A method for generating a filtered noise signal, which includes the steps of generating a broadband signal having optimized (reduced or minimized) dynamic range, and filtering the broadband signal in a notch filter to generate a broadband signal whose frequency-amplitude spectrum has one or more notches (the "filtered noise" signal). In preferred embodiments, the filtered noise signal is a voltage signal suitable for application to an ion trap during a mass spectrometry operation. The invention enables rapid generation of different filtered noise signals (for use in different mass spectrometry experiments) by filtering a single, optimized broadband signal using a set of different notch filters, each having a simple, easily implementable design. The invention enables rapid generation of filtered noise signals (for example, in real time during mass spectrometry experiments) without prior knowledge of the mass spectrum of unwanted ions to be ejected from a trap during application of the filtered noise signal to the trap. The invention also enables rapid generation of a filtered noise signal having no missing frequency components outside the notches of the notch filter employed to generate the filtered noise signal. Digital values indicative of the amplitude, frequency, and phase of each sinusoidal (or other periodic) component of an optimized broadband signal can be iteratively generated by a digital computer in accordance with the invention, and the digital values can then be processed to generate an analog version of the optimized broadband signal.