Complete Identification of Permissible Sampling Rates for First-Order Sampling of Multi-Band Bandpass Signals

The first-order sampling of multi-band bandpass signals with arbitrary band positions is considered in this paper. Gaps between the spectral sub-bands are utilized to achieve lower sampling rates than the Nyquist. The lowest possible sampling rate along with other permissible sampling rates is identified via a unique partition of the frequency axis. With the complete identification of all the permissible sampling rates, a necessary and sufficient sampling theorem for multi-band bandpass signals is presented in terms of a series of csinc-interpolators

Filtering of irregularly sampled signals

Some systems are capable to provide information only at irregular time intervals, or to preserve only the most representative samples of a signal, in a way to reduce the amount of recorded information. Consequently, signals stemming from these systems, are irregularly sampled and need to be processed under this form. The aim of our paper is to propose a N-order low-pass and band-pass filtering tool applied to such irregularly sampled signals. The originality of the procedure resides in the absence of total reconstruction of the original signal by any interpolation method. The signal, whose information are only known at some instants, is directly processed. From an analogical transfer function representing the processing to undertake (filtering), the corresponding state space system is first determined, then solved and discretised with nonuniform time intervals. Thus, general and Butterworth lowpass and band-pass filters are developed. The irregularly sampled filter is compared to the normal filter having fixed sample intervals.Certains systèmes ne fournissent des informations qu'à des intervalles de temps irréguliers, ou ne conservent d'un signal que les échantillons les plus représentatifs dans le but de réduire la quantité d'informations enregistrées. Par conséquent, les signaux issus de ces systèmes, sont échantillonnés irrégulièrement ou à pas variable et il est nécessaire de les traiter sous cette forme. Nous proposons ici un outil de filtrage passe-bas et passe-bande d'ordre Ns'appliquant à de tels signaux échantillonnés à pas variable. L'originalité de la procédure réside en l'absence de reconstruction totale du signal d'origine par une quelconque interpolation. Nous traitons en effet directement le signal dont les informations ne sont connues qu'à certains instants à intervalles de temps irréguliers. Pour cela, à partir d'une fonction de transfert continue représentant le traitement à effectuer (filtrage), nous déterminons le système d'état correspondant, puis nous le résolvons et le discrétisons avec des intervalles de temps non constants. Nous développons alors des filtres passe-bas et passe-bande de type général et de type Butterworth, et nous comparons le filtrage de signaux échantillonnés à pas variable au filtrage classique de signaux à pas d'échantillonnage fixe

Optimized techniques for real-time microwave and millimeter wave SAR imaging

Microwave and millimeter wave synthetic aperture radar (SAR)-based imaging techniques, used for nondestructive evaluation (NDE), have shown tremendous usefulness for the inspection of a wide variety of complex composite materials and structures. Studies were performed for the optimization of uniform and nonuniform sampling (i.e., measurement positions) since existing formulations of SAR resolution and sampling criteria do not account for all of the physical characteristics of a measurement (e.g., 2D limited-size aperture, electric field decreasing with distance from the measuring antenna, etc.) and nonuniform sampling criteria supports sampling below the Nyquist rate. The results of these studies demonstrate optimum sampling given design requirements that fully explain resolution dependence on sampling criteria. This work was then extended to manually-selected and nonuniformly distributed samples such that the intelligence of the user may be utilized by observing SAR images being updated in real-time. Furthermore, a novel reconstruction method was devised that uses components of the SAR algorithm to advantageously exploit the inherent spatial information contained in the data, resulting in a superior final SAR image. Furthermore, better SAR images can be obtained if multiple frequencies are utilized as compared to single frequency. To this end, the design of an existing microwave imaging array was modified to support multiple frequency measurement. Lastly, the data of interest in such an array may be corrupted by coupling among elements since they are closely spaced, resulting in images with an increased level of artifacts. A method for correcting or pre-processing the data by using an adaptation of correlation canceling technique is presented as well --Abstract, page iii