B. Gopinath

Bio: B. Gopinath is an academic researcher from Bell Labs. The author has contributed to research in topics: Filter (signal processing) & Stopband. The author has an hindex of 3, co-authored 5 publications receiving 93 citations.

Charge-routing networks

Abstract: The fundamental techniques for charge manipulation achievable with MOS charge-coupling technology include storage, transfer, splitting, combining, insertion, and extraction. We idealize and generalize these operations to define a general class of networks for discrete-time linear filtering. A p-phase charge-routing network (CRN) consists of a collection of storage cells divided into p subgroups and a routing procedure controlled by a p-phase clock. During a particular clock phase, charge is routed from a particular subgroup of storage cells into another subgroup. In this manner charge is routed successively through each subgroup of cells and a periodically time-varying linear discrete-time network is defined by specifying matrices of weight values associated with the routing procedure. Analysis of a p -phase CRN yields a reduced system of linear time-invariant dynamic state equations convenient for signal-processing studies. Necessary and sufficient conditions on such a system of state equations are given for realizability as a p -phase CRN. The varied structures attainable with CRN's can realize infinite inpulse-response filter transfer functions. However, certain fundamental restrictions exist on the class of transfer functions realizable with CRN's. In particular, we show the existence of forbidden zones within the unit circle in the z-plane, where poles (or natural modes) of a CRN cannot occur. A parallel can be drawn between classical RC networks and charge-routing networks. Both types of networks have substantial restrictions on the class of filters they can by themselves realize. For RC networks, we know the limitations can be overcome by the addition of another component (inductance or operational amplifier). A similar potential may exist for CRN's. This paper provides a foundation for a general theory that could offer realizability conditions and sythesis procedures for discrete-time filtering via charge routing networks.

Coefficient inaccuracy in transversal filtering

Abstract: Coefficient inaccuracy in transversal filters is known to degrade the frequency response, particularly in stopband regions. The magnitude of the stopband degradation increases with the number of stages n, the length of the impulse response. A widely used formula for the error in frequency response is proportional to √n. By extending recent results on random trigonometric polynomials, we show that for random additive coefficient errors with variance σ2, the error ΔH(ω) in frequency response for targe n is such that where log denotes the natural logarithm This result leads to an absolute bound on attainable stopband rejection for any band-select transversal filter with given coefficient inaccuracy. In particular, the result places a definite limitation on the quality of band-select filtering that can be achieved using a ccd split-electrode filter. It also implies bounds for the peak sidelobes of random radar arrays.

Multiplexed filtering with charge transfer devices

Abstract: A multiplexed filter structure using a single charge-transfer device (CTD) with 2N stages of delay, switched weight values, and two adders can be used to implement a bank of N second-order recursive filters. Structures of this type can be combined to implement a bank of higher order recursive filters, offering a potentially economical realization for multichannel filtering applications. An important limitation of the CTD delay line is due to the effect of charge transfer inefficiency (CTI), which introduces dispersion to the frequency response of the delay stages. By viewing the multiplexed structure as a multichannel filter with N inputs and N outputs, general expressions for the N2transfer functions can be derived which exhibit the dependence on the coefficient e of CTI. For small e, the asymptotic deviation of the transfer functions and the poles of the transfer functions from their desired behaviors (when e = 0) is examined. In particular, for the case where the N desired second-order filters have distinct poles, e.g., filters tuned to different resonant frequencies, it is shown that the pole positions are perturbed by a term of the order of eN, indicating that the effect of CTI is negligibly small. Included in the paper are results on the asymptotic dependence on e of the interchannel crosstalk due to CTI.

Coefficient inaccuracy in FIR filters

Abstract: Coefficient inaccuracy in FIR filters is known to degrade the frequency response particularly in stopband regions The magnitude of the stopband degradation increases with the number of stages N, the length of the impulse response A widely used formula for the error in frequency response is proportional to \sqrt{N} Recently, we have found that for random additive coefficient errors with variance σ2, the maximum error in frequency response for large N is given by \sigma\sqrt{N\logN} This result is applied to an empirical formula relating the minimum number of stages, N, to specified lowpass filter performance parameters The results lead to absolute bounds on attainable stopband rejection for band-select FIR filters The realization of transversal filters with charge-coupled devices (CCD's) is particularly relevant to this study

Multiplexed filtering with charge-transfer devices

Abstract: A multiplexed filter structure using a single charge-transfer device (CTD) with 2N stages of delay, switched weight values, and two adders can be used to implement a bank of N second-order recursive filters. Structures of this type can be combined to implement a bank of higher order recursive filters, offering a potentially economical realization for multichannel filtering applications.

A tutorial on the positive realization problem

Abstract: This paper is a tutorial on the positive realization problem, that is the problem of finding a positive state-space representation of a given transfer function and characterizing existence and minimality of such representation. This problem goes back to the 1950s and was first related to the identifiability problem for hidden Markov models, then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory. Within this framework, developing some ideas sprang in the 1960s, during the 1980s, the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem. In this paper, the reader is carried through the key ideas which have proved to be useful in order to tackle this problem. In order to illustrate the main results, contributions and open problems, several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided.

Multitone signals with low crest factor

Abstract: Using some results from the recent mathematics literature, we show how to generate signals with perfect low-pass or bandpass spectra which have very low crest factors (under 6 dB). An application to multitone frequency response testing is given.

On the existence and construction of good codes with low peak-to-average power ratios

Abstract: The first lower bound on the peak-to-average power ratio (PAPR) of a constant energy code of a given length n, minimum Euclidean distance and rate is established. Conversely, using a nonconstructive Varshamov-Gilbert style argument yields a lower bound on the achievable rate of a code of a given length, minimum Euclidean distance and maximum PAPR. The derivation of these bounds relies on a geometrical analysis of the PAPR of such a code. Further analysis shows that there exist asymptotically good codes whose PAPR is at most 8 log n. These bounds motivate the explicit construction of error-correcting codes with low PAPR. Bounds for exponential sums over Galois fields and rings are applied to obtain an upper bound of order (log n)/sup 2/ on the PAPRs of a constructive class of codes, the trace codes. This class includes the binary simplex code, duals of binary, primitive Bose-Chaudhuri-Hocquenghem (BCH) codes and a variety of their nonbinary analogs. Some open problems are identified.

Nonnegative realization of a linear system with nonnegative impulse response

Abstract: Let H(z) be a rational transfer function, with associated nonnegative impulse response sequence. The paper considers the question: When does there exist a triple A/spl isin/R/sup N/spl times/N/, b/spl isin/R/sup N/, c/spl isin/R/sup N/ with all nonnegative entries H(z)=c'(zI-A)/sup -1/b? An essentially complete characterization is given of the H(z) allowing such a realization, in terms of the location of the pole or poles of H(z) with maximum modulus.

Peak-to-average power ratio in high-order OFDM

Abstract: The problem of peak-to-average power ratio (PAPR) of high-order orthogonal frequency-division modulation (OFDM) is considered. Using results on level crossing of random processes, an upper bound on the probability that the PAPR of an OFDM signal will exceed a given value is derived. Numerical computations are used to show that this bound is tight for low-pass OFDM systems. The central limit theorem is used to find an asymptotic expression for the bound when the number of carriers N grows to infinity. The central limit theorem is also used to find an asymptotic expression for another bound that is based on the envelope of the OFDM signal, and is tighter for bandpass systems. It is shown that, effectively, the PAPR grows as 2lnN and not linearly with N, and by developing a lower bound on the probability that the PAPR of an OFDM signal will exceed a given value, it is shown that asymptotically most OFDM symbols have a PAPR close to 2lnN. Some approaches to coping with the PAPR problem are discussed in light of the obtained results.