Abstract: A system and method for producing and controlling a random signal with simultaneous control of both the power spectral density (PSD) and kurtosis (100) where a controlled signal is measured from a transducer, and converted to a PSD (111) using a Fast Fourier Transform (FFT). The measured PSD is compared (117) with a reference PSD (121) where an adaptive filter (119) is updated to compensate for the error. Simultaneously the kurtosis of the measured data is computed (125) and compared to a reference kurtosis (123). A feedback control loop (127) is employed to adjust the kurtosis of a white noise random generator with variable kurtosis (101). This white noise is then filtered by the adaptive filter (119) to provide the output signal used to drive the control process.