A sliding-mode observer is proposed in order to estimate the phase-to-phase trapezoidal back-EMF in a brushless DC motor by using only the measurements of the stator currents and voltages. The main feature of the proposed observer is that it is not sensitive to the switching noise and no filtering is required. The back-EMF estimate was then used to deduce the six rotor positions of the motor. In addition, a method to obtain an estimate of the rotor speed of the motor, by exploiting the mathematical relationship between the speed and the back-EMF, is presented. The observer of the trapezoidal back-EMF is implemented practically on a DSP board. Simulation and experimental results are given to show the performance of the observer.