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We report on the sensitivities to frequency and amplitude noise of optical frequency discriminators based on Fabry–Pérot interferometers and the frequency modulation (Pound–Drever–Hall) technique. The response to frequency and amplitude noise is obtained by analyzing the demodulated transients to phase or amplitude steps impressed on the incident frequency modulated light. The responses in the Fourier frequency domain are then obtained by performing the Laplace transform of the demodulated transients. As expected, when the laser frequency is coincident with the Fabry–Pérot resonance, this discriminator is completely immune to amplitude noise. To simulate real operations, the amplitude noise immunity is evaluated in the presence of small detunings between the laser frequency and the Fabry–Pérot resonance. Diagrams of the responses to both types of noise are reported for symmetric and asymmetric resonators. The Pound–Drever–Hall discriminator turns out to be insensitive to the asymmetry of the Fabry–Pérot resonator. The performed evaluations lead to a simple estimation of the minimum detectable frequency noise in terms of a given laser intensity noise.