A new technique to de-Dopplerize microphone signals from moving sources of sound is derived. Currently available time domain de-Dopplerization techniques require oversampling and interpolation of the microphone time data. In contrast, the technique presented in this dissertation performs the de-Dopplerization entirely in the frequency domain eliminating the need for oversampling and interpolation of the microphone data. As a consequence, the new de-Dopplerization technique is computationally more efficient. The new de-Dopplerization technique is then implemented into a frequency domain beamforming algorithm to locate moving sources of sound. The mathematical formulation for the implementation of the new de-Dopplerization technique is presented for sources moving along a linear trajectory and for sources moving along a circular trajectory, i.e. rotating sources. The resulting frequency domain beamforming method to locate moving sound sources is then validated using numerical simulations for various source configurations (e.g. emission angle, emission frequency, and source velocity), and different processing parameters (e.g. time window length). Numerical datasets for sources with linear motion as well as for rotating sources were simulated. For comparison purposes, selected datasets were also processed using traditional time domain beamforming. The results from the numerical simulations show that the frequency domain beamforming method is at least 10 times faster than the traditional time domain beamforming method with the same performance. Furthermore, the results show that as the number of microphones and/or grid points increase, the processing time for the traditional time domain beamforming method increases at a rate 20 times larger than the rate of increase in processing time of the new frequency domain beamforming method. / Ph. D.