  Quantum-inspired superresolution methods surpass the Rayleigh limit in
imaging, or the analogous Fourier limit in spectroscopy. This is achieved by
carefully extracting the information carried in the emitted optical field by
engineered measurements. An alternative to complex experimental setups is to
use simple homodyne detection and customized data analysis. We experimentally
investigate this method in the time-frequency domain and demonstrate the
spectroscopic superresolution for two distinct types of light sources: thermal
and phase-averaged coherent states. The experimental results are backed by
theoretical predictions based on estimation theory.
