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Yayın Decomposition of the nodal conductance matrix of a planar resistive grid and derivation of its eigenvalues and eigenvectors using the kronecker product and sum with application to cnn image filters(IEEE, 2016-12) Tavşanoğlu, Ahmet VedatIt is shown that an (M× N)-node planar resistive grid can be decomposed into two sub-grids; one made up of M N-node horizontal and the other of N M-node vertical linear resistive grids which corresponds to decomposing its nodal conductance matrix (NCM) into the Kronecker sum of the NCMs of horizontal and vertical linear grids. This enables the analytical expressions of the eigenvalues and eigenvectors of the NCMs of the sub-grids as well as those of the planar resistive grid to be expressed in terms of those of the two linear grids, whose analytical expressions are well known. For a Cellular Neural Network (CNN) Gabor-type filter (GTF) we define generalized nodal conductance matrices (GNCMs) that correspond to the NCMs of the resistive sub-grids, show that each Kronecker decomposition has a counterpart in CNN GTF and prove that each GNCM, its counterpart NCM and the corresponding temporal state matrices are related through unitary diagonal similarity transformations. Consequently, we prove that the eigenvalues of the temporal state matrix of a spatial band-pass CNN GTF are the same as those of its counterpart spatial low-pass CNN image filter, hence their temporal transient behaviors are similar in settling to a forced response.Yayın Spectral correlation of a digital pulse stream modulated by a cyclostationary sequence in the presence of timing jitter(IEEE-INST Electrical Electronics Engineers Inc, 2009-02) Öner, Mustafa MengüçCyclostationarity is an inherent characteristic of many communication signals, which can be exploited for performing various signal processing tasks. Imperfections in the signal generation that affect the cyclic statistics of a signal may lead to a degradation in the performance of signal processing algorithms which make use of this cyclostationary behaviour. One typical source of imperfection encountered in digital signalling techniques is random jitter in the pulse timing. In this work, we systematically derive analytical expressions for the cyclic statistics of digital baseband signalling schemes in the presence of timing jitter, under the assumption that the generating wide sense cyclostationary data sequence and the stationary jitter process are statistically independent.
