Andreas Jakobsson

Multi-pitch estimation

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. (Less)

Matched-filter bank interpretation of some spectral estimators

We make use of a matched-filter bank (MAFI) approach to derive spectral estimators for stationary signals with mixed spectra, We show that the Capon spectral estimator as well as the more recently ...

Cisoid parameter estimation in the colored noise case: asymptotic Cramer-Rao bound, maximum likelihood, and nonlinear least-squares

The problem of estimating the parameters of complex-valued sinusoidal signals (cisoids, for short) from data corrupted by colored noise occurs in many signal processing applications. We present a simple formula for the asymptotic (large-sample) Cramer-Rao bound (CRB) matrix associated with this problem. The maximum likelihood method (MLM), which estimates both the signal and noise parameters, attains the performance corresponding to the asymptotic CRB, as the sample length increases. More interestingly, we show that a computationally much simpler nonlinear least-squares method (NLSM), which estimates the signal parameters only, achieves the same performance in large samples.

Joint High-Resolution Fundamental Frequency and Order Estimation

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.

Exploiting temperature dependency in the detection of NQR signals

Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting and identifying land mines. Unfortunately, the practical use of NQR is restricted by the low signal-to-noise ratio (SNR), and the means to improve the SNR are vital to enable a rapid, reliable, and convenient system. In this paper, an approximate maximum-likelihood detector (AML) is developed, exploiting the temperature dependency of the NQR frequencies as a way to enhance the SNR. Numerical evaluation using both simulated and real NQR data indicate a significant gain in probability of accurate detection as compared with the current state-of-the-art approach.

Computationally efficient two-dimensional Capon spectrum analysis

We present a computationally efficient algorithm for computing the 2-D Capon (1969) spectral estimator. The implementation is based on the fact that the 2-D data covariance matrix will have a Toeplitz-block-Toeplitz structure, with the result that the inverse covariance matrix can be expressed in closed form by using a special case of the Gohberg-Heinig (1974) formula that is a function of strictly the forward 2-D prediction matrix polynomials. Furthermore, we present a novel method, based on a 2-D lattice algorithm, to compute the needed forward prediction matrix polynomials and discuss the difference in the so-obtained 2-D spectral estimate as compared with the one obtained by using the prediction matrix polynomials given by the Whittle-Wiggins-Robinson (1963, 1965) algorithm. Numerical simulations illustrate the improved resolution as well as the clear computational gain in comparison to both the well-known classical implementation and the method published by Liu et al.(see IEEE Trans. Aerosp. Electron. Syst., vol.34, p.1314-19, 1998).

Efficient Implementation of Iterative Adaptive Approach Spectral Estimation Techniques

This paper presents computationally efficient implementations for several recent algorithms based on the iterative adaptive approach (IAA) for uniformly sampled one- and two-dimensional data sets, considering both the complete data case, and the cases when the data sets are missing samples, either lacking arbitrary locations, or having gaps or periodically reoccurring gaps. By exploiting the methods inherent low displacement rank, together with the development of suitable Gohberg-Semencul representations, and the use of data dependent trigonometric polynomials, the proposed implementations are shown to offer a reduction of the necessary computational complexity by at least one order of magnitude. Numerical simulations together with theoretical complexity measures illustrate the achieved performance gain.

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

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

Optimal Filter Designs for Separating and Enhancing Periodic Signals

In this paper, we consider the problem of separating and enhancing periodic signals from single-channel noisy mixtures. More specifically, the problem of designing filters for such tasks is treated. We propose a number of novel filter designs that 1) are specifically aimed at periodic signals, 2) are optimal given the observed signal and thus signal adaptive, 3) offer full parametrizations of periodic signals, and 4) reduce to well-known designs in special cases. The found filters can be used for a multitude of applications including processing of speech and audio signals. Some illustrative signal examples demonstrating its superior properties as compared to other related filters are given and the properties of the various designs are analyzed using synthetic signals in Monte Carlo simulations.

Frequency-selective detection of nuclear quadrupole resonance signals

Nuclear quadrupole resonance (NQR) offers an unequivocal method of detecting and identifying both hidden explosives, such as land mines, and a variety of narcotics. Unfortunately, the practical use of NQR is restricted by a low signal-to-noise ratio (SNR), and means to improve the SNR are vital to enable a rapid, reliable, and convenient system. In this paper, we introduce a frequency-selective approximate maximum-likelihood (FSAML) detector, operating on a subset of the available frequencies, making it robust to the typically present narrow-band interference. The method exploits the inherent temperature dependency of the NQR frequencies as a way to enhance the SNR. Numerical evaluations, using both simulated and real NQR data, indicate a significant gain in probability of accurate detection as compared to a current state-of-the-art approach.