Signals designed for recovery after clipping — I. Localization of infinite products

It is shown for signals of the form s(t) = g(t) + cos ct, where g is band-limited to [−b, b], 0 < 6 < c < ∞, and (−1)
^k
s(KΠ/c) > 0 (e.g., if |g(t)| < 1), that the zeros of s in the interval (t − T, t + T) allow reconstruction of s(t) with a relative error less than 2e
^−λT
(1 − e
^−λT
)
⁻²
, where λ = b − c. The reconstruction algorithm gives an effective way of localizing the infinite product representation for s(t). Some practical aspects of the algorithm are discussed. The scheme offers advantages for the recovery of signals after nonlinear distortion, such as occurs, for example, in magnetic recording.