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Extracting a shape function for a signal with intra-wave frequency modulation.

ABSTRACT: In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape function could be any smooth 2?-periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that the shape function is a periodic function with respect to its phase function, we can identify certain low-rank structure of the signal. This low-rank structure enables us to extract the shape function from the signal. Once the shape function is obtained, the instantaneous frequency with intra-wave modulation can be recovered from the shape function. We demonstrate the robustness and efficiency of our method by applying it to several synthetic and real signals. One important observation is that this approach is very stable to noise perturbation. By using the shape function approach, we can capture the intra-wave frequency modulation very well even for noise-polluted signals. In comparison, existing methods such as empirical mode decomposition/ensemble empirical mode decomposition seem to have difficulty in capturing the intra-wave modulation when the signal is polluted by noise.

SUBMITTER: Hou TY

PROVIDER: S-EPMC4792404 | biostudies-literature | 2016 Apr

REPOSITORIES: biostudies-literature

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Extracting a shape function for a signal with intra-wave frequency modulation.

Hou Thomas Y TY Shi Zuoqiang Z

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences 20160401 2065

In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape functio ...[more]

PMID: 26953176

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Project description:Electrocardiography is the gold standard for electrical heartbeat activity, but offers no direct measurement of mechanical activity. Mechanical cardiac activity can be assessed non-invasively using, e.g., ballistocardiography and recently, medical radar has emerged as a contactless alternative modality. However, all modalities for measuring the mechanical cardiac activity are affected by respiratory movements, requiring a signal separation step before higher-level analysis can be performed. This paper adapts a non-linear filter for separating the respiratory and cardiac signal components of radar recordings. In addition, we present an adaptive algorithm for estimating the parameters for the non-linear filter. The novelty of our method lies in the combination of the non-linear signal separation method with a novel, adaptive parameter estimation method specifically designed for the non-linear signal separation method, eliminating the need for manual intervention and resulting in a fully adaptive algorithm. Using the two benchmark applications of (i) cardiac template extraction from radar and (ii) peak timing analysis, we demonstrate that the non-linear filter combined with adaptive parameter estimation delivers superior results compared to linear filtering. The results show that using locally projective adaptive signal separation (LoPASS), we are able to reduce the mean standard deviation of the cardiac template by at least a factor of 2 across all subjects. In addition, using LoPASS, 9 out of 10 subjects show significant (at a confidence level of 2.5%) correlation between the R-T-interval and the R-radar-interval, while using linear filters this ratio drops to 6 out of 10. Our analysis suggests that the improvement is due to better preservation of the cardiac signal morphology by the non-linear signal separation method. Hence, we expect that the non-linear signal separation method introduced in this paper will mostly benefit analysis methods investigating the cardiac radar signal morphology on a beat-to-beat basis.

Dataset Information

Extracting a shape function for a signal with intra-wave frequency modulation.

Publications

Extracting a shape function for a signal with intra-wave frequency modulation.

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