To extend the high-frequency bandwidth, we can isolate the top octave using high pass filtering and then generating harmonics of this. The generation of harmonics can be done through a simple full-wave rectification, which is computationally cheap and not amplitude-dependent. As an alternative single-sideband modulation can be used, giving precise control over the number and amplitude of the harmonics. In theory, envelope estimation can be used to extract the original high-frequency envelope and regenerating high frequencies using a noise source. The sparse information available in the small bandwidth will probably be too limited to extract a proper envelope.