Sustainability, Uncertainty, and Risk: Time-Frequency Relationships

Uncertainty, information and time-frequency distributions *

The well-known uncertaintly principle is often invoked in signal processing. It is also often considered to have the same implications in signal analysis as does the uncertainty principle in quantum mechanics. The uncertainty principle is often incorrectly interpreted to mean that one cannot locate the time-frequency coordinates of a signal with arbitrarily good precision, since, in quantum mec...

Sequences with Minimal Time-Frequency Uncertainty

A central problem in signal processing and communications is to design signals that are compact both in time and frequency. Heisenberg’s uncertainty principle states that a given function cannot be arbitrarily compact both in time and frequency, defining an “uncertainty” lower bound. Taking the variance as a measure of localization in time and frequency, Gaussian functions reach this bound for ...

Risk, Uncertainty and Optimism in Venture Capital Relationships

We develop a dynamic, structural model to quantitatively assess the effects of risk, uncertainty and asymmetric beliefs about project quality on the characteristics of venture capital relationships. We estimate the model parameters with data about the distributions of total investments, payoffs, risks and returns of venture capital projects. Entrepreneurial optimism mitigates the agency costs o...

Uncertainty Relations and Time-Frequency Distributions for Unsharp Observables

This paper deals with a new framework in analyzing the formal mathematical correspondence between quantum mechanics and time-frequency representations of a signal. It is also shown that joint time-frequency distributions have a close link with Heisenberg uncertainty relations if the observables are taken as fuzzy entities. This result contradicts the arguments of Cohen [IEEE Proc. 77(7):941 (19...

Dynamic convex risk measures: time consistency, prudence, and sustainability