Peter Kabal

Partial-Response Signaling

This paper presents a unified study of partial-response signaling (PRS) systems and extends previous work on the comparison of PRS schemes. A PRS system model is introduced which enables the investigation of PRS schemes from the viewpoint of spectral properties such as bandwidth, nulls, and continuity of derivatives. Several desirable properties of PRS systems and their relation to system functions are indicated and a number of useful schemes, some of them not previously analyzed, are presented. These systems are then compared using as figures of merit speed tolerance, minimum eye width, and signal-to-noise ratio (SNR) degradation over ideal binary transmission. A new definition of speed tolerance, which takes into account multilevel outputs and the effect of sampling time, is introduced and used in the calculation of speedtolerance figures. It is shown that eye width, a performance measure that has not been used previously in comparing PRS systems, can be calculated analytically in many cases. Exact values as well as bounds on the SNR degradation for the systems under consideration are presented. The effect of precoding on system performance is also analyzed.

Parametric localization of distributed sources

Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method. >

The computation of line spectral frequencies using Chebyshev polynomials

Line spectral frequencies provide an alternate parameterization of the analysis and synthesis filters used in linear predictive coding (LPC) of speech. In this paper, a new method of converting between the direct form predictor coefficients and line spectral frequencies is presented. The system polynomial for the analysis filter is converted to two even-order symmetric polynomial with interlacing roots on the unit circle. The line spectral frequencies are given by the positions of the roots of these two auxiliary polynomials. The response of each of these polynomials on the unit circle is expressed as a series expansion in Chebyshev polynomials. The line spectral frequencies are found using an iterative root finding algorithm which searches for real roots of a real function. The algorithm developed is simple in structure and is designed to constrain the maximum number of evaluations of the series expansions. The method is highly accurate and can be used in a form that avoids the storage of trigonometric tables or the computation of trigonometric functions. The reconversion of line spectral frequencies to predictor coefficients uses an efficient algorithm derived by expressing the root factors as an expansion in Chebyshev polynomials.

Speech/music discrimination for multimedia applications

Automatic discrimination of speech and music is an important tool in many multimedia applications. Previous work has focused on using long-term features such as differential parameters, variances and time-averages of spectral parameters. These classifiers use features estimated over windows of 0.5-5 seconds, and are relatively complex. We present our results of combining the line spectral frequencies (LSFs) and zero crossing-based features for frame-level narrowband speech/music discrimination. Our classification results for different types of music and speech show the good discriminating power of these features. Our classification algorithms operate using only a frame delay of 20 ms, making them suitable for real-time multimedia applications.

Wideband array processing using a two-sided correlation transformation

A new method for broadband array processing is proposed. The method is based on unitary transformation of the signal subspaces. We apply a two-sided transformation on the correlation matrices of the array. It is shown that the two-sided correlation transformation (TCT) has a smaller subspace fitting error than the coherent signal-subspace method (CSM). It is also shown that unlike CSM, the TCT algorithm can generate unbiased estimates of the directions-of-arrival, regardless of the bandwidth of the signals. The capability of the TCT and CSM methods for resolving two closely spaced sources is compared. The resolution threshold for the new technique is much smaller than that for CSM. >

Pitch prediction filters in speech coding

Prediction error filters which combine short-time prediction (formant prediction) with long-time prediction (pitch prediction) in a cascade connection are examined. A number of different solution methods (autocorrelation, covariance, Burg) and implementations (transversal and lattice) are considered. It is found that the F-P cascade (formant filter before the pitch filter) outperforms the P-F cascade for the both transversal- and lattice-structured predictors. The performances of the transversal and lattice forms are similar. The solution method that yields a transversal structure requires a stability test and, if necessary, a consequent stabilization. The two cascade forms are implemented as part of an APC coder to evaluate their relative subjective performance. >

Bit loading with BER-constraint for multicarrier systems

We present discrete adaptive bit loading algorithms for multicarrier systems with uniform (nonadaptive) power allocation operating in a frequency selective fading environment. The algorithms try to maximize the overall throughput of the system while guaranteeing that the mean bit error rate (BER) remains below a prescribed threshold. We also study the impact of imperfect subcarrier signal-to-noise ratio information on throughput performance. Results show that the proposed algorithms have approximately the same throughput and mean BER as the optimal allocation while having a significantly lower computational complexity relative to other algorithms with near-optimal allocations. Moreover, when compared with algorithms that employ approximations to water filling, the computational complexity is comparable while the overall throughput is closer to the optimum.

An information theoretic approach to source enumeration in array signal processing

In this paper, a new information theoretic algorithm is proposed for signal enumeration in array processing. The approach is based on predictive description length (PDL) that is defined as the length of a predictive code for the set of observations. We assume that several models, with each model representing a certain number of sources, will compete. The PDL criterion is computed for the candidate models and is minimized over all models to select the best model and to determine the number of signals. In the proposed method, the correlation matrix is decomposed into two orthogonal components in the signal and noise subspaces. The maximum likelihood (ML) estimates of the angles-of-arrival are used to find the projection of the sample correlation matrix onto the signal and noise subspaces. The summation of the ML estimates of these matrices is the ML estimate of the correlation matrix. This method can detect both coherent and noncoherent signals. The proposed method can be used online and can be applied to time-varying systems and target tracking.

Shaping multidimensional signal spaces. I. Optimum shaping, shell mapping

The structure of the regions which provide the optimum tradeoff between gamma /sub s/ (shaping gain) and CER (constellation-expansion ratio) and between gamma /sub s/ and PAR (peak to average power ratio) in a finite dimensional space is introduced. Analytical expressions are derived for the corresponding tradeoff curves. In general, the initial parts of the curves have a steep slope. This means that an appreciable portion of the maximum shaping gain, corresponding to a spherical region, can be achieved with a small value of CER/sub s/, PAR. The technique of shell mapping is introduced. This is a change of variable which maps the optimum shaping region to a hypercube truncated within a simplex. This mapping is a useful tool in computing the performance, and also in facilitating the addressing of the optimum shaping region. Using the shell mapping, a practical addressing scheme is presented that achieves a point on the optimum tradeoff curves. For dimensionalities around 12, the point achieved is located near the knee of the corresponding tradeoff curve. For larger dimensionalities, a general shaping region with two degrees of freedom is used. This region provides more flexibility in selecting the tradeoff point. >

Stability and performance analysis of pitch filters in speech coders

This paper analyzes the stability and performance of pitch filters in speech coding when pitch prediction is combined with formant prediction. A computationally simple stability test based on a sufficient condition is formulated for pitch synthesis filters. For typical orders of pitch filters, this sufficient test is very tight. Based on the test, a simple stabilization technique that minimizes the loss in prediction gain of the pitch predictor is employed to generate stable synthesis filters. Finally, it is observed that the quality of decoded speech improves significantly when stable synthesis filters are employed.