Time–frequency analysis

About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.

Multiridge detection and time-frequency reconstruction

Abstract: The ridges of the wavelet transform, the Gabor transform, or any time-frequency representation of a signal contain crucial information on the characteristics of the signal. Indeed, they mark the regions of the time-frequency plane where the signal concentrates most of its energy. We introduce a new algorithm to detect and identify these ridges. The procedure is based on an original form of Markov chain Monte Carlo algorithm especially adapted to the present situation. We show that this detection algorithm is especially useful for noisy signals with multiridge transforms. It is a common practice among practitioners to reconstruct a signal from the skeleton of a transform of the signal (i.e., the restriction of the transform to the ridges). After reviewing several known procedures, we introduce a new reconstruction algorithm, and we illustrate its efficiency on speech signals and its robustness and stability on chirps perturbed by synthetic noise at different SNRs.

Matching Demodulation Transform and SynchroSqueezing in Time-Frequency Analysis

Abstract: The authors introduce an iterative algorithm, called matching demodulation transform (MDT), to generate a time-frequency (TF) representation with satisfactory energy concentration. As opposed to conventional TF analysis methods, this algorithm does not have to devise ad-hoc parametric TF dictionary. Assuming the FM law of a signal can be well characterized by a determined mathematical model with reasonable accuracy, the MDT algorithm can adopt a partial demodulation and stepwise refinement strategy for investigating TF properties of the signal. The practical implementation of the MDT involves an iterative procedure that gradually matches the true instantaneous frequency (IF) of the signal. Theoretical analysis of the MDT's performance is provided, including quantitative analysis of the IF estimation error and the convergence condition. Moreover, the MDT-based synchrosqueezing algorithm is described to further enhance the concentration and reduce the diffusion of the curved IF profile in the TF representation of original synchrosqueezing transform. The validity and practical utility of the proposed method are demonstrated by simulated as well as real signal.

Improved instantaneous frequency estimation using an adaptive short-time Fourier transform

Abstract: Instantaneous frequency estimation (IFE) arises in a variety of important applications, including FM demodulation. We present here a new time-frequency representation (TFR)-based approach to IFE based on an adaptive short-time Fourier transform (ASTFT). This TFR leads naturally to a type of short-term ML estimator of the IF. To further improve the performance, we apply a multistate hidden Markov model (HMM)-based post-estimation tracker. The end result is up to a 16-dB reduction in the threshold SNR over the frequency discriminator (FD) and an 8-dB improvement over the phase-locked loop (PLL) for a Rayleigh fading channel.

Time Frequency and Wavelets in Biomedical Signal Processing

Abstract: Body Explorer (CD ROM) by Andreas Bulling, et. al., Springer-Verlag, BerWHeidelburgL’Jew York, 1997. ISBN: 3-540-14681-4, $39.95. In 1996 the data from the Visible Human Male of the National Library of Medicine in Washington was made available to a team of researchers from the Anatomical Institute of the Technical University in Munich. The results of their analysis led to the creation of the Body Explorer, an interactive software program that offers 250 anatomical images in cross-section of the Visible Human Male. The CD is available in both English and German and is presented in a Windows user-interface. A Pentium PC with Windows 95 or higher or Windows NT with a minimum of 16 MB RAM is required for use of the software. This product can be considered an anatomical atlas, having no text to accompany the images. All cross-sectional images are displayed in the transverse (horizontal) plane, spanning the longitudinal axis of the body. The images derive from actual photographs of the Visible Human Male and are aligned in 5-mm increments from head to toe. The user is able to select a plane of interest from the system’s navigator, which depicts the level of the plane in sagittal and coronal views. Additionally, one can locate an anatomical feature among a series of levels based on a keyword search. The CD comes with a helpful instructional booklet that outlines the functions of the software. An online version of the booklet is also available. Several practical functions are included in the program such as a zoom tool for examining views from under 10% to over 1000% of actual size. Two forms of anatomy identification are offered; names of anatomical structures are either labeled individually or they can be selected in physiological groups. In particular, structures may be identified according to their affiliation with a functional group such as the bones, cardiovascular system, connective tissue, peripheral nervous system, or apparatus of locomotion. The program fumishes 10,000 anatomical labels with typically 70 per slice-the anatomy of interest can be labeled in either Latin, English or German. Furthermore, it is possible to superimpose images from multiple levels. All of these tools operate only on the selected images in the transverse plane; the program does not provide close-up views or labels in any other plane. The difficulties that one may encounter with this CD arise in the functions that search for the anatomy of interest. The instructions on searching for a particular structure were vague, and the booklet did not specify a reset button for clearing the search menu. Moreover, the instructions claim that the user may simultaneously view the labels of several functional groups on a cross-sectional image, but this option only works if one is selecting groups that are in consecutive order in the menu. These are only minor flaws that, for the most part, can be overcome with sufficient use of the software. The potential user would perhaps benefit most from a perusal of the authors’ web-site information. Here, one can find an overview of the product’s features and also test the functions of the software. Their web address is www.anatomie.med.tu-muenchen.dejbody/ index.htm. This product is an excellent tool for learning anatomical details and would be a practical resource for students, teachers and physicians.