Periodic signals can be decomposed into sets of sinusoids having frequencies that are integer multiples of a fundamental frequency. The problem of finding such fundamental frequencies from noisy observations is important in many speech and audio applications, where it is commonly referred to as pitch estimation. These applications include analysis, compression, separation, enhancement, automatic transcription and many more. In this book, an introduction to pitch estimation is given and a number of statistical methods for pitch estimation are presented. The basic signal models and associated estimation theoretical bounds are introduced, and the properties of speech and audio signals are discussed and illustrated. The presented methods include both single- and multi-pitch estimators based on statistical approaches, like maximum likelihood and maximum a posteriori methods, filtering methods based on both static and optimal adaptive designs, and subspace methods based on the principles of subspace orthogonality and shift-invariance. The application of these methods to analysis of speech and audio signals is demonstrated using both real and synthetic signals, and their performance is assessed under various conditions and their properties discussed. Finally, the estimators are compared in terms of computational and statistical efficiency, generalizability and robustness. Table of Contents: Fundamentals / Statistical Methods / Filtering Methods / Subspace Methods / Amplitude Estimation

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Multi-Pitch Estimation

This paper describes an algorithm for land mine detection using sensor data generated by a ground-penetrating radar (GPR) system that uses edge histogram descriptors for feature extraction and a possibilistic K -nearest neighbors (K-NNs) rule for confidence assignment. The algorithm demonstrated the best performance among several high-performance algorithms in extensive testing on a large real-world datasets associated with the difficult problem of land mine detection. The superior performance of the algorithm is attributed to the use of the possibilistic K -NN algorithm, thereby providing important evidence supporting the use of possibilistic methods in real-world applications. The GPR produces a 3-D array of intensity values, representing a volume below the surface of the ground. First, a computationally inexpensive prescreening algorithm for anomaly detection is used to focus attention and identify candidate signatures that resemble mines. The identified regions of interest are processed further by a feature extraction algorithm to capture their salient features. We use translation-invariant features that are based on the local edge distribution of the 3-D GPR signatures. Specifically, each 3-D signature is divided into subsignatures, and the local edge distribution for each subsignature is represented by a histogram. Next, the training signatures are clustered to identify prototypes. The main idea is to identify few prototypes that can capture the variations of the signatures within each class. These variations could be due to different mine types, different soil conditions, different weather conditions, etc. Fuzzy memberships are assigned to these representatives to capture their degree of sharing among the mines and false alarm classes. Finally, a possibilistic K-NN-based rule is used to assign a confidence value to distinguish true detections from false alarms. The proposed algorithm is implemented and integrated within a complete land mine prototype system. It is trained, field-tested, evaluated, and compared using a large-scale cross-validation experiment that uses a diverse dataset acquired from four outdoor test sites at different geographic locations. This collection covers over 41 807 m2 of ground and includes 1593 mine encounters.

Detection and Discrimination of Land Mines in Ground-Penetrating Radar Based on Edge Histogram Descriptors and a Possibilistic $K$ -Nearest Neighbor Classifier

The use of geoscience methods for terrestrial forensic searches

In this paper, we present a novel method for joint estimation of the fundamental frequency and order of a set of harmonically related sinusoids based on the multiple signal classification (MUSIC) estimation criterion. The presented method, termed HMUSIC, is shown to have an efficient implementation using fast Fourier transforms (FFTs). Furthermore, refined estimates can be obtained using a gradient-based method. Illustrative examples of the application of the algorithm to real-life speech and audio signals are given, and the statistical performance of the estimator is evaluated using synthetic signals, demonstrating its good statistical properties.

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Joint High-Resolution Fundamental Frequency and Order Estimation

This paper presents cost-effective low-rank techniques for designing robust adaptive beamforming (RAB) algorithms. The proposed algorithms are based on the exploitation of the cross-correlation between the array observation data and the output of the beamformer. First, we construct a general linear equation considered in large dimensions whose solution yields the steering vector mismatch. Then, we employ the idea of the full orthogonalization method (FOM), an orthogonal Krylov subspace based method, to iteratively estimate the steering vector mismatch in a reduced-dimensional subspace, resulting in the proposed orthogonal Krylov subspace projection mismatch estimation (OKSPME) method. We also devise adaptive algorithms based on stochastic gradient (SG) and conjugate gradient (CG) techniques to update the beamforming weights with low complexity and avoid any costly matrix inversion. The main advantages of the proposed low-rank and mismatch estimation techniques are their cost-effectiveness when dealing with high-dimension subspaces or large sensor arrays. Simulations results show excellent performance in terms of the output signal-to-interference-plus-noise ratio (SINR) of the beamformer among all the compared RAB methods.

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Robust Adaptive Beamforming Based on Low-Rank and Cross-Correlation Techniques

Nuclear quadrupole resonance (NQR) is a radio-frequency technique that can be used to detect the presence of quadrupolar nuclei, such as the 14N nucleus prevalent in many explosives and narcotics. In a typical application, one observes trains of decaying NQR echoes, in which the decay is governed by the spin echo decay time(s) of the resonant line(s). In most detection algorithms, these echoes are simply summed to produce a single echo with a higher signal-to-noise ratio, ignoring the decaying echo structure of the signal. In this paper, after reviewing current NQR signal models, we propose a novel NQR data model of the full echo train and detail why and how these echo trains are produced. Furthermore, we refine two recently proposed approximative maximum-likelihood detectors that enable the algorithms to optimally exploit the proposed echo train model. Extensive numerical evaluations based on both simulated and measured NQR data indicate that the proposed detectors offer a significant improvement as compared to current state-of-the-art detectors

Exploiting Spin Echo Decay in the Detection of Nuclear Quadrupole Resonance Signals

Nuclear quadrupole resonance (NQR) is a solid-state radio frequency (RF) spectroscopic technique, allowing the detection of compounds containing quadrupolar nuclei, a requirement fulfilled by many high explosives and narcotics. The practical use of NQR is restricted by the inherently low signal-to-noise ratio (SNR) of the observed signals, a problem that is further exacerbated by the presence of strong RF interference (RFI). The current literature focuses on the use of conventional, multiple-pulsed NQR (cNQR) to obtain signals. Here, we investigate an alternative method called stochastic NQR (sNQR), having many advantages over cNQR, one of which is the availability of signal-of-interest free samples. In this paper, we exploit these samples forming a matched subspace-type detector and a detector employing a prewhitening approach, both of which are able to efficiently reduce the influence of RFI. Further, many of the ideas already developed for cNQR, including providing robustness to uncertainties in the assumed complex amplitudes and exploiting the temperature dependencies of the NQR spectral components, are recast for sNQR. The presented detectors are evaluated on both simulated and measured trinitro-toluene (TNT) data.

Robust Detection of Stochastic Nuclear Quadrupole Resonance Signals

In passive sonar, narrowband adaptive beamforming techniques can be exploited to increase the signal-to-interference-plus-noise ratio (SINR), providing that array steering vector (ASV) errors and cross-spectral density matrix (CSDM) estimation errors can be controlled. When beamforming large aperture, many-element arrays in dynamic scenarios, the number of stationary snapshots available for CSDM estimation can be small compared to the number of array elements, leading to the problem of snapshot deficiency. Furthermore, common narrowband approaches become computationally prohibitive for large bandwidths. Here, we exploit the wideband nature of passive sonar signals to alleviate snapshot deficiency and reduce computational complexity. Narrowband robust Capon beamformers (RCBs), which exploit ellipsoidal ASV uncertainty sets to maintain high SINR, are extended to the wideband problem via the steered covariance matrix (STCM) method, yielding wideband RCBs (WBRCBs). To further reduce computational complexity and speed up algorithm convergence, subarray techniques are also incorporated, yielding wideband subarray RCBs (WBSARCBs). These algorithms, which are applicable to arbitrary array geometries, are evaluated using simulated and experimental passive sonar data.

Wideband Robust Capon Beamforming for Passive Sonar

In this paper, a novel linearly constrained robust Capon beamformer (LCRCB) framework is proposed. In the LCRCB, linear constraints can be used, e.g., for beampattern control and ellipsoidal array steering vector sets can be exploited, using robust Capon beamforming techniques, e.g., to allow for arbitrary array steering vector errors, such as those arising from calibration errors. The LCRCB is applicable to arbitrary array geometries and can be computed efficiently. For the limiting case that the ellipsoid is a point, we show that the LCRCB coincides with a linearly constrained minimum variance beamformer. To show the utility of the LCRCB, mainbeam and null-pattern control examples are included.

Linearly Constrained Robust Capon Beamforming

Nuclear quadrupole resonance (NQR) is a solid-state radio frequency (RF) spectroscopic technique that allows for the detection of many narcotics and highly explosive substances. Unfortunately, the practical use of NQR is often restricted by the presence of strong RF interference (RFI). In this letter, extending our recent work on stochastic NQR (sNQR), we propose acquiring signal-of-interest free samples, containing only corrupting signals, and exploiting them to reduce the effects of RFI on conventional NQR (cNQR) measurements. Similar to the sNQR case, the presented detectors are able to substantially outperform previous cNQR detectors when RFI is present.

S. D. Somasundaram

Papers

Exploiting Spin Echo Decay in the Detection of Nuclear Quadrupole Resonance Signals

Robust Detection of Stochastic Nuclear Quadrupole Resonance Signals

Wideband Robust Capon Beamforming for Passive Sonar

Linearly Constrained Robust Capon Beamforming

Countering Radio Frequency Interference in Single-Sensor Quadrupole Resonance