  In the currently accepted model for cosmic baryon evolution, Cosmic Dawn and
the Epoch of Reionization are significant times when first light from the first
luminous objects emerged, transformed and subsequently ionized the primordial
gas. The 21 cm hyperfine transition of neutral hydrogen, redshifted from these
cosmic times to a frequency range of 40 to 200 MHz, has been recognized as an
important probe of the physics of CD/EoR. The global 21-cm signal is predicted
to be a spectral distortion of a few 10's to a few 100's of mK, which is
expected to be present in the cosmic radio background as a trace additive
component. SARAS, Shaped Antenna measurement of the background RAdio Spectrum,
is a spectral radiometer purpose designed to detect the weak 21-cm signal from
CD/EoR. An important subsystem of the radiometer, the digital correlation
spectrometer, is developed around a high speed digital signal processing
platform called pSPEC. pSPEC is built around two quad 10 bit analog-to-digital
converters and a Virtex 6 field programmable gate array, with provision for
multiple Gigabit Ethernet and 4.5 Gbps fibre optic interfaces. Here we describe
the system design of the digital spectrometer, the pSPEC board, and the
adaptation of pSPEC to implement a high spectral resolution of about 61 kHz,
high dynamic range correlation spectrometer covering the entire CD/EoR band. As
the SARAS radiometer is required to be deployed in remote locations where
terrestrial radio frequency interference is a minimum, the spectrometer is
designed to be compact, portable and operating off internal batteries. The
paper includes an evaluation of the spectrometer's susceptibility to radio
frequency interference and capability to detect signals from CD/EoR.
