P. P. Vaidyanathan

Professor of Electrical Engineering

Email contact: ppvnath@systems.caltech.edu

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.

Another area of interest here is in extending the above concepts and results for the case of multidimensional (MD) signals. A two dimensional (2D) signal x(n0,n1) is a function of two variables n0, n1 such as the horizontal and vertical directions of an image. In a similar way one defines three and higher dimensional signals (e.g., video). In applications such as image and video compression and coding, it is of interest to extend the concepts of multirate systems and filter banks to the case of MD signals. The group has made contributions in this direction, particularly in the areas of MD sampling rate alterations, and filter bank design.


P. P. Vaidyanathan (S'80--M'83--SM'88--F'91) was born in Calcutta, India on Oct. 16, 1954. He received the B.Sc. (Hons.) degree in physics and the B.Tech. and M.Tech. degrees in radiophysics and electronics, all from the University of Calcutta, India, in 1974, 1977 and 1979, respectively, and the Ph.D degree in electrical and computer engineering from the University of California at Santa Barbara in 1982. He was a post doctoral fellow at the University of California, Santa Barbara from Sept. 1982 to March 1983. In March 1983 he joined the electrical engineering department of the Calfornia Institute of Technology as an Assistant Professor, and since 1993 has been Professor of electrical engineering there. His main research interests are in digital signal processing, multirate systems, wavelet transforms and adaptive filtering.

Dr. 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 is currently an associate editor for the journal IEEE Signal Processing letters, and a consulting editor for the journal Applied and computational harmonic analysis. Dr. Vaidyanathan has authored about 200 papers in IEEE journals and conferences, and is the author of the book Multirate systems and filter banks. He has written several chapters for various signal processing handbooks. He was a recepient of the Award for excellence in teaching at the California Institute of Technology for the years 1983-1984, 1992-93 and 1993-94. He also received the NSF's Presidential Young Investigator award in 1986. In 1989 he received the IEEE ASSP Senior Award for his paper on multirate perfect-reconstruction filter banks. In 1990 he was recepient of the S. K. Mitra Memorial Award from the Institute of Electronics and Telecommuncations Engineers, India, for his joint paper in the IETE journal. He was also the coauthor 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 Fellow of the IEEE in 1991. He received the 1995 F. E. Terman Award of the American Society for Engineering Education, sponsored by Hewlett Packard Co. He has been chosen a distinguished lecturer for the IEEE Signal Processing Society for the year 1996-97.


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Last updated March 1998.