Spectral hole-burning (SHB) technology is considered for > 10-GHz instantaneous bandwidth signal-processing applications. In this context we report on what is believed to be the first demonstration of a SHB microwave spectrometer. A set of gratings engraved in a SHB crystal is used to filter one sideband of the optically carried microwave signal. The setup is confined to narrow-bandwidth operation, over a 35-MHz-wide interval. The first findings confirm the validity of the architecture in terms of spectral resolution, angular channel separation, and simultaneous detection of multiple spectral lines. (C) 2001 Optical Society of America.