This paper addresses a forensic tool used to assess audio authenticity. The proposed method is based on detecting phase discontinuity of the power grid signal; this signal, referred to as electric network frequency (ENF), is sometimes embedded in audio signals when the recording is carried out with the equipment connected to an electrical outlet or when certain microphones are in an ENF magnetic field. After down-sampling and band-filtering the audio around the nominal value of the ENF, the result can be considered a single tone such that a high-precision Fourier analysis can be used to estimate its phase. The estimated phase provides a visual aid to locating editing points (signalled by abrupt phase changes) and inferring the type of audio editing (insertion or removal of audio segments). From the estimated values, a feature is used to quantify the discontinuity of the ENF phase, allowing an automatic decision concerning the authenticity of the audio evidence. The theoretical background is presented along with practical implementation issues related to the proposed technique, whose performance is evaluated on digitally edited audio signals.

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

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.

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.

We detail in this paper an L ₁ -norm Linearly constrained normalized least-mean-square (L ₁ -CNLMS) algorithm and its weighted version (L ₁ -WCNLMS) applied to solve problems whose solutions have some degree of sparsity, such as the beamforming problem in uniform linear arrays, standard hexagonal arrays, and (non-standard) hexagonal antenna arrays. In addition to the linear constraints present in the CNLMS algorithm, the L ₁ -WCNLMS and the L ₁ -CNLMS algorithms take into account an L ₁ -norm penalty on the filter coefficients, which results in sparse solutions producing thinned arrays. The effectiveness of both algorithms is demonstrated via computer simulations. When employing these algorithms to antenna array problems, the resulting effect due to the L ₁ -norm constraint is perceived as a large aperture array with few active elements. Although this work focuses the algorithm on antenna array synthesis, its application is not limited to them, i.e., the L ₁ -CNLMS is suitable to solve other problems like sparse system identification and signal reconstruction, where the weighted version, the L ₁ -WCNLMS algorithm, presents superior performance compared to the L ₁ -CNLMS 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.