In this paper, we present a multiple stage vector quantization technique which allows easy expansion of the original vector quantizer design to operate at higher bit rates for lower distortion. The computation and storage reduction is achieved by the fact that the overall requirements are the sum of the requirements of each stage instead of an exponentially increasing function of the bit rate as in the original one stage design. In the case of Euclidean distance measures such as the log area ratio measure, experimental results show that the quantizer performance is very close to a theoretically predicted asymptotically optimal rate distortion relationship.

In most applications of adaptive filtering algorithms to the telephone echo cancellation problem, a linear model is assumed for the hybrid. In this paper, a nonlinear model based on a Volterra series representation is adopted. By using a new and efficient nonlinear frequency domain adaptive algorithm, a nonlinear model for a hybrid in an actual connection has been identified. The nonlinear model is found to be 8 db more accurate than the linear model. The problem of automatic gain control in the design of a full-duplex telephone network with LPC vocoder in the loop, and its interaction with the echo canceller and the hybrid nonlinearity is also discussed.

A new non-linear adaptive filter is presented. The algorithm is based on the Volterra series implemented in the frequency domain. For a finite memory of length N, the algorithm converges to the equivalent time domain non-linear adaptive filter as proposed by Roy and Sherman [1]. The frequency domain implementation offers a significant reduction in computation. For the second order Volterra series, the proposed algorithm requires O(N2) multiply-adds for N output points as opposed to an O(N3) for the time domain algorithm. For a large number of taps (≥ 32), the linear version of the proposed algorithm also offers a significant reduction in computation. Another advantage is its fast convergence to the Wiener solution due to the "pseudo-orthogonality" obtained by adapting in the frequency domain.

Vector Quantization is applied to modify a 2400 bps LPC vocoder to operate at 800 bps, while retaining acceptable intelligibility and naturalness of quality. The design of this speech compression system is discussed and compared to other very low bit rate vocoders. Advantages of vector quantization over a scalar technique are examined in detail, and several new properties are presented.

An information theory approach to the theory and practice of linear predictive coded (LPC) speech compression systems is developed. It is shown that a traditional LPC system can be viewed as a minimum distortion or nearest-neighbor system where the distortion measure is a minimum discrimination information between a speech process model and an observed frame of actual speech. This distortion measure is used in an algorithm for computer-aided design of block source codes subject to a fidelity criterion to obtain a 750-bits/s speech compression system that resembles an LPC system but has a much lower rate, a larger memory requirement, and requires no on-line LPC analysis. Quantitative and informal subjective comparisons are made among our system and LPC systems.

With rare exception, all presently available narrowband speech coding systems implement scalar quantization (independent quantization) of the transmission parameters (such as reflection coefficients or transformed reflection coefficients in LPC systems). In this paper a new approach called Vector Quantizatlon is presented. For very low data rates, realistic experiments have shown that vector quantization can achieve a given level of average distortion with fifteen to twenty fewer bits per frame than that required for optimized scalar quantizing approachs presently in use.

Based upon the theoretical development of a recent paper on scalar parameter quantization of speech reflection coefficients, an experimental comparison study of two quantization methods was undertaken. Quantitative results and subjective evaluation by an experienced listener indicated that as much as 8-10 bits/frame could be eliminated for the same degree of distortion by using the minimum deviation method which embeds parameter probability density information into the quantization process.

A training sequence of speech data is used to design a two-step speech compression system, based upon either single speakers or multiple speakers. The system is designed to minimize an average spectral distortion over the training sequence, leading to an identification step using linear prediction techniques followed by a vector quantizer. The system is then used to compress test sequences of speech data, leading to much lower bit rates than obtained using scalar quantization for equivalent distortions. For the same numerical distortion, 20-bits/frame were required using optimal scalar bit allocation and quantization, whereas 8-bits/frame were required using vector quantization. Results are presented in the form of numerical distortion measures and analog tapes of synthesized speech.

Energy and power analogies are used for the analysis of cascaded (possibly time varying) lattice digital filters. This approach leads to the requirements for passivity of the sections, and a procedure for the removal of zero-input parasitic oscillations, and a few miscellaneous results.

Asymptotically accurate approximations for quantizer performance were developed by Gish and Pierce. Variational techniques were used to obtain asymptotically optimal performance. In this correspondence, optimal performance is demonstrated simply without variational techniques using Holder's and Jensen's inequalities.

A comparison of reflection coefficient, log area and inverse sine quantization is presented. The approach makes use of analytically tractable results without numerical approximations or direct frequency domain calculation. By using parameters obtained from a speech data base, specific bit allocations are obtained which insure that a prescribed maximum spectral deviation is not exceeded for each analysis frame. It is shown that overall, inverse sine quantization requires the minimum number of coding levels followed by log area quantization and then reflection coefficients. With the exception of the first two coefficients, however, the differences among the methods are shown to be rather minimal.

The first-passage time problem for a continuous one-dimensional Markov process is reviewed, and upper bounds are obtained for both the probability of failure (or passage and the moments of the time to failure, in terms of the mean time to failure. In addition, stationary Gaussian variables arising from systems withNdegrees of freedom that have autocorrelation functions of the form \begin{equation} R(r) = e^{-b \mid \tau \mid} \sum_{k=1}^{N} d_k^2 \cos \omega_k \tau \end{equation} are shown to be derivable from a2N-dimensional (or2N- 1, if one of the\omega_kis zero) Markov process that possesses a "pseudoenvelope," which is itself the result of a one-dimensional Markov process. This pseudo-envelope can be used as a bound on the magnitude of the Gaussian variable, and its first-passage time problem can be solved explicitly or utilized to obtain convenient bounds for the probability of failure of the Gaussian process.