A fault detection system is provided to extract fault signature from the time-domain stator current signal of a motor under varying load operations by solving a joint blind deconvolution-demodulation problem, where the stator current of a motor under varying operating conditions is modeled as a stator current of a steady operating condition influenced by the system response vector and a load modulation vector. A proximal alternating linearized minimization-type method is used to solve the joint blind deconvolution-demodulation problem, assuming that the spectrum of the sought-after signal is sparse. Motor fault detection is then performed using the recovered stator current of a steady operating condition.