Topic
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.
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TL;DR: The Stockwell transform (ST), recently developed for geophysics, combines features of the Fourier, Gabor and wavelet transforms; it reveals frequency variation over time or space and is a potentially effective tool to visualize, analyze, and process medical imaging data.
Abstract: The Stockwell transform (ST), recently developed for geophysics, combines features of the Fourier, Gabor and wavelet transforms; it reveals frequency variation over time or space. This valuable information is obtained by Fourier analysis of a small segment of a signal at a time. Localization of the Fourier spectrum is achieved by filtering the signal with frequency-dependent Gaussian scaling windows. This multi-scale time–frequency analysis provides information about which frequencies occur and more importantly when they occur. Furthermore, the Stockwell domain can be directly inferred from the Fourier domain and vice versa. These features make the ST a potentially effective tool to visualize,analyze, and process medical imaging data. The ST has proven useful in noise reduction and tissue texture analysis. Herein, we focus on the theory and effectiveness of the ST for medical imaging. Its effectiveness and comparison with other linear time–frequency transforms, such as the Gabor and wavelet transforms, are discussed and demonstrated using functional magnetic resonance imaging data.
71 citations
TL;DR: In this article, a new distribution that provides high concentration in the time-frequency domain is proposed, based on the S-method and multi-window approach, where different order Hermite functions are employed as multiple windows.
Abstract: A new distribution that provides high concentration in the time-frequency domain is proposed. It is based on the S-method and multiwindow approach, where different order Hermite functions are employed as multiple windows. The resulting distribution will be referred to as the multiwindow S-method. It preserves favourable properties of the standard S-method, whereas the distribution concentration is improved by using Hermite functions of just a few first orders. The proposed distribution is appropriate for radar signal analysis, as it will be proven by experimental examples.
71 citations
TL;DR: New chirp rate and instantaneous frequency estimators designed for frequency-modulated signals are introduced and paves the way to the real-time computation of a time-frequency representation, which is both invertible and sharply localized in frequency.
Abstract: This letter introduces new chirp rate and instantaneous frequency estimators designed for frequency-modulated signals. These estimators are first investigated from a deterministic point of view, then compared together in terms of statistical efficiency. They are also used to design new recursive versions of the vertically synchrosqueezed short-time Fourier transform, using a previously published method (D. Fourer, F. Auger, and P. Flandrin, “Recursive versions of the Levenberg-Marquardt reassigned spectrogram and of the synchrosqueezed STFT,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. , Mar. 2016, pp. 4880–4884). This study paves the way to the real-time computation of a time-frequency representation, which is both invertible and sharply localized in frequency.
71 citations
TL;DR: A new variant of a block transmission based on 4-Weighted Fractional Fourier Transform (4-WFRFT), which contains a compatible process of single-carrier (SC) and multi-car carrier (MC) modulation, which could achieve a better performance than or equal to those of SC and MC systems in selective fading channels.
Abstract: We propose a new variant of a block transmission based on 4-Weighted Fractional Fourier Transform (4-WFRFT), which contains a compatible process of single-carrier (SC) and multi-carrier (MC) modulation. The 4-WFRFT system has an even and symmetrical bit energy distribution on the timefrequency plane that it could achieve a better performance than or equal to those of SC and MC systems in selective fading channels. The approach of 4-WFRFT may facilitate unification of the two competitive carrier schemes, and improve the distortion resistance capability of communication system.
71 citations
TL;DR: A new SST method called high-order synchrosqueezing wavelet transform is proposed to achieve a highly energy-concentrated time-frequency representation (TFR) for nonstationary signals with wide frequency range and fast varying IF.
71 citations