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Signal processing techniques have been developed that use differentstrategies to bypass the Nyquist sampling theorem in order to recover moreinformation than a traditional discrete Fourier transform. Here we examinethree such methods: filter diagonalization, compressed sensing, andsuper-resolution. We apply them to a broad range of signal forms commonly foundin science and engineering in order to discover when and how each method can beused most profitably. We find that filter diagonalization provides the bestresults for Lorentzian signals, while compressed sensing and super-resolutionperform better for arbitrary signals.

Benchmarking Compressed Sensing, Super-Resolution, and Filter Diagonalization