On typical echo paths, the proportionate normalized least-mean-squares (PNLMS) adaptation algorithm converges significantly faster than the normalized least-mean-squares (NLMS) algorithm generally used in echo cancelers to date. In PNLMS adaptation, the adaptation gain at each tap position varies from position to position and is roughly proportional at each tap position to the absolute value of the current tap weight estimate. The total adaptation gain being distributed over the taps is carefully monitored and controlled so as to hold the adaptation quality (misadjustment noise) constant. PNLMS adaptation only entails a modest increase in computational complexity.

Entropy coders, such as Huffman and arithmetic coders, achieve compression by exploiting nonuniformity in the probabilities under which a random variable to be coded takes on its possible values. Practical realizations generally require running adaptive estimates of these probabilities. An analysis of the relationship between estimation quality and the resulting coding efficiency suggests a particular scheme, dubbed scaled-count, for obtaining such estimates. It can optimally balance estimation accuracy against a need for rapid response to changing underlying statistics. When the symbols being coded are from a binary alphabet, simple hardware and software implementations requiring almost no computation are possible. A scaled-count adaptive probability estimator of the type described in this paper is used in the arithmetic coder of the JBIG and JPEG image coding standards.

An image compression algorithm is presented that is suitable for transmitting a high-resolution (400 dot/in) black-and-white (two-tone) facsimile image over a packet network. The algorithm decomposes the image into nondroppable (essential) and droppable (supplementary) bits. The nondroppable bits describe the image at low resolution (200 dot/in) and can be coded with any of the standard CCITT Group 3 or Group 4 techniques. Thus, the algorithm is compatible with the large installed base of Group 3 facsimile machines. The droppable (supplementary) bits are approximately 45% of the total number of bits and can be dropped by the network to relieve congestion. The supplementary bits are encoded with a predictive Huffman method. Resynchronization after missing some of the supplementary information presents no serious difficulties. The algorithm is information preserving, assuming that all droppable bits are available, and its compression efficiency is equal to or better than that of direct two-dimensional Group 3 or 4 CCITT encoding of the high-resolution (400 dot/in) image. Frame memory is not needed.>

A new single-chip echo canceller has been developed. In addition to offering improved performance over an earlier single-chip echo canceller [14], the new canceller has many desirable features not available before. The most important of these features is that multiples of the chip can be connected in cascade to synthesize very long impulse responses. This paper describes the new features implemented on the chip and characterizes its performance.

We describe a recently constructed 12-channel digital echo canceler that interfaces directly with the 8-bit μ255 PCM now standard for digital transmission in the telephone plant. The four most interesting features of the canceler are time sharing of circuitry to reduce per channel costs, floating-point multiplication, loop-gain normalization, and the use of a test channel for fault detection. Extensive laboratory and field testing has shown the canceler to be working well.

Several aspects of the design of digital frequency synthesizers are considered, and a detailed analysis of the spectral purity of digitally synthesized frequencies is given. These results are then applied to a specific application: the testing of A/D and D/A converters.

A new structure for an analog-to-digital converter encoding to the μ-law companding characteristic is described. Timing accuracy substitutes for component accuracy so that no precision components are required and integration is made easier. Numerous models have been constructed and found to work exceptionally well.

The technique of nearly instantaneous companding (NIC) that we describe processesn-bit μ-law or A-law encoded pulse-code modulation (PCM) to a reduced bit rate. A block ofNsamples (typicallyN \cong 10) is searched for the sample having the largest magnitude, and each sample in the block is then reencoded to a nearly uniform quantization having (n - 2) bits and an overload point at the top of the chord of the maximum sample. Since an encoding of this chord must be sent to the receiver along with the uniform reencoding, the resulting bit rate isf_{s}(n -2 + 3/N)bits/s where fsis the sampling rate. The algorithm can be viewed as an adaptive PCM algorithm that is compatible with the widely used μ-law andA-law companded PCM. Theoretical and empirical evidence is presented which indicates a performance slightly better than (n - 1) bit companded PCM (the bit rate is close to that of (n - 2) bit PCM). A feature which distinguishes NIC from most other bit-rate reduction techniques is a performance that is largely insensitive to the statistics of the input signal.

An upper bound on the error probability of a decision-feedback equalizer which takes into account the effect of error propagation is derived. The bound, which assumes independent data symbols and noise samples, is readily evaluated numerically for arbitrary tap gains and is valid for multilevel and nonequally likely data. One specific result for equally likely binary symbols is that if the worst case intersymbol interference when the firstJfeedback taps are Set to zero is less than the original signal voltage, then the error probability is multiplied by at most a factor of2^Jrelative to the error probability in the absence of decision errors at highS/Nratios. Numerical results are given for the special case of exponentially decreasing tap gains. These results demonstrate that the decision-feedback equalizer has a lower error probability than the linear zero-forcing equalizer when there is both a highS/Nratio and a fast roll-off of the feedback tap gains.

We introduce the reproducing-kernel Hilbert space (RKHS) associated with the characteristic functional of a random process and use it to develop a general RKHS theory for non-Gaussian detection. Previously known results for choosing between processes with Gaussian and Poisson statistics are obtained as specializations of this theory.

Using reproducing-kernel Hilbert space (RKHS) techniques, we obtain new results for three different parameter estimation problems. The new results are 1) an explicit formula for the minimum-variance unbiased estimate of the arrival time of a step function in white Gaussian noise, 2) a new interpretation of the Bhattacharyya bounds on the variance of an unbiased estimate of a function of regression coefficients, and 3) a concise formula for the Cramér-Rao bound on the variance of an unbiased estimate of a parameter determining the covariance of a zero-mean Gaussian process.

The concept of a white Gaussian noise (WGN) innovations process has been used in a number of detection and estimation problems. However, there is fundamentally no special reason why WGN should be preferred over any other process, say, for example, an nth-order stationary autoregressive process. In this paper, we show that by working with the proper metric, any Gaussian process can be used as the innovations process. The proper metric is that of the associated reproducing kernel Hilbert space. This is not unexpected, but what is unexpected is that in this metric some basic concepts, like that of a causal operator and the distinction between a causal and a Volterra operator, have to be carefully reexamined and defined more precisely and more generally. It is shown that if the problem of deciding between two Gaussian processes is nonsingular, then there exists a causal (properly defined) and causally invertible transformation between them. Thus either process can be regarded as a generalized innovations process. As an application, it is shown that the likelihood ratio (LR) for two arbitrary Gaussian processes can, when it exists, be written in the same form as the LR for a known signal in colored Gaussian noise. This generalizes a similar result obtained earlier for white noise. The methods of Gohberg and Krein, as specialized to reproducing kernel spaces, are heavily used.