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 10s to a few 100s 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 spectrometers susceptibility to radio frequency interference and capability to detect signals from CD/EoR.
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