Christoph Wiesmeyr

The Large Time-Frequency Analysis Toolbox 2.0

The Large Time Frequency Analysis Toolbox (LTFAT) is a modern Octave/Matlab toolbox for time-frequency analysis, synthesis, coefficient manipulation and visualization. It’s purpose is to serve as a tool for achieving new scientific developments as well as an educational tool. The present paper introduces main features of the second major release of the toolbox which includes: generalizations of the Gabor transform, the wavelets module, the frames framework and the real-time block processing framework.

Representing and Counting the Subgroups of the Group

We deduce a simple representation and the invariant factor decompositions of the subgroups of the group , where and are arbitrary positive integers. We obtain formulas for the total number of subgroups and the number of subgroups of a given order.

Efficient Algorithms for Discrete Gabor Transforms on a Nonseparable Lattice

The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space on a subgroup. Most of the literature focuses on separable subgroups, in this paper we will survey existing methods for a generalization to arbitrary groups, as well as present an improvement on existing methods. Comparisons are made with respect to the computational complexity, and the running time of optimized implementations in the C programming language. The new algorithms have the lowest known computational complexity for nonseparable lattices and the implementations are freely available for download. By summarizing general background information on the state of the art, this article can also be seen as a research survey, sharing with the readers experience in the numerical work in Gabor analysis.

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on lp-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples.

Construction of approximate dual wavelet frames

This paper presents a computationally realizable approach for the construction of an approximate dual wavelet frame. We are considering wavelet frames on the real line obtained by appropriate translation and dilation of a single given atom. We show asymptotic results in operator norm. Also we present numerical results to demonstrate the realizability of the approximation.

3D detection of periodic limb movements in sleep

The standard polysomnographic method for detecting periodic limb movements in sleep (PLMS) includes measuring the electromyography (EMG) signals from electrodes at the left and right tibialis anterior muscles. This procedure has disadvantages as the cabling affects the patients quality of sleep and the electrodes tend to come off during the night, deteriorating data quality. We used contactless monitoring of body movements by a 3D time-of-flight camera mounted above the bed. Changes in the 3D silhouette indicate motion. Contactless detection of PLMS has several substantial advantages over the EMG and provides more complete and more specific diagnostic data: (1) Motor events caused by other leg muscles than tibialis anterior muscles are fully captured by the 3D method, but missed by EMG. (2) 3D does not react to tonic muscle contractions, where such contractions cause strong deflections in EMG which are annotated as limb movements by most PSG apparatus. Another aspect turned out to be of high practical relevance: Deflections in EMG traces are frequently caused by poor electrode contacts, potentially causing false movement annotations. This can lead to substantial overestimation of the automatically computed PLM index. Contactless sensing completely avoids such problems.The standard polysomnographic method for detecting periodic limb movements in sleep (PLMS) includes measuring the electromyography (EMG) signals from electrodes at the left and right tibialis anterior muscles. This procedure has disadvantages as the cabling affects the patients quality of sleep and the electrodes tend to come off during the night, deteriorating data quality. We used contactless monitoring of body movements by a 3D time-of-flight camera mounted above the bed. Changes in the 3D silhouette indicate motion. Contactless detection of PLMS has several substantial advantages over the EMG and provides more complete and more specific diagnostic data: (1) Motor events caused by other leg muscles than tibialis anterior muscles are fully captured by the 3D method, but missed by EMG. (2) 3D does not react to tonic muscle contractions, where such contractions cause strong deflections in EMG which are annotated as limb movements by most PSG apparatus. Another aspect turned out to be of high practical relevance: Deflections in EMG traces are frequently caused by poor electrode contacts, potentially causing false movement annotations. This can lead to substantial overestimation of the automatically computed PLM index. Contactless sensing completely avoids such problems.

Train Detection and Tracking in Optical Time Domain Reflectometry (OTDR) Signals

We propose a novel method for the detection of vibrations caused by trains in an optical fiber buried nearby the railway track. Using optical time-domain reflectometry vibrations in the ground caused by different sources can be detected with high accuracy in time and space. While several algorithms have been proposed in the literature for train tracking using OTDR signals they have not been tested on longer recordings. The presented method learns the characteristic pattern in the Fourier domain using a support vector machine (SVM) and it becomes more robust to any kind of noise and artifacts in the signal. The point-based causal train tracking has two stages to minimize the influence of false classifications of the vibration detection. Our technical contribution is the evaluation of the presented algorithm based on two hour long recording and demonstration of open problems for commercial usage.

A real-time algorithm for train position monitoring using optical time-domain reflectometry

We propose an algorithm which uses an optical time-domain reflectometer (OTDR) for real-time tracking of trains. OTDR sensing, often also termed distributed acoustical sensing (DAS), measures the Rayleigh backscattering of a light pulse along an optical fiber. The resulting signal provides information on local acoustic pressure at linearly spaced positions along the fiber. While different approaches for train tracking with DAS are described in the literature, the results have been evaluated only for short time recordings with few train crossings. In this paper we provide details on the tracking performance of a novel algorithm that finds and tracks trains over 15km. Furthermore, this is the first contribution that uses ground truth data to assess the performance of the method. For the evaluation two one hour recordings are used.

Contactless 3D detection of respiratory effort

Respiratory effort is a major feature for detection and classification of apneas in polysomnography. Presently, somnologists apply flow sensors and/or rip belts at the thorax and abdomen for this purpose, causing practical problems with the montage and re-adjustment during the night and disturbing patients´ sleep. Contactless measurements would be a desirable alternative. We utilized a 3D time-of-flight camera to monitor respiratory-related chest movements to decipher epochs of normal breathing and apnea. Time-synchronized comparisons of 3D measurements of chest movements due to respiration to signals from rip belts and nasal airflow proved that the 3D sensor provided equivalent results. This new technique could support the diagnosis of sleep apnea and Cheyne-Stokes breathing. It simplifies the procedure, saves personnel capacity, improves data quality and releases the burden to the patient by replacing body-mounted sensors and cabling.

3D detection of the central sleep apnoea syndrome

Abstract In polysomnography, an oronasal thermal airflow sensor and respiratory inductance plethysmography (RIP) belts at thorax and abdomen are used to detect central sleep apnoea. These sensors are uncomfortable to wear, can disturb the patient’s sleep, and data quality can be significantly di-minished if a sensor slips off the patient. Contactless meas-urements would be a desirable alternative. We utilized a 3D time-of-flight sensor to monitor respiratory-related chest movements to decipher epochs of normal breathing and ap-noea in ten adult patients with a total of 467 apnoea events. Time-synchronized comparisons of 3D measurements of chest movements due to respiration to polysomnography signals from rip belts and nasal airflow proved that the 3D sensor provided largely equivalent results. This new tech-nique could support the diagnosis of central sleep apnoea and Cheyne-Stokes respiration.