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The Zak-OTFS input/output (I/O) relation is predictable and non-fading when the delay and Doppler periods are greater than the effective channel delay and Doppler spreads, a condition which we refer to as the crystallization condition. When the crystallization condition is satisfied, we describe how to integrate sensing and communication within a single Zak-OTFS subframe by transmitting a pilot in the center of the subframe and surrounding the pilot with a pilot region and guard band to mitigate interference between data symbols and pilot. At the receiver we first read off the effective channel taps within the pilot region, and then use the estimated channel taps to recover the data from the symbols received outside the pilot region. We introduce a framework for filter design in the delay-Doppler (DD) domain where the symplectic Fourier transform connects aliasing in the DD domain (predictability of the I/O relation) with time/bandwidth expansion. The choice of pulse shaping filter determines the fraction of pilot energy that lies outside the pilot region and the degradation in BER performance that results from the interference to data symbols. We demonstrate that Gaussian filters in the DD domain provide significant improvements in BER performance over the sinc and root raised cosine filters considered in previous work. We also demonstrate that, by limiting DD domain aliasing, Gaussian filters extend the region where the crystallization condition is satisfied. The Gaussian filters considered in this paper are a particular case of factorizable pulse shaping filters in the DD domain, and this family of filters may be of independent interest., Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible

Fingerprints are the most widely deployed form of biometric identification. No two individuals share the same fingerprint because they have unique biometric identifiers. This paper presents an efficient fingerprint verification algorithm which improves matching accuracy. Fingerprint images get degraded and corrupted due to variations in skin and impression conditions. Thus, image enhancement techniques are employed prior to singular point detection and minutiae extraction. Singular point is the point of maximum curvature. It is determined by the normal of each fingerprint ridge, and then following them inward towards the centre. The local ridge features known as minutiae is extracted using cross-number method to find ridge endings and ridge bifurcations. The proposed algorithm chooses a radius and draws a circle with core point as centre, making fingerprint images rotationally invariant and uniform. The radius can be varied according to the accuracy depending on the particular application. Morphological techniques such as clean, spur and H-break is employed to remove noise, followed by removing spurious minutiae. Templates are created based on feature vector extraction and databases are made for verification and identification for the fingerprint images taken from Fingerprint Verification Competition (FVC2002). Minimum Euclidean distance is calculated between saved template and the test fingerprint image template and compared with the set threshold for matching decision. For the performance evaluation of the proposed algorithm various measures, equal error rate (EER), Dmin at EER, accuracy and threshold are evaluated and plotted. The measures demonstrate that the proposed algorithm is more effective and robust., Comment: Conference