  For efficient spectroscopic redshift identification of early galaxies in the
northern hemisphere, we aim to combine the Large Millimeter Telescope (LMT)
with a wide-band heterodyne receiver, FINER, which will cover radio frequencies
of 120--360 GHz and offer a 3--21 GHz intermediate frequency (IF) per sideband
and polarization. To take full advantage of such wide IFs, we present a novel
10.24-GHz-wide digital spectrometer, DRS4 (Elecs Industry Co., Ltd.). It
incorporates 20.48 Gsps samplers with an FPGA-based digital signal processing
module. To mitigate the noise contamination from the image sideband, it is
equipped with a digital sideband separation function to improve the sideband
rejection up to 25 dB. Laboratory performance evaluations show that it exhibits
an Allan time of at least ~100 s and a total power dynamic range of at least 7
dB. These results demonstrate its capability of instantaneously wide-band
spectroscopy toward high-redshift galaxies with position-switching
observations.
