  Amplitude demodulation is a classical operation used in signal processing.
For a long time, its effective applications in practice have been limited to
narrowband signals. In this work, we generalize amplitude demodulation to
wideband signals. We pose demodulation as a recovery problem of an oversampled
corrupted signal and introduce special iterative schemes belonging to the
family of alternating projection algorithms to solve it. Sensibly chosen
structural assumptions on the demodulation outputs allow us to reveal the high
inferential accuracy of the method over a rich set of relevant signals. This
new approach surpasses current state-of-the-art demodulation techniques apt to
wideband signals in computational efficiency by up to many orders of magnitude
with no sacrifice in quality. Such performance opens the door for applications
of the amplitude demodulation procedure in new contexts. In particular, the new
method makes online and large-scale offline data processing feasible, including
the calculation of modulator-carrier pairs in higher dimensions and poor
sampling conditions, independent of the signal bandwidth. We illustrate the
utility and specifics of applications of the new method in practice by using
natural speech and synthetic signals.
