We developed a wideband multi-channel merge-split fast Fourier transform spectrometer (FFTS) using analog-to-digital convertors (ADC) for signal sampling and field-programmable gate arrays (FPGA) for real-time spectrum generation. The FFTS constitutes the backend of the sub-mm wave heterodyne spectroscopy telescope to observe emitted radiations from rotational transitions of CO (J: 2 → 1 and J: 3 → 2) with 50 arc sec angular resolution, aiming to provide the first comprehensive survey of molecular clouds in the Milky Way and nearby galaxies from the northern hemisphere (Hanle, India) at these frequencies. The FFTS provides 8 GHz instantaneous bandwidth at 1.6 MHz spectral resolution (extendable to 0.8 or 0.4 MHz) comprising four channels (spanning 218.898 to 220.898 GHz, 229.038 to 231.038 GHz, 329.087 to 331.087 GHz, and 344.295 to 346.295 GHz frequency bands) belonging to two receiver chains at 230 and 345 GHz operating in a double side band configuration. The channel placement for these four channels is done to cover ¹³CO (J:2 → 1) transition at 220.398 GHz, ¹²CO (J:2 → 1) transition at 230.538 GHz, ¹³CO (J:3 → 2) transition at 330.588 GHz, and ¹²CO (J:3 → 2) transition at 345.796 GHz with 1.5 GHz margin for red-shifts. Spectrometer design is presented along with spectral line profile simulations, hardware configuration, proposed methodology, system specifications, and scalable field-programmable gate arrays (FPGA) implementation architecture. Elements in the instrument design leverage simultaneous multi-channel acquisition for optimized FPGA utilization by merging the channel pair from the sideband separating (2SB) second stage intermediate frequency (IF) mixer during Fourier transform and subsequently splitting the generated spectra. System characterization results are presented, confirming instruments capable of stable spectroscopy with a wide bandwidth (instantaneous 8 GHz with four 2 GHz channels) and high-spectral sampling (1 / 0.5 / 0.25 MHz corresponding to scalable fast Fourier transform length of 4k / 8k / 16k respectively) that provides adequate spectral resolution for the science case. Wide dynamic range (49.3 dB) and fine radiometric resolution required for relative spectroscopic measurements is realized by sampling IF signals with 12-bits ADCs. Variable spectral accumulation time facilitates improvements in the signal to noise ratio proportional to the square root of the number of coherent averaged cycles, covering various target dependent (longer dwell time for a single target) or scanning dependent (e.g., drift scanning mode matching earth’s rotation) dwell time requirements.