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This paper provides a detailed analysis of the performance of systems recently proposed by various authors in which the received signal is Fourier transformed in real time (usually with a surface acoustic wave device) and then filtered by a multiplication of the transformed signal by an appropriate transfer function. We shall refer to this operation as transform domain filtering. General expressions for the output waveforms of the system will be derived, and a specific example illustrating the performance of the system when operating in the presence of a narrow-band interferer plus additive white Gaussian noise will be presented. It will be shown that certain filtering techniques not feasible in conventional systems, such as filtering with ideal bandpass filters, become straightforward using transform domain filtering. Finally, a receiver will be described which will eliminate that intersymbol interference between adjacent data symbols due to filtering at the receiver.