Niclas Sandgren

Spectral analysis of irregularly-sampled data: Paralleling the regularly-sampled data approaches

The spectral analysis of regularly-sampled (RS) data is a well-established topic, and many useful methods are available for performing it under different sets of conditions. The same cannot be said about the spectral analysis of irregularly-sampled (IS) data: despite a plethora of published works on this topic, the choice of a spectral analysis method for IS data is essentially limited, on either technical or computational grounds, to the periodogram and its variations. In our opinion this situation is far from satisfactory, given the importance of the spectral analysis of IS data for a considerable number of applications in such diverse fields as engineering, biomedicine, economics, astronomy, seismology, and physics, to name a few. In this paper we introduce a number of IS data approaches that parallel the methods most commonly used for spectral analysis of RS data: the periodogram (PER), the Capon method (CAP), the multiple-signal characterization method (MUSIC), and the estimation of signal parameters via rotational invariance technique (ESPRIT). The proposed IS methods are as simple as their RS counterparts, both conceptually and computationally. In particular, the fast algorithms derived for the implementation of the RS data methods can be used mutatis mutandis to implement the proposed parallel IS methods. Moreover, the expected performance-based ranking of the IS methods is the same as that of the parallel RS methods: all of them perform similarly on data consisting of well-separated sinusoids in noise, MUSIC and ESPRIT outperform the other methods in the case of closely-spaced sinusoids in white noise, and CAP outperforms PER for data whose spectrum has a small-to-medium dynamic range (MUSIC and ESPRIT should not be used in the latter case).

Smoothed nonparametric spectral estimation via cepsturm thresholding - Introduction of a method for smoothed nonparametric spectral estimation

Cepstrum thresholding is shown to be an effective, automatic way of obtaining a smoothed nonparametric estimate of the spectrum of a stationary signal. In the process of introducing the cepstrum thresholding-based spectral estimator, we discuss a number of results on the cepstrum of a stationary signal, which might also be of interest to researchers in spectral analysis and allied topics, such as speech processing

Using prior knowledge in SVD-based parameter estimation for magnetic resonance spectroscopy-the ATP example

We introduce the knowledge-based singular value decomposition (KNOB-SVD) method for exploiting prior knowledge in magnetic resonance (MR) spectroscopy based on the SVD of the data matrix. More specifically, we assume that the MR data are well modeled by the superposition of a given number of exponentially damped sinusoidal components and that the dampings /spl alpha//sub k/, frequencies /spl omega//sub k/, and complex amplitudes /spl rho//sub k/ of some components satisfy the following relations: /spl alpha//sub k/=/spl alpha/ (/spl alpha/=unknown),/spl omega//sub k/=/spl omega/+(k-1)/spl Delta/ (/spl omega/=unknown,/spl Delta/=known), and /spl rho//sub k/=c/sub k//spl rho/ (/spl rho/=unknown,c/sub k/=known real constants). The adenosine triphosphate (ATP) complex, which has one triple peak and two double peaks whose dampings, frequencies, and amplitudes may in some cases be known to satisfy the above type of relations, is used as a vehicle for describing our SVD-based method throughout the paper. By means of numerical examples, we show that our method provides more accurate parameter estimates than a commonly used general-purpose SVD-based method and a previously suggested prior knowledge-based SVD method.

Frequency-domain method based on the singular value decomposition for frequency-selective NMR spectroscopy

In several applications of NMR spectroscopy the user is interested only in the components lying in a small frequency band of the spectrum. A frequency selective analysis deals precisely with this kind of NMR spectroscopy: parameter estimation of only those spectroscopic components that lie in a preselected frequency band of the NMR data spectrum, with as little interference as possible from the out-of-band components and in a computationally efficient way. In this paper we introduce a frequency-domain singular value decomposition (SVD)-based method for frequency selective spectroscopy that is computationally simple, statistically accurate, and which has a firm theoretical basis. To illustrate the good performance of the proposed method we present a number of numerical examples for both simulated and in vitro NMR data.

Automatic Smoothing of Periodograms

Thresholding the cepstrum associated with the periodogram is a smoothing technique that appears to be very useful for variance reduction. Here the thresholding is performed via the methods SThresh and EbayesThresh. They both work fine in the broadband spectra case, even if some of the data is missing. The SThresh method appears to be more efficient as it shows a smaller variance and is faster computationally. The smoothing methods are also shown to perform well on a real-life broadband signal

On Nonparametric Estimation of 2-D Smooth Spectra

We consider the problem of smoothed nonparametric estimation of two-dimensional (2-D) spectra. In the one-dimensional (1-D) scenario, several methods have been developed in the past for the computation of nonparametric spectral estimates with lower variance than that of the standard periodogram. Some of these techniques can also be extended to the 2-D case. However, such methods usually require a careful selection of certain design parameters, which can be hard to make. The spectral estimator proposed here is based on cepstrum thresholding and is shown to have significantly lower variance than the standard 2-D periodogram. Moreover, the thresholding is performed in a simple and practically automatic manner without the requirement of extensive prior knowledge about the signal of interest

A model averaging approach for equalizing sparse communication channels

In communication applications it is important for equalization to have a good estimate of the channel over which the signal was transferred. In this paper we introduce the concept of model averaging, where several channel estimates are used in a weighted manner, to sparse communication channel estimation and equalization for channels with intersymbol interference. We show via numerical examples that the bit-error-rate (BER) can be reduced by our suggested method, compared to the BERs obtained using channel estimation methods not assuming any sparsity of the channel.

Using prior knowledge in SVD-based NMR spectroscopy - the ATP example

We introduce the KNOB-SVD (knowledge based singular value decomposition) method for exploiting prior knowledge in NMR spectroscopy based on the singular value decomposition (SVD) of the data matrix. The ATP (adenosine triphosphate) complex, often modeled as a sum of seven exponentially damped sinusoids, is used as a vehicle for describing our SVD-based method throughout the paper. By means of a simple numerical example we show that our method provides more accurate parameter estimates than a commonly used general-purpose SVD-based method and a previously suggested prior knowledge-based SVD method using the same type of prior knowledge as considered herein.

Cepstrum Thresholding Scheme for Nonparametric Estimation of Smooth Spectra

Simple and efficient nonparametric spectral estimation is becoming more important as a signal processing tool in applied measurement science. A novel spectral analysis technique based on cepstrum thresholding is presented, which is shown to be an effective semi-automatic way of obtaining a smoothed nonparametric estimate of the spectrum of a stationary signal. The numerical study includes an example involving a moving average (MA) signal, where it is shown that the proposed spectral estimator outperforms significantly the standard periodogram

Frequency-Selective Analysis of Multichannel Magnetic Resonance Spectroscopy Data

In several practical magnetic resonance spectroscopy (MRS) applications the user is interested only in the spectral content of a specific frequency band of the spectrum. A frequency-selective (or sub-band) method estimates only the parameters of those spectroscopic components that lie in a preselected frequency band of the spectrum in a computationally efficient manner. Multichannel MRS is a technique that employs phased-array receive coils to increase the signal-to-noise ratio (SNR) in the spectra by combining several simultaneous measurements of the magnetic resonance (MR) relaxation of an excited sample. In this paper we suggest a frequency-selective multichannel parameter estimation approach that combines the appealing features (high speed and improved SNR) of the two techniques above. The presented method shows parameter estimation accuracies comparable to those of existing full-band multichannel techniques in the high SNR case, but at a considerably lower computational complexity, and significantly better parameter estimation accuracies in low SNR scenarios