P. P. Vaidyanathan

Professor of Electrical Engineering

Research Interest

Professor Vaidyanathan and his research group are interested in several aspects of modern digital signal processing. This includes multirate digital signal processing (which has many applications including speech and image compression), fast techniques for adaptive filtering, recursive estimation and extrapolation, signal compression, and robust digital filtering structures.

Multirate signal processing is a technique where the sampling rates at various internal points in the signal processor are kept as small as possible in order to improve computational efficiency. One of the many applications of such a system is in subband coding of speech and image signals. Here, a discrete-time signal x(n) is split into M subband signals xk(n) by use of a bank of filters Hk(z), 0 k M - 1 as shown in the figure. Each of the subband signals is then decimated by the maximum possible ratio M and encoded. During the encoding process, the peculiarities of the subband (such as the statistical average of the energy, the perceptive importance, and so on) are taken into consideration in order to maximize coding efficiency. The encoded signal is typically transmitted or stored as appropriate. In order to reconstruct the original signal or image, the subband signals are interpolated to obtain the original sampling rate and then recombined through the set of synthesis filters Fk(z), 0 k M - 1. The reconstructed signal is usually required to be an acceptable replica of x(n).

In practice the signal suffers from four distortions: aliasing (due to decimation), coding error, and amplitude and phase distortions (due to filtering). A very important problem in this context is to minimize or eliminate all these distortions. Professor Vaidyanathan's group has shown that it is possible to completely eliminate aliasing, and amplitude and phase distortions, at finite cost, by judicious choice of the filters Hk(z) and Fk(z). A number of filter banks of this type of arbitrary M have been designed by the group during the last few years. New theoretical frameworks and lattice structures have been developed for this purpose based on the concept of losslessness in digital systems. The use of multirate processing in the digital audio industry is also being explored here. The ideas have also been extended to the case of linear-phase filters which are ore appropriate in image-coding applications. Many of our results in to the case of two-dimensional signals. The direct application of these will be in image coding and compression.

The concept of paraunitariness (or losslessness) opens up an entirely whole direction in linear algebra, for it is an extension of unitary matrices to the case of matrix functions. A considerable amount of effort has been spent by Professor Vaidyanathan's group in exploring the properties of Paraunitary systems, with signal processing applications include multirate filter bank design, and design of low noise and low sensitivity digital lattice structures which are free from limit-cycle oscillations. Several structures and results have been developed in this group for the design of such numerically robust digital filter structures based on losslessness and passivity. The structures include both FIR and IIR systems; and both single rate and multirate systems.

The group is also interested in the theory and applications of wavelet transforms, and also their relations to filter banks. Wavelet transforms are a new family of transforms that can be applied for the decomposition a signal using an orthonormal or biorthonormal set of basis functions. In some applications these have several advantages over traditional transformation techniques such as the Fourier transform, cosine transform and so forth. It has been shown that wavelet transforms have a direct relationship with filter banks. In fact, paraunitary filter banks, introduced by Prof. Vaidyanathan in 1987 have close connection with orthonormal wavelet transforms and wavelet packets. The fusion of the wavelet community with the filter bank community has opened up several new research avenue, problems, and applications. Prof. Vaidyanathan's group is studying some of these, in order to develop efficient techniques for the design of orthonormal and biorthonormal wavelet basis functions with regularity properties.

Biography

Prof. P. P. Vaidyanathan received the B.Sc. (Hons.) degree in Physics and the B.Tech. and M.Tech. degrees in Radio Physics and Electronics, all from the University of Calcutta, India, in 1974, 1977 and 1979, respectively. He received his PhD degree in Electrical and Computer Engineering from the University of California at Santa Barbara in 1982 and served as a postdoctoral fellow at the University of California, Santa Barbara from September 1982 to March 1983. Dr. Vaidyanathan joined the Electrical Engineering Department at the California Institute of Technology in 1983, and has been a full professor since 1993. Dr. Vaidyanathan has served as Executive Officer for the Electrical Engineering Department at Caltech from 2002-2005. His main research interests are in digital signal processing, multirate systems, signal processing for digital communications, system theory, and genomic signal processing.

Prof. Vaidyanathan served as Vice-Chairman of the Technical Program committee for the 1983 IEEE International Symposium on Circuits and Systems, and as the Technical Program Chairman for the 1992 IEEE International symposium on Circuits and Systems. He was an Associate Editor for the IEEE Transactions on Circuits and Systems for the period 1985-1987, and later as an Associate Editor for the journal IEEE Signal Processing letters, and a consulting editor for the journal Applied and Computational Harmonic Analysis. In 1992, he was a guest editor for special issues of the IEEE Trans. on Signal Processing and the IEEE Trans. on Circuits and Systems II, on the topics of filter banks, wavelets and sub-band coders.

Prof. Vaidyanathan has authored more than 360 papers in journals and conferences, and is the author of the book entitled Multirate Systems and Filter Banks (Englewood Cliffs, NJ: Prentice Hall 1993). He has written several chapters for various signal-processing handbooks. He is a recipient of the Award for Excellence in Teaching at the California Institute of Technology for the years 1983-1984, 1992-93 and 1993-94. In 1986, he received the NSF's Presidential Young Investigator award. In 1989, he received the IEEE ASSP Senior Award for his paper on multirate perfect-reconstruction filter banks. In 1990, he was recipient of the S. K. Mitra Memorial Award from the Institute of Electronics and Telecommunications Engineers, India, for his joint paper in the IETE journal. He was also the co-author of a paper on linear-phase perfect reconstruction filter banks in the IEEE SP Transactions, for which the first author (Truong Nguyen) received the Young outstanding author award in 1993. Dr. Vaidyanathan was elected IEEE Fellow in 1991.

Publications

• Journal Articles


~1985 | 1986 | 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008

• Conference Publications


~1985 | 1986 | 1987 | 1988 | 1989 | 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008

• Text Books



• P. P. Vaidyanathan, Multirate systems and filter banks, Prentice Hall, Englewood Cliffs, 1993.

• P. P. Vaidyanathan, Quantization and robustness in digital signal processors, this will be completed in a year.

• Theses


• P. P. Vaidyanathan, ``Some algorithms for digital signal processing,'' Masters' dissertation, Institute of Radiophysics and Electronics, University of Calcutta, India, 1979.

• P. P. Vaidyanathan, ``A general theory and synthesis procedure for low sensitivity digital filter structures,'' Ph. D. dissertation, Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA, September 1982.

• Caltech Reports


• P. P. Vaidyanathan and K. Swaminathan, ``Uniform DSB QMF banks that are entirely free from aliasing,'' Technical report, California Institute of Technology, Pasadena, CA, May 1986.

• P. P. Vaidyanathan, ``Quantization effects in multirate filter banks,'' Tech. Report. California Institute of Technology, Pasadena, CA, July 1987.

• T. Q. Nguyen and P. P. Vaidyanathan, ``Two-channel PR FIR QMF bank design package,'' Tech. Report. California Institute of Technology, Pasadena, CA, April 1989.

• P. P. Vaidyanathan and V. P. Sathe, ``Fast techniques for bandlimited extrapolation of finite-length sequences,'' Tech. Report. California Institute of Technology, Pasadena, CA, June 1989.

• R. D. Koilpillai, T. Q. Nguyen and P. P. Vaidyanathan, ``New results in the theory of crosstalk-free transmultiplexers,'' Tech. Report. California Institute of Technology, Pasadena, CA, Sept. 1989.

• A. K. Soman and P. P. Vaidyanathan, ``Linear phase paraunitary filter banks: theory, factorizations, and applications,'' Tech. Report. California Institute of Technology, Pasadena, CA, May 1992.

• Book Chapters



• P. P. Vaidyanathan, ``Design and implementation of digital FIR filters,'' in Handbook on Digital Signal Processing, edited by D. F. Elliott, Academic Press Inc., pp. 55-172, 1987.

• P. P. Vaidyanathan, ``Low noise and low sensitivity digital filters,'' in Handbook on Digital Signal Processing, edited by D. F. Elliott, Academic Press Inc., pp. 359-479, 1987.

• P. P. Vaidyanathan, ``Robust digital filter structures,'' in Handbook for digital signal processing, edited by S. K. Mitra and J. F. Kaiser, pp. 419--490, John Wiley, 1993.

• P. P. Vaidyanathan and Igor Djokovic, ``Wavelet transforms,'' in The Circuits and Filters Handbook edited by W. K. Chen, CRC Press, Inc., 1995.

• P. P. Vaidyanathan, ``Sampling theorems from wavelet and filter bank theory'', in Microsystems technology for multimedia applications, ed., B. Sheu, M. Ismail, E. Sanchez-Sinencio, and T. H. Wu, IEEE Press, pp. 179--189, April-May 1995 ( invited chapter).