Showing papers by "Er'el Granot published in 2020"

Fundamental limitations of dispersion mitigation filters.

Abstract: We investigate the fundamental limitations of dispersion mitigation filters. By analyzing the dispersion compensating process from basic principles, we demonstrate how a digital filter can mitigate arbitrarily weak dispersion without oversampling. We calculate the maximum distance the signal can pass with and without dispersion compensation, beyond which no data decoding is possible. Furthermore, we show the exact mathematical relation between this maximum distance and the length of the compensating filter - with and without a Forward Error Correction (FEC).

Analytical boundary-based method for diffraction calculations

Abstract: We present a simple method for calculation of diffraction effects in a beam passing an aperture. It follows the well-known approach of Miyamoto and Wolf, but is simpler and does not lead to singularities. It is thus shown that in the near-field region, i.e., at short propagation distances, most results depend on values of the beam's field at the aperture's boundaries, making it possible to derive diffraction effects in the form of a simple contour integral over the boundaries. For a uniform, i.e., plane-wave incident beam, the contour integral predicts the diffraction effects exactly. Comparisons of the analytical method and full numerical solutions demonstrate highly accurate agreement between them.

Mitigating weak dispersion in affordable RF-over-fiber channels

Abstract: A dispersion-compensating filter for next-generation low-cost analog and digital optical links is developed. In these high-frequency optical channels, even weak dispersion can be detrimental to data encoding (e.g., radar detection). Dispersion-compensating filters must be affordable for these low-cost channels, and they must be reliable for weak dispersion channels. In this paper, we design a dispersion-compensating filter based on three properties of the analog channel: weak modulation depth, a spectrally bounded signal, and a low-dispersion channel. We calculate the fundamental performance limits of the channel with and without the filter and quantify the improvement. Furthermore, numerical simulations are taken to estimate the filter’s performances for both pulse amplitude modulation digital channels and for analog ones. The simulations agree with the analytical derivation, and, in both cases, the filter’s integration improves the channels’ performances considerably.

An Overlooked Scenario of “Reswitching” in the Austrian Structure of Production

Abstract: Since Samuelson’s (1966) reswitching example in the 1960s, it became clear that the Average Production Period (APP) is not necessarily a decreasing function of the interest rate. Recently, Fillieule (2007) and Hulsmann (2010) have shown that Samuelson’s example is not a mere curiosity. They showed that in a reasonable production structure model, the length of production increases with the interest rate instead of decreasing. However, their model did not present “reswitching” behavior. In this paper a generic model of the structure of production, in which both Fillieule’s and Hulsmann’s models are specific cases, is presented. It shows that the APP has a nonmonotonic dependence on the interest rate, which resembles a “reswitching” behavior: it increases for low-interest rates up to a maximum value, and then decreases back to almost the initial value. The decrease occurs within a relatively narrow range of interest rates, which may explain why it was missed in the literature.