Bandlimited signals and differential equations play fundamental roles in signal processing and communications, yet their relationship remains largely unexplored. In this work, we investigate how bandlimitedness emerges in the solutions to a class of differential equations that exhibit time-domain and frequency-domain self-duality. We derive the necessary and sufficient conditions in time and frequency domains under which solutions of such equations are bandlimited. Through illustrative examples of well-known bandlimited signals and their associated differential equations, we elaborate on the realization of the derived conditions. Furthermore, we demonstrate how bandlimited behavior can be induced in otherwise non-bandlimited systems by introducing suitable differential operators. We briefly discuss a potential research direction on the applications of such differential equations in generative models as well. However, the main purpose of this work is to present the analytical results.
A tracking system can efficiently track a target if the motion model used by the system match the target's motion model. The Interacting Multiple Model (IMM) algorithm is commonly employed in tracking systems for this purpose. IMM uses a set of models to represent the possible evolution of the target's state. Since the target's motion can switch between different modes, the IMM algorithm must switch accordingly. The switching between models is governed by the Transition Probability Matrix (TPM), which plays a key role in determining both the estimation accuracy and the response time of the tracker. In the conventional Interacting Multiple Model (CIMM) algorithm, the TPM is pre-defined and set heuristically. The diagonal elements of the TPM represent the probability that a model will continue in its current state, which directly affects the accuracy of the estimate. A higher value for the diagonal elements typically leads to more accurate estimates in the case of model matched filtering. However, larger diagonal elements also result in slower model switching, as the off-diagonal elements determine the speed at which models switch during changes in the target's motion. This creates a tradeoff between accuracy and responsiveness, limiting the performance of the CIMM algorithm. To address this limitation, this paper proposes a likelihood-based approach (ATPM_L) for updating the TPM. In the proposed method, the likelihood of each model is computed with respect to the current scan measurement and the TPM update factor is derived based on these likelihoods. This likelihood-based approach satisfies both accuracy and switching speed requirements of TPM in IMM algorithm. This algorithm also offers a faster model switching mechanism compared to all existing TPM update algorithms.
Microwave Photonic technologies show rapid growth in current era of high-speed data communication, due to its support with broad bandwidth, immunity to electromagnetic interference, excellent isolation and high frequency operation capabilities. In this work, an optical QPSK communication system is proposed that operates with different input bit rate data streams. The architecture is further extended for the transmission of a Time Division Multiplexed (TDM) data stream with improved data handling capability and extracting different bit streams of data at the receiver end. Modelling of hardware architectures are carried out in a standard simulation environment. The paper describes about the architecture models in detail along with the results obtained during the evaluation process. In these architectures, a highly stable Mode Lock Laser (MLL) is used to provide the optical carrier signal. The time multiplexed signal over a single hardware increases the data handling capability suitable for high-speed data links.
Optical Beam Forming has emerged as a pivotal technology for modern communication systems as well as for wide band radar applications. The photonics technologies possess inherent advantages like low loss, immunity to electromagnetic interference along with its capability of true-time-delay beam steering. Here, we report on an Optical beam forming network using Fiber Bragg Gratings (FBGs) for the formation of multi beams during transmit operation of a radar system.The proposed architecture exploits the wavelength-dependent dispersion characteristics of FBGs to realize precise and reconfigurable time delays required for multi-beam formation.By mapping different wavelengths to independent delay paths, simultaneous transmit beams are formed without the limitations of conventional electronic phase shifters, such as beam squint and bandwidth constraints. In addition to modeling, the proposed architecture is evaluated experimentally considering a linaer array consisting 3, where controlled delay values of 0 ps, 25 ps, and 50 ps are provided to realize progressive time delays across the antennaarray to form the beam.
This paper investigates the design and performance of a non-conventional dielectric dome integrated with a 1x8 microstrip patch antenna array operating in the C-band at 5.65 GHz. The primary objective is to enhance the overall performance of the antenna array through dome integration. Two dome configurations, referred to as Design 1 and Design 2, are analyzed with variations in shape and thickness to evaluate their influence on the array characteristics. Without the dome, the array exhibits a scanning capability limited to 50 degrees with a peak boresight gain of 15.61 dBi. When Dome Design 1 is incorporated, the boresight gain increases by 1.64 dBi compared to the standalone array, while maintaining a similar scanning range of up to 50 degrees. In contrast, Dome Design 2 results in a slight reduction in boresight gain by 0.28 dBi but improves the scanning capability, extending it up to 65 degrees. The proposed structure is suitable for applications such as beam-steering antennas in radar communication systems.
