Sampling with a filter: largest T comes from f_s = F_m + F_p

When a digital lowpass filter sits between ideal A/D and D/A, the largest sampling period isn't plain Nyquist, because aliasing is fine outside the kept band. The spectral copy's left edge is f_s - F_m, and it only has to stay at or above the kept edge F_p, so T = 1/(F_m + F_p) and w_c = 2 pi F_p T. A highpass that keeps up to F_m is different: aliasing enters from w = pi inward, so it needs full Nyquist. Students grasp this quickly from stacked plots of the copy at three sampling rates with the kept band shaded.