Search Results (6)

One of the best known time–frequency tools for examining non-transient signals is the linear canonical windowed transform, which has been used extensively in signal processing and related domains. In this paper, by involving the harmonic analysis for the linear canonical Dunkl transform, we introduce and then study the linear canonical Dunkl windowed transform (LCDWT). Given that localization operators are both theoretically and practically relevant, we will focus in this paper on a number of time–frequency analysis topics for the LCDWT, such as the $L^p$ boundedness and compactness of localization operators for the LCWGT. Then, we study their trace class characterization and show that they are in the Schatten–von Neumann classes. Then, we study their spectral properties in order to give some results on the spectrograms for the LCDWT. Full article

In this work, we introduce the quaternion linear canonical S-transform, which is a generalization of the linear canonical S-transform using quaternion. We investigate its properties and seek the different types of uncertainty principles related to this transformation. The obtained results can be looked as an extension of the uncertainty principles for the quaternion linear canonical transform and the quaternion windowed linear canonical transform. Full article

The quaternion windowed linear canonical transform is a tool for processing multidimensional data and enhancing the quality and efficiency of signal and image processing; however, it has disadvantages due to the noncommutativity of quaternion multiplication. In contrast, reduced biquaternions, as a special case of four-dimensional algebra, possess unique advantages in computation because they satisfy the multiplicative exchange rule. This paper proposes the reduced biquaternion windowed linear canonical transform (RBWLCT) by combining the reduced biquaternion signal and the windowed linear canonical transform that has computational efficiency thanks to the commutative property. Firstly, we introduce the concept of a RBWLCT, which can extract the time local features of an image and has the advantages of both time-frequency analysis and feature extraction; moreover, we also provide some fundamental properties. Secondly, we propose convolution and correlation operations for RBWLCT along with their corresponding generalized convolution, correlation, and product theorems. Thirdly, we present a fast algorithm for RBWLCT and analyze its computational complexity based on two dimensional Fourier transform (2D FTs). Finally, simulations and examples are provided to demonstrate that the proposed transform effectively captures the local RBWLCT-frequency components with enhanced degrees of freedom and exhibits significant concentrations. Full article

A distinction is made between data rescue (i.e., copying, digitizing, and archiving) and data recovery that implies deciphering, interpreting, and transforming early instrumental readings and their metadata to obtain high-quality datasets in modern units. This requires a multidisciplinary approach that includes: palaeography and knowledge of Latin and other languages to read the handwritten logs and additional documents; history of science to interpret the original text, data, and metadata within the cultural frame of the 17th, 18th, and early 19th centuries; physics and technology to recognize bias of early instruments or calibrations, or to correct for observational bias; and astronomy to calculate and transform the original time in canonical hours that started from twilight. The liquid-in-glass thermometer was invented in 1641 and the earliest temperature records started in 1654. Since then, different types of thermometers have been invented, based on the thermal expansion of air or selected thermometric liquids with deviation from linearity. Reference points, thermometric scales, and calibration methodologies were not comparable, and not always adequately described. Thermometers had various locations and exposures, e.g., indoor, outdoor, on windows, gardens or roofs, facing different directions. Readings were made only one or a few times a day, not necessarily respecting a precise time schedule: this bias is analysed for the most popular combinations of reading times. The time was based on sundials and local Sun, but the hours were counted starting from twilight. In 1789–1790, Italy changed system and all cities counted hours from their lower culmination (i.e., local midnight), so that every city had its local time; in 1866, all the Italian cities followed the local time of Rome; in 1893, the whole of Italy adopted the present-day system, based on the Coordinated Universal Time and the time zones. In 1873, when the International Meteorological Committee (IMC) was founded, later transformed into the World Meteorological Organization (WMO), a standardization of instruments and observational protocols was established, and all data became fully comparable. In dealing with the early instrumental period, from 1654 to 1873, the comparison, correction, and homogenization of records is quite difficult, mainly because of the scarcity or even absence of metadata. This paper deals with this confused situation, discussing the main problems, but also the methodologies to recognize missing metadata, distinguish indoor from outdoor readings, correct and transform early datasets in unknown or arbitrary units into modern units, and, finally, in which cases it is possible to reach the quality level required by the WMO. The aim is to explain the methodology needed to recover early instrumental records, i.e., the operations that should be performed to decipher, interpret, correct, and transform the original raw data into a high-quality dataset of temperature, usable for climate studies. Full article

In this paper, we generalize the N-dimensional Heisenberg’s inequalities for the windowed linear canonical transform (WLCT) of a complex function. Firstly, the definition for N-dimensional WLCT of a complex function is given. In addition, the N-dimensional Heisenberg’s inequality for the linear canonical transform (LCT) is derived. It shows that the lower bound is related to the covariance and can be achieved by a complex chirp function with a Gaussian function. Finally, the N-dimensional Heisenberg’s inequality for the WLCT is exploited. In special cases, its corollary can be obtained. Full article

The problem of single-channel reception of global positioning system (GPS) communication waveforms makes passive sensing of aerial target difficult because of forward scatter. This paper proposes a novel aerial target passive sensing method based on linear canonical transformation (LCT) using the forward scattered satellite communication waveforms. The proposed method firstly preprocesses the received signal based on the characteristics of the traditional satellite tracking loop and the forward scattered satellite communication waveforms to effectively suppress the interference of the direct wave through DC removal. Then, the Gaussian noise and multipath interference in the channel are suppressed by applying a rectangular window to its linear canonical domain. Finally, aerial target sensing is performed based on the peak value of signals in the linear canonical transform domain. The characteristic signal is constructed by analyzing the satellite communication waveforms. Combining the linear canonical transform with the matched filter (MF) to estimate the target parameter. Simulation results show that the proposed method can effectively perform the aerial target sensing by using satellite communication waveforms in the forward scatter scenario. Full article