Discrete Hermite Functions Research Articles

Dilated and Shifted Discrete Hermite Functions With Minimum Time-Bandwidth Product

In this letter, a novel method is proposed to generate discrete approximations of continuous Hermite–Gaussian functions with noninteger shift and dilation. Moreover, the approximations preserve orthogonality. In addition, the discrete Hermite–Gaussian functions reach the minimum time-bandwidth product under discrete version of Gabor uncertainty principle. Two applications are demonstrated. In fractional delay application, the proposed method is compared with the windowing method and proved to have smaller delay error. Another one is the signal expansion based on the proposed complete orthogonal basis.

Efficient Compression of QRS Complexes Using Hermite Expansion

We propose a novel algorithm for the compression of ECG signals, in particular QRS complexes. The algorithm is based on the expansion of signals with compact support into a basis of discrete Hermite functions. These functions can be constructed by sampling continuous Hermite functions at specific sampling points. They form an orthogonal basis in the underlying signal space. The proposed algorithm relies on the theory of signal models based on orthogonal polynomials. We demonstrate that the constructed discrete Hermite functions have important ad- vantages compared to continuous Hermite functions, which have previously been suggested for the compression of QRS complexes. Our algorithm achieves higher compression ratios compared with previously reported algorithms based on continuous Hermite functions, discrete Fourier, cosine, or wavelet transforms.

Integrating Spatio-temporal Information in Image Sequence Analysis to Enforce Consistency of Interpretation

We present a technique of image-sequence analysis which ensures consistency of interpretation in terms of the classification of segmented regions, both spatially within an image and temporally through a sequence of forward-looking infrared images taken from a low-flying aircraft. The technique is based on classical relaxation labeling techniques but is novel in that it treats segmented regions assingle entitiesthat have both spatial and temporal neighbors. This enables classification probabilities both to be propagated through the sequence and to be used in the minimization of the Kullback entropy of information. Sample results are shown from the application of the method to a 12-s sequence of infrared images that have been segmented using co-occurrence-based techniques. For completeness, the paper also describes the whole analysis algorithm including segmentation, texture analysis using discrete Hermite functions, and classification using neural network techniques.© British Crown copyright 1998. Published with the permission of the Defence Evaluation and Research Agency on behalf of the Controller of HMSO.