Wang Yubo, Veluvolu Kalyana C
School of Life Science and Technology, Xidian University, ShannXi, Xi'an 710071, China.
School of Electronics Engineering, Kungpook National University, Daegu 702-701, South Korea.
Sensors (Basel). 2017 Jun 14;17(6):1386. doi: 10.3390/s17061386.
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.
由于生物信号具有非线性和非平稳特性，对其进行分析往往很困难。这就需要使用时频分解方法来分析这些信号中常常与潜在现象相关的细微变化。本文提出了一种新方法，通过采用一个简单的截断傅里叶级数模型，即带限多重傅里叶线性组合器（BMFLC），来分析此类信号的时变特性。与早期设计不同的是，我们首先确定了施加在信号模型上的稀疏性，以便将该模型重新表述为一个稀疏线性回归模型。然后通过一种凸优化算法估计所提出模型的系数。使用基准测试信号对所提方法的性能进行了分析。采用能量比指标来量化频谱性能，结果表明所提方法Sparse - BMFLC具有较高的平均能量比（0.9976），并且优于诸如短时傅里叶变换（STFT）、连续小波变换（CWT）和BMFLC卡尔曼平滑器等现有方法。此外，所提方法的重建误差总体为6.22%。
