Degradation of signal-to-noise ratio due to amplitude distortion

The effect of filtering on the signal-to-noise ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worst-case amplitude ripple. The problem is formulated as an optimization in the Hilbert space L₂. The form of the worst-case amplitude ripple is specified, and the degradation in the SNR is derived in closed form. It is shown that, when the maximum passband amplitude ripple is 2δ (peak-to-peak), the SNR is degraded by at most (1-δ²), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple under 0.42 dB