Miniaturization of optical spectrometers is important to enable spectroscopic analysis to play a role in in situ, or even in vitro and in vivo characterization systems. However, scaled-down spectrometers generally exhibit a strong trade-off between spectral resolution and operating bandwidth, and are often engineered to identify signature spectral peaks only for specific applications. In this paper, we propose and demonstrate a novel global sampling strategy with distributed filters for generating ultra-broadband pseudo-random spectral responses. The geometry of all-pass ring filters is tailored to ensure small self- and cross-correlation for effective information acquisition across the whole spectrum, which dramatically reduces the requirement on sampling channels. We employ the power of reconfigurable photonics in spectrum shaping by embedding the engineered distributed filters. Using a moderate mesh of MZIs, we create 256 diverse spectral responses on a single chip and demonstrate a resolution of 20 pm for single spectral lines and 30 pm for dual spectral lines over a broad bandwidth of 115 nm, to the best of our knowledge achieving a new record of bandwidth-to-resolution ratio. Rigorous simulations reveal that this design will readily be able to achieve single-picometer-scale resolution. We further show that the reconfigurable photonics provides an extra degree of programmability, enabling user-defined features on resolution, computation complexity, and relative error. The use of SiN integration platform enables the spectrometer to exhibit excellent thermal stability of ±2.0 °C, effectively tackling the challenge of temperature variations at picometer-scale resolutions.