An interesting subclass of bandpass signals {h} is described wherein the zero crossings of h determine h within a multiplicative constant. The members may have complex zeros, but it is necessary that h should have no zeros in common with its Hilbert transform ĥ other than real simple zeros. It is then sufficient that the band be less than an octave in width. The subclass is shown to include full‐carrier upper‐sideband signals (of less than an octave bandwidth). Also it is shown that full‐carrier lower‐sideband signals have only real simple zeros (for any ratio of upper and lower frequencies) and, hence, are readily identified by their zero crossings. However, under the most general conditions for uniqueness, the problem of actually recovering h from its sign changes appears to be very difficult and impractical.
We develop inequalities for the fraction of a bandlimited function's Lp norm which can be concentrated on any set of small 'Nyquist density'. We mention two applications. First, that a bandlimited function corrupted by impulsive noise can be reconstructed perfectly, provided the noise is concentrated on a set of Nyquist density < 1/7r. Second, that a wideband signal supported on a set of Nyquist density < 1/7r can be reconstructed stably from noisy data, even when the low frequency information is completely missing.
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