A low-cost digital pulsed nuclear quadrupole resonance (NQR) radio-spectrometer is proposed, all main modules of digital processing and synthesis of which on the field-programmable gate array (FPGA) are implemented. The input sensitivity of the device is of the order of 3 uV to 5 uV which allows conducting NQR studies in samples of relatively small dimensions. The application of the developed methods of NQR pulsed radio spectroscopy made it possible to increase spectral resolution, improve spectral shape and significantly reduce the time of research. In the case of studying InSe and GaSe crystals, spectra with signal-to-noise ratio (SNR) values of 41.9 dB were observed in samples with a volume of 0.1 cm3. As the results of the research have shown, the characteristics of the proposed spectrometer make it effective when used to observe free induction decay (FID) signals of a significant number of isotopes of elements with quadrupolar nuclei.