Torque and e.m.f. of an induction motor can be derived from the air-gap flux density. The paper shows a new method for computing the flux density distribution of constant air-gap width machines, neglecting magnetic saturation, by making use of very efficient techniques widely used in the field of discrete signals processing: the Fast Fourier Transform (FFT) and the Discrete Circular Convolution. The mutual inductances between the phases of the machine are obtained with a single, very simple formula, in terms of the machine's windings distribution and the geometric dimensions, which is solved with the FFT. As the method can handle arbitrary winding conductor distributions, it is highly suitable to the analysis of the magnetic field and electromagnetic torque in machines with stator or rotor faults, such as inter-turn short circuits or broken bars.