G.M. Cortelazzo and R. Manduchi. On the determination of all the sublattices of preassigned index and its application to multidimensional subsampling. IEEE Transactions on Circuits and Systems for Video Technology, 3(4):318--320, August 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... D = E 1 DeltaE 2 ; E 1 ; E 2 unimodular (2) The Fourier transform relationship for a subsampled signal s(x) is S(f ) 1 d(D) X v2C U (f Gamma v) 3) The coset representative vectors C may be generated by a lexicographical enumeration of the diagonal vector Delta of the Smith form [2]. The Fourier transform is invariant to upsampling, hence expansion followed by decimation produces Y (f ) S(f ) 1 d(D) X v2C U (f Gamma v) 4) In a filter bank system the i th channel is extracted from input u(x) by the operation of an analysis filter H i (f ) followed by a ....

G. Cortelazzo and R. Manduchi, "On the determination of all the sublattices of preassigned index and its application to multidimensional subsampling," IEEE Trans. Circuits Syst. Video Technol., vol. 3, pp. 318-- 320, Aug 1993.

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G.M. Cortelazzo and R. Manduchi. On the determination of all the sublattices of preassigned index and its application to multidimensional subsampling. IEEE Transactions on Circuits and Systems for Video Technology, 3(4):318--320, August 1993.

No context found.

G. M. Cortelazzo and R. Manduchi, "On the determination of all the sublattices of preassigned index and its application to multidimensional subsampling," IEEE Trans. Circuits Syst. Video Technol., vol. 3, pp. 318--320, Aug. 1993.

....are used extensively throughout the paper, together with the adopted nomenclature. Section 2.1.1 contains facts already known in the literature, which we report here in order to make the paper self contained. For their proofs, as well as for more details, the reader is addressed to [13] 14] 3] [15], 12] 16] Section 2.1.2 reports some novel results. 2.1.1 Background and Nomenclature R denotes the set of real numbers, Z is the set of integers. We denote vectors by small boldface letters and matrices by capital boldface letters. Their entries are named after the following example: a def = ....

....given a signal h(x) we will say that h r (x) h(Nx r) 0 r N , is the r th N polyphase component of h(x) Let n be an integer. Then the distinct sublattices having index n in LAT (A) are fLAT (AH i )g, where fH i g are the matrices in Hermite normal form with determinant equal to n [15]. We adopt the following definition for the Fourier transform of a signal h(a) defined on a lattice = LAT (A) H(f) X a2 h(a)e Gammaj 2 f T a = X n 2Z M h(An)e Gammaj 2 f T An (6) H(f) is periodic on the dual lattice = LAT (A GammaT ) where A GammaT def = A ....

G.M. Cortelazzo and R. Manduchi. On the determination of all the sublattices of preassigned index and its application to multidimensional subsampling. IEEE Trans. Circuits Syst. Video Techn., 3(4):318-- 320, August 1993.

....As in the 1 D case, the purpose of the interpolator is to cancel the undesired spectral repetitions of the shaping filter (see Fig. 2) The following issues must be taken care of in the M D case: 1. M D sampling lattices admit more than just one sublattice for a given decimation ratio [9] [5]. Each sublattice induces a different geometry of the spectral repetitions of the shaping filter. In this work, we show that, given the desired frequency response mask, certain sublattices make for the easy interpolation of the samples of the shaping filter, while other ones are unsuitable. In our ....

G.M. Cortelazzo and R. Manduchi. On the determination of all the sublattices of preassigned index and its application to multidimensional subsampling. IEEE Trans. Circuits Syst. Video Techn., 3(4):318--320, August 1993.

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