In rotor-slot-harmonic-based speed detection schemes, a grid-connected induction motor's rotational speed isresolved from the phase of a rotor slot harmonic signal for condition monitoring purposes. In such schemes,frequency-selective digital filters are often applied to attenuate interferences in sampled motor currents before rotorslot harmonic signals are extracted. This paper demonstrates that the use of linear-phase filters, which is a family ofdigital filters with linear phase responses, helps preserve the rotor slot harmonic signal's phase during the filteringoperation. This paper also shows that, for grid-connected induction motors with periodically time-varying loads, therotor slot harmonic signal's frequency is modulated by periodic speed oscillations and hence contains multiple sidebandsin the frequency spectrum. Experimental results further show that linear-phase filters allow for a more accuratedetection of the induction motor speed than filters with nonlinear phase responses.