  A simplified digital spectrometer for the study of $\gamma$-rays with
energies up to $\sim100$ MeV is presented and tested. The spectrometer is only
consisted of a fast digital oscilloscope and three scintillation detectors
which can work in single or in coincidence modes: two BGO-detectors comprising
$\varnothing\,7.62\times7.62$ cm BGO-crystalls and one plastic detector which
includes an organic polystyrene-based scintillator. The basic properties of the
spectrometer (energy resolution, time resolution, $\gamma$-rays detection
efficiency) were studied exhaustively also using a Geant4-based Monte-Carlo
simulation. Several numerical algorithms for processing of waveforms in offline
mode were proposed and tested to perform digital timing, pulse area measurement
and processing of pile-up events without rejection. As a result, the
spectrometer demonstrated $\sim10\%$ better energy resolution than was obtained
by a common 10-bit CAMAC ADC with the same detectors. And the developed
algorithm based on the pulse shape analysis for processing of pile-up events
showed high efficiency under severe conditions (the portion of pile-ups
contained $\sim30\%$). The measured maximum counting rate of the spectrometer
was $1.8\times10^5$ waveforms/sec.
