In this study, a novel type of Fourier transform radio spectrometer (termed as all-digital radio spectrometer; ADRS) has been developed in which all functionalities comprising a radio spectrometer including a sampler and Fourier computing unit were implemented as a soft-core on a field-programmable gate array (FPGA). A delay-line-based ramp-compare analog-to-digital converter (ADC), one of completely digital ADC, was used, and two primary elements of the ADC, 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 the quantization bit rate $n$ are limited by the relation, $tau = frac{1}{2^{n}f}$, where $tau$ is the latency of the delay element of the delay-line. Given that the typical latency of the delay element implemented on FPGAs is $sim10$ ps, adoption of a low quantization bit rate, which satisfies the requirements for radio astronomy, facilitates the realization of a high sampling rate up to $sim$100 GSa/s. In addition, as the proposed ADRS does not require a discrete ADC and can be implemented on mass-produced evaluation boards, its fabrication cost is much lower than that of conventional spectrometers. The ADRS prototype was fabricated with values of $f$ = 600 MSa/s and $n$ = 6.6 using a PYNQ-Z1 evaluation board, with a $tau$ of 16.7 ps. The performance of the prototype, including its linearity and stability, was measured, and a test observation was conducted using the Osaka Prefecture University 1.85-m mm-submm telescope; this confirmed the potential application of the prototype in authentic radio observations. With 10 times better cost performance ($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.
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