs when the input signal-to-noise ratio is low and sampling is at Nyquist rate. Increase in the sampling rate gradually reduces the additional loss in both cases.