Abstract
It is often difficult to analyze biological signals because of their nonlinear and non-stationary characteristics. This necessitates the usage of time-frequency decomposition methods for analyzing the subtle changes in these signals that are often connected to an underlying phenomena. This paper presents a new approach to analyze the time-varying characteristics of such signals by employing a simple truncated Fourier series model, namely the band-limited multiple Fourier linear combiner (BMFLC). In contrast to the earlier designs, we first identified the sparsity imposed on the signal model in order to reformulate the model to a sparse linear regression model. The coefficients of the proposed model are then estimated by a convex optimization algorithm. The performance of the proposed method was analyzed with benchmark test signals. An energy ratio metric is employed to quantify the spectral performance and results show that the proposed method Sparse-BMFLC has high mean energy (0.9976) ratio and outperforms existing methods such as short-time Fourier transfrom (STFT), continuous Wavelet transform (CWT) and BMFLC Kalman Smoother. Furthermore, the proposed method provides an overall 6.22% in reconstruction error.
Highlights
The recent advances in technology have paved the way for deployment of reliable biological sensors in clinical practice
To analyze and quantify the performance of the time-frequency decomposition of the proposed sparse-band-limited multiple Fourier linear combiner (BMFLC), it is compared to well known methods such as short-time Fourier transfrom (STFT) and continuous Wavelet transform (CWT)
The results indicate that the sparsity constraint employed in Sparse-BMFLC could help in providing an accurate time-frequency decomposition as compared to BMFLC-KS, and the proposed Sparse-BMFLC has good robustness to noise contamination
Summary
The recent advances in technology have paved the way for deployment of reliable biological sensors in clinical practice. A wide variety of such sensors have been developed to measure biosignals that reflect various underlying physiological phenomena. Gyroscope and accelerometers are employed for pathological and physiological tremor signal measurement [1], accelerometers are employed for cardiac mechanical vibrations monitoring [2], infrared sensors are employed for respiration motion monitoring [3], and common electrodes are employed for brain and heart electrical activity measurement [4,5]. Most of the physiological signals are non-stationary due to the complex nature of the biological systems. Very subtle changes in the time-frequency characteristics of these signals can potentially correspond to an underlying condition. Analysis of biosignals require high resolution time-frequency decomposition methods to effectively detect these subtle changes
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