Clipping and Signal Determinism: Two Algorithms Requiring Validation

Reconstruction of multidimensional signals from zero crossings

“…Specifically, we state the following theorem: It is also possible to generalize Theorem 5.1 to allow unique specification with broader classes of sign information than the S,(wI,w2) as defined in equation (12).…”

“…Voelcker [11] has shown that for anglemodulated systems, knowledge of the zero crossing locations of the modulated signal is equivalent to knowledge of samples of the signal before modulation; thus if the original signal is bandlimited, then the zero crossings of the modulated signal are sufficient to uniquely specify it. Fairly recently, in response to experimental results presented by Voelcker and Requicha [12], Logan [9] developed a new class of bandpass signals which are uniquely specified by their zero crossings. Specifically, Logan showed that a signal with a bandwidth of less than one octave is uniquely specified by its zero crossings if it has no zeros in common with its Hiibert transform other than real simple zeros.…”

Multiwindow Gabor-type Representations and Signal Representation by Partial Information

“…However, they do not provide an algorithm for signal reconstruction from its zero crossings, nor do they address the important issue of stability. Algorithms for one-dimensional signals were put forward by Voelecker and Requicha [31]. These algorithms were modified by Rotem and Zeevi [24], and applied in reconstruction of images from their zero crossings.…”

The reconstruction of analog signals from the sign of their noisy samples

“…In general the binary signal sgn(s(t)] does not uniquely determine s(t) even when s(t) is an analytic function. For example, when s(t) is a bandlimited function and thehard-limitersgn x is replaced by a strictly monotonic transformation *(x), then s(t) can be recovered from the bandlimited version of O[s(t)] by using a recursive algorithm based on the principle of contraction mapping; this was accomplished by Landau when (x) -sgn x whether s(t) is bandlimited or not (see, for example, [3]). …”

“…Comparing (44) with (46) we note that the transmitter power C 2 in the white noise case is proportional to the variation parameter D of the signal and to (1/6 3 ) whereas in the colored noise case the transmitter power is independent of D and…”