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In this study, a novel type of Fourier transform radio spectrometer (termedas all-digital radio spectrometer; ADRS) has been developed in which allfunctionalities comprising a radio spectrometer including a sampler and Fouriercomputing unit were implemented as a soft-core on a field-programmable gatearray (FPGA). A delay-line-based ramp-compare analog-to-digital converter(ADC), one of completely digital ADC, was used, and two primary elements of theADC, an analog-to-time converter (ATC) and a time-to-digital converter (TDC),were implemented on the FPGA. The sampling rate of the ADRS $f$ and thequantization bit rate $n$ are limited by the relation, $\tau =\frac{1}{2^{n}f}$, where $\tau$ is the latency of the delay element of thedelay-line. Given that the typical latency of the delay element implemented onFPGAs is $\sim10$ ps, adoption of a low quantization bit rate, which satisfiesthe requirements for radio astronomy, facilitates the realization of a highsampling rate up to $\sim$100 GSa/s. In addition, as the proposed \ADRS doesnot require a discrete ADC and can be implemented on mass-produced evaluationboards, its fabrication cost is much lower than that of conventionalspectrometers. The ADRS prototype was fabricated with values of $f$ = 600 MSa/sand $n$ = 6.6 using a PYNQ-Z1 evaluation board, with a $\tau$ of 16.7 ps. Theperformance of the prototype, including its linearity and stability, wasmeasured, and a test observation was conducted using the Osaka PrefectureUniversity 1.85-m mm-submm telescope; this confirmed the potential applicationof the prototype in authentic radio observations. With 10 times better costperformance ($\sim$800 USD GHz$^{-1}$) than conventional radio spectrometers,the prototype facilitates cost-effective coverage of intermediate frequency(IF) bandwidths of $\sim100$ GHz in modern receiver systems.

Observational demonstration of a low-cost fast Fourier transform spectrometer with a delay-line-based ramp-compare ADC implemented on FPGA