  We show experimentally that the fundamental ingredient of wave-based signal
differentiation, namely zeros of the scattering matrix that lie exactly on the
real axis, can be imposed at will and in situ by purposefully perturbing an
overmoded random scattering system. The resulting unprecedented flexibility
overcomes current limitations of wave-based differentiators, both regarding
their extreme vulnerability due to fabrication inaccuracies or environmental
perturbations as well as their lack of in situ adaptability. Moreover, in
addition to current miniaturization efforts, we suggest that integrability of
wave processors can also be achieved by endowing existing bulky everyday-life
systems that naturally scatter waves with a second signal-processing
functionality. We demonstrate our technique by placing a programmable
metasurface inside a 3D disordered metallic box: the hundreds of available
degrees of freedom allow us to impose at will reflection zeros on a connected
port, such that the reflected signal envelope is the temporal derivative of the
incident one. We demonstrate our ability to toggle between differentiation of
envelopes modulated onto distinct carriers. We also parallelize multiple
differentiation operations on the same device and implement higher-order
differentiators. Our "over-the-air" temporal differentiator for microwave
carriers may find civilian and military applications in processing wireless
communication or radar signals, for data segmentation and compression, as well
as machine vision and hearing. Our generic concept is also applicable to
optical, acoustic, and elastic scattering.
