Linear canonical domains and degrees of freedom of signals and systems

We discuss the relationships between linear canonical transform (LCT) domains, fractional Fourier transform (FRT) domains, and the space-frequency plane. In particular, we show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and monotonically ordered by the corresponding fractional order parameter and provides a more transparent view of the evolution of light through an optical system modeled by LCTs. We then study the number of degrees of freedom of optical systems and signals based on these concepts. We first discuss the bicanonical width product (BWP), which is the number of degrees of freedom of LCT-limited signals. The BWP generalizes the space-bandwidth product and often provides a tighter measure of the actual number of degrees of freedom of signals. We illustrate the usefulness of the notion of BWP in two applications: efficient signal representation and efficient system simulation. In the first application we provide a sub-Nyquist sampling approach to represent and reconstruct signals with arbitrary space-frequency support. In the second application we provide a fast discrete LCT (DLCT) computation method which can accurately compute a (continuous) LCT with the minimum number of samples given by the BWP. Finally, we focus on the degrees of freedom of first-order optical systems with multiple apertures. We show how to explicitly quantify the degrees of freedom of such systems, state conditions for lossless transfer through the system and analyze the effects of lossy transfer. © Springer International Publishing Switzerland 2016

Effect of spatial distribution of partial information on the accurate recovery of optical wave fields

We consider the problem of recovering a signal from partial and redundant information distributed over two fractional Fourier domains. This corresponds to recovering a wave field from two planes perpendicular to the direction of propagation in a quadratic-phase multilens system. The distribution of the known information over the two planes has a significant effect on our ability to accurately recover the field. We observe that distributing the known samples more equally between the two planes, or increasing the distance between the planes in free space, generally makes the recovery more difficult. Spreading the known information uniformly over the planes, or acquiring additional samples to compensate for the redundant information, helps to improve the accuracy of the recovery. These results shed light onto redundancy and information relations among the given data for a broad class of systems of practical interest, and provide a deeper insight into the underlying mathematical problem. © 2016 Optical Society of America

Degrees of freedom of optical systems and signals with applications to sampling and system simulation

We study the degrees of freedom of optical systems and signals based on space-frequency (phase space) analysis. At the heart of this study is the relationship of the linear canonical transform domains to the space-frequency plane. Based on this relationship, we discuss how to explicitly quantify the degrees of freedom of first-order optical systems with multiple apertures, and give conditions for lossless transfer. Moreover, we focus on the degrees of freedom of signals in relation to the space-frequency support and provide a sub-Nyquist sampling approach to represent signals with arbitrary space-frequency support. Implications for simulating optical systems are also discussed. © 2013 Optical Society of America

Condition number in recovery of signals from partial fractional fourier domain information

The problem of estimating unknown signal samples from partial measurements in fractional Fourier domains arises in wave propagation. By using the condition number of the inverse problem as a measure of redundant information, we analyze the effect of the number of known samples and their distributions. © OSA 2013

Fast algorithms for digital computation of linear canonical transforms

Fast and accurate algorithms for digital computation of linear canonical transforms (LCTs) are discussed. Direct numerical integration takes O(N2) time, where N is the number of samples. Designing fast and accurate algorithms that take O(N logN) time is of importance for practical utilization of LCTs. There are several approaches to designing fast algorithms. One approach is to decompose an arbitrary LCT into blocks, all of which have fast implementations, thus obtaining an overall fast algorithm. Another approach is to define a discrete LCT (DLCT), based on which a fast LCT (FLCT) is derived to efficiently compute LCTs. This strategy is similar to that employed for the Fourier transform, where one defines the discrete Fourier transform (DFT), which is then computed with the fast Fourier transform (FFT). A third, hybrid approach involves a DLCT but employs a decomposition-based method to compute it. Algorithms for two-dimensional and complex parametered LCTs are also discussed. © Springer International Publishing Switzerland 2016

Culture and Communication: Cultural Variations and Media Effectiveness

Advances in communication technologies have made great progress in bridging time and distance, but social and cultural differences are still formidable obstacles to effective communication. Communication processes occur in specific cultural contexts, with unique normative beliefs, assumptions, and shared symbols. Culture influences what people communicate, to whom they communicate, and how they communicate. There has been little systematic cross‐cultural research to explicate the effects of communication media on communication effectiveness. This article proposes cultural effects on perceptions of media effectiveness. The authors advance conceptual knowledge by presenting new perspectives on the cultural effects on individuals’ perception of media and their effectiveness