An implicit sampling theorem for bounded bandlimited functions

Entropy of Highly Correlated Quantized Data

“…Before proceeding further, we investigate and establish additional properties of , and other important quantities that we will need. Lemmas will be stated as needed; their proofs will be provided in Section V, or in Appendix D. We begin by finding approximate expressions for the conditional pdf For tractability we would like to drop the smaller of the two function terms in the above expression, which leads us to the upper bound (9) The following lemma shows that is an asymptotically tight upper bound to .…”

“…While this is not a result about the entropy of the quantized samples of a random process, it nonetheless shows a comparable behavior. For the same type of signals, Cvetkovic and Daubechies [7] and Ishwar et al [8] describe schemes for encoding the output of a sampler and dithered scalar quantizer, with rate again increasing as (see also [9] for an earlier discussion of the dithering method, without the low rate encoding of [7] and [8]). Finally, for bounded, nonbandlimited deterministic signals, Kumar et al [10] describe a scheme for coding the output of a sampler and dithered scalar quantizer with rate depending on the tail of the spectrum.…”

Interpolation of 2-D signals from their isolated zeros

“…The main difference is that the interpolation is derived from the sine wave crossing interpolation given in [Bar-David 1974] and discussed in [Marvasti 087], that is n~-oo where x(t) is a bandlimited signal with cosine wave crossings at {tn, n -any integer}. The constant C is the amplitude of the sinusoidal signal.…”

“…The proof of Corollary 4 is similar to Theorem 1. The main difference is that the interpolation is derived from the sine wave crossing interpolation given in [Bar-David 1974] and discussed in [Marvasti 1987], that is,…”

Reconstruction of multidimensional signals from zero crossings

“…One method of modifying signals so that all of their zeros become real is to add a sinusoid of sufficient amplitude at a frequency corresponding to the band edge [10]; another is to repeatedly differentiate the signal [8]. Some modulation schemes have also been shown to produce signals with only real zeros [6].…”