Identification of Operators with Bandlimited Symbols

Measurement of Time-Variant Linear Channels

“…A comparison of our result to Heisenberg's uncertainty principle is described in [KP05], in particular, we would like to point to connections with minimal rectangles in phase space as described in [FS97].…”

Linear Independence of Gabor Systems in Finite Dimensional Vector Spaces

“…This result, given as Theorem 1 in Section 2, has implications for operator identification (e.g., [2,11]), for the structure of the discrete short-time Fourier transform, and for the robust coding of signals transmitted over lossy channels. Theorems 2 and 3 in Section 3 summarize these implications.…”

On the identification of parametric underspread linear systems

“…Kailath was the first to recognize that the identifiability of a timevarying linear system H from a single observation is directly tied to the area of the region R in the delay-Doppler space that contains H(δ(t)) [1]. Kailath's seminal work in [1] laid the foundations for the future works of Bello [2], Kozek and Pfander [3], and Pfander and Walnut [4], which establish the nonidentifiability of overspread linear systems-defined as systems with area(R) > 1-and provide constructive proofs for the identifiability of underspread linear systems-defined as systems with area(R) < 1. In this paper, we study the problem of identification of underspread linear systems (ULSs) whose responses can be described by a finite set of delays and Doppler-shifts.…”

“…Unlike most of the existing work in the literature, however, our goal in this paper is to explicitly characterize conditions on the bandwidth and temporal support of the input signal that ensure identification of such ULSs, henceforth referred to as parametric ULSs, from single observations. Specifically, note that the constructive proofs provided in [1][2][3][4] are for the identification of arbitrary ULSs. None of these results therefore shed any light on the bandwidth and temporal support of the input signal needed to ensure identification of parametric ULSs.…”

“…None of these results therefore shed any light on the bandwidth and temporal support of the input signal needed to ensure identification of parametric ULSs. On the contrary, the constructive proofs of [1][2][3][4] require use of input signals with infinite bandwidth and temporal support.…”