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Abstract
We present a design method for designing 3D Mth band eigenfilters with 48-hedral symmetry, along with their application to sampling structure conversion of 3D signals defined on the face centered cubic (FCC) or body centered cubic (BCC) lattice to cartesian cubic (CC) lattice. While we present experimental results for FCC and BCC lattices, since these are commonly used 3D lattices, the design formulations we present are valid for other 3D lattices with 48-hedral symmetry as well. The sampling structure conversion of a signal sampled on FCC (or BCC) lattice to the CC lattice is a 3D interpolation problem, with the upsampling operation defined using the FCC (or BCC) lattice. In the design formulation for 3D eigenfilters, we impose the Mth band constraint, the so-called zero direct component (DC) leakage constraint, and the 48-hedral symmetry of the 3D filter impulse response. The Mth band constraint ensures that the original input samples are preserved at the output and the zero DC leakage results in the suppression of the zero (DC) frequency in the aliases due to the upsampling operation, thus improving the quality of the interpolated output. The symmetry results in the reduction of independent parameters in the filter design.
Additional information
Notes on contributors
Qutubuddin Saifee
Qutubuddin Saifee is currently pursuing his Ph. D at the Department of Electrical Engineering, Indian Institute of Technology, Bombay. His main research interests are in the area of Multi-dimensional signal processing, Video codecs, and Image processing.
E-mail: [email protected]
Pushkar G. Patwardhan
Pushkar G. Patwardhan is currently with Tensilica India as a Senior Technical Lead (DSP), and also with the Department of Electrical Engineering, Indian Institute of Technology, Bombay, as a post-doctoral researcher. His main research interests are in the area of Multi-dimensional Systems and Signal Processing, Filter-banks and Wavelets, and their applications.
E-mail: [email protected]
Aniruddha Adiga
Aniruddha Adiga is currently pursuing his Masters at Department of Electrical Engineering, Indian Institute of Technology Bombay in the area of signal processing under the guidance of Prof. V.M. Gadre.
E-mail: [email protected]
Vikram M. Gadre
Vikram M. Gadre is a Professor in the Department of Electrical Engineering, Indian Institute of Technology, Bombay (IIT, Bombay). He has been on the faculty of IIT, Bombay for over fifteen years to date. His areas of interest in research include communications and signal processing with special emphasis on wavelets and multi-resolution signal processing. Details of his professional qualifications and achievements can be found at the URL: http:// www.ee.iitb.ac.in/wiki/faculty/vmgadre.
E-mail: [email protected]