This article proposes a receiving device in which arbitrary input signals are subject to pre-detector processing for the subsequent implementation of the idea of compressing broadband modulated pulses with a matched filter to increase the signal-to-noise ratio and improve resolution. For this purpose, a model of a dispersive delay line is developed based on series-connected high-frequency time delay lines with taps in the form of bandpass filters, and analysis of this model is performed as a part of the radio receiving device with chirp signal compression. The article presents the mathematical description of the processes of formation and compression of chirp signals based on their matched filtering using the developed model and proposes the block diagram of a radio receiving device using the principle of compression of received signals. The proposed model can be implemented in devices for receiving unknown signals, in particular in passive radar. It also can be used for studying signal compression processes based on linear frequency modulation in traditional radar systems.