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A method to model the performance of permanent-magnet synchronous motors (PMSMs) as a set of chained blocks capable of filtering in both spatial and frequential domains is introduced in this paper. The proposed tool is based on the convolution integral, which naturally connects both spatial and frequential domains in a formal way and relates the geometry of the motor directly with its frequency response. With this new instrument, the designer can easily and precisely appraise the resulting effect of any of the blocks which affect the performance of the motor. Furthermore, conversely, the designer can also synthesize the suitable modification of a block to obtain the desired performance of a motor. The analysis of the PMSM shown here is focused on, but not limited to, the generation of induced electromotive force (EMF) and of cogging torque, as the main causes of torque vibration. An experimental validation of the method has been performed showing good agreement between theoretical predictions, simulations, and experimental results. As a first practical result, this paper presents a motor design based on the analytical synthesis of a spatial filter that enables the selective elimination of EMF harmonics through geometrical arrangement of the magnets.