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The performance of a chirp transform spectrometer can be significantly improved through a digital dispersive matching network. In this paper, we present the development of a new design, the adaptive digital chirp processor (ADCP), which generates an expander chirp signal with dispersive characteristics matching those of the surface acoustic wave filter behaving as a compressor/convolver. This matching signal (i.e., the chirp) is generated by a digital direct synthesizer and is then bandpass filtered, level regulated, up-converted, and frequency tripled in order to achieve the required bandwidth of 430 MHz. The design of the matching network and the signal processing of the resulting dispersive signal demanded a rational and optimum combination of different technologies, such as quadrature modulation, high-performance spectral filtering, ultra-stable frequency sources, and a theoretical analysis of the circuit design by using a numerical model of the ADCP.