José Antonio Apolinário

Convergence analysis of the binormalized data-reusing LMS algorithm

Normalized least mean squares algorithms for FIR adaptive filtering with or without the reuse of past information are known to converge often faster than the conventional least mean squares (LMS) algorithm. This correspondence analyzes an LMS-like algorithm: the binormalized data-reusing least mean squares (BNDR-LMS) algorithm. This algorithm, which corresponds to the affine projection algorithm for the case of two projections, compares favorably with other normalized LMS-like algorithms when the input signal is correlated. Convergence analyses in the mean and in the mean-squared are presented, and a closed-form formula for the mean squared error is provided for white input signals as well as its extension to the case of a colored input signal. A simple model for the input-signal vector that imparts simplicity and tractability to the analysis of second-order statistics is fully described. The methodology is readily applicable to other adaptation algorithms of difficult analysis. Simulation results validate the analysis and ensuing assumptions.

Constrained adaptation algorithms employing Householder transformation

This paper presents a tutorial-like detailed explanation of linearly constrained minimum-variance filtering in order to introduce an efficient implementation that utilizes Householder transformation (HT). Through a graphical description of the algorithms, further insight on linearly constrained adaptive filters was made possible, and the main differences among several algorithms were highlighted. The method proposed herein, based on the HT, allows direct application of any unconstrained adaptation algorithm as in a generalized sidelobe canceller (GSC), but unlike the GSC, the HT-based approach always renders efficient implementations. A complete and detailed comparison with the GSC model and a thorough discussion of the advantages of the HT-based approach are also given. Simulations were run in a beamforming application where a linear array of 12 sensors was used. It was verified that not only the HT approach yields efficient implementation of constrained adaptive filters, but in addition, the beampatterns achieved with this method were much closer to the optimal solution than the beampatterns obtained with GSC models with similar computational complexity.

Set-Membership Proportionate Affine Projection Algorithms

Proportionate adaptive filters can improve the convergence speed for the identification of sparse systems as compared to their conventional counterparts. In this paper, the idea of proportionate adaptation is combined with the framework of set-membership filtering (SMF) in an attempt to derive novel computationally efficient algorithms. The resulting algorithms attain an attractive faster converge for both situations of sparse and dispersive channels while decreasing the average computational complexity due to the data discerning feature of the SMF approach. In addition, we propose a rule that allows us to automatically adjust the number of past data pairs employed in the update. This leads to a set-membership proportionate affine projection algorithm (SM-PAPA) having a variable data-reuse factor allowing a significant reduction in the overall complexity when compared with a fixed data-reuse factor. Reduced-complexity implementations of the proposed algorithms are also considered that reduce the dimensions of the matrix inversions involved in the update. Simulations show good results in terms of reduced number of updates, speed of convergence, and final mean-squared error.

Low-complexity constrained affine-projection algorithms

This paper proposes low-complexity constrained affine-projection (CAP) algorithms. The algorithms are suitable for linearly constrained filtering problems often encountered in communications systems. The CAP algorithms derived in this paper trade convergence speed and computational complexity in the same way as the conventional affine-projection (AP) algorithm. In addition, data-selective versions of the CAP algorithm are derived based on the concept of set-membership filtering. The set-membership constrained affine-projection (SM-CAP) algorithms include several constraint sets in order to construct a space of feasible solutions for the coefficient updates. The SM-CAP algorithms include a data-dependent step size that provides fast convergence and low mean-squared error. The paper also discusses important aspects of convergence and stability of constrained normalized adaptation algorithms and shows that normalization may introduce bias in the final solution.

Evaluating digital audio authenticity with spectral distances and ENF phase change

This paper discusses the use of spectral distances obtained from adaptive filters employed as linear predictors and phase change of the electric network frequency to evaluate digital audio authenticity. An authenticity evaluation may be of paramount importance for audio forensics and may help a criminalistic laboratory when dealing with audio evidence in a court of law. We present in this paper a theoretical background of the proposed scheme and show results with digitally edited speech.

The constrained conjugate gradient algorithm

Based on the condition for equivalence between linearly constrained minimum-variance (LCMV) filters and their generalized sidelobe canceler (GSC) implementations, we derive the new constrained conjugate gradient (CCG) algorithm. We discuss the use of orthogonal and nonorthogonal blocking matrices for the GSC structure and how the choice of this matrix may affect the relationship with the LCMV counterpart. The newly derived algorithm was tested in a computer experiment for adaptive multiuser detection and showed excellent results.

On the equivalence of RLS implementations of LCMV and GSC processors

This letter compares the transients of the constrained recursive least squares (CRLS) algorithm with the generalized sidelobe canceler (GSC) employing the recursive least squares (RLS) algorithm. We prove that the two adaptive implementations are equivalent everywhere regardless of the blocking matrix chosen. This guarantees that algorithm tuning is not affected by the blocking matrix. This result differs from the more restrictive case for transient equivalence of the constrained least mean-square (CLMS) algorithm and the GSC employing the least mean square (LMS) algorithm, for in this case the blocking matrix needs to be unitary.

Speech privacy for modern mobile communication systems

Speech privacy techniques are used to scramble clear speech into an unintelligible signal in order to avoid eavesdropping. Some analog speech-privacy equipments (scramblers) have been replaced by digital encryption devices (comsec), which have higher degree of security but require complex implementations and large bandwidth for transmission. However, if speech privacy is wanted in a mobile phone using a modern commercial codec, such as the AMR (adaptive multirate) codec, digital encryption may not be an option due to the fact that it requires internal hardware and software modifications. If encryption is applied before the codec, poor voice quality may result, for the vocoder would handle digitally encrypted signal resembling noise. On the other hand, analog scramblers may be placed before the voice encoder without causing much penalty to its performance. Analog scramblers are intended in applications where the degree of security is not too critical and hardware modifications are prohibitive due to its high cost. In this article we investigate the use of different techniques of voice scramblers applied to mobile communications vocoders. We present our results in terms of LPC and cepstral distances, and PESQ values.

A new fast QR algorithm based on a priori errors

This letter presents a new fast QR algorithm based on Givens rotations using a priori errors. The principles behind the triangularization of the weighted input data matrix via QR decomposition and the type of errors used in the updating process are exploited in order to investigate the relationships among different fast algorithms of the QR family. These algorithms are classified according to a general framework and a detailed description of the new algorithm is presented.

Edit Detection in Speech Recordings via Instantaneous Electric Network Frequency Variations

In this paper, an edit detection method for forensic audio analysis is proposed. It develops and improves a previous method through changes in the signal processing chain and a novel detection criterion. As with the original method, electrical network frequency (ENF) analysis is central to the novel edit detector, for it allows monitoring anomalous variations of the ENF related to audio edit events. Working in unsupervised manner, the edit detector compares the extent of ENF variations, centered at its nominal frequency, with a variable threshold that defines the upper limit for normal variations observed in unedited signals. The ENF variations caused by edits in the signal are likely to exceed the threshold providing a mechanism for their detection. The proposed method is evaluated in both qualitative and quantitative terms via two distinct annotated databases. Results are reported for originally noisy database signals as well as versions of them further degraded under controlled conditions. A comparative performance evaluation, in terms of equal error rate (EER) detection, reveals that, for one of the tested databases, an improvement from 7% to 4% EER is achieved, respectively, from the original to the new edit detection method. When the signals are amplitude clipped or corrupted by broadband background noise, the performance figures of the novel method follow the same profile of those of the original method.