On-chip spectrometers have the potential to offer dramatic size, weight, and power advantages over conventional benchtop instruments for many applications such as spectroscopic sensing, optical network performance monitoring, hyperspectral imaging, and radio-frequency spectrum analysis. Existing on-chip spectrometer designs, however, are limited in spectral channel count and signal-to-noise ratio. Here we demonstrate a transformative on-chip digital Fourier transform spectrometer that acquires high-resolution spectra via time-domain modulation of a reconfigurable Mach-Zehnder interferometer. The device, fabricated and packaged using industry-standard silicon photonics technology, claims the multiplex advantage to dramatically boost the signal-to-noise ratio and unprecedented scalability capable of addressing exponentially increasing numbers of spectral channels. We further explore and implement machine learning regularization techniques to spectrum reconstruction. Using an 'elastic-D1' regularized regression method that we develop, we achieved significant noise suppression for both broad (>600 GHz) and narrow (<25 GHz) spectral features, as well as spectral resolution enhancement beyond the classical Rayleigh criterion.