基于多项式调频Fourier变换的信号分量提取方法

为了从含有噪声的混合信号中有效提取各个信号分量, 提出一种基于多项式调频Fourier变换的分量提取方法. 通过研究Fourier变换和分数阶Fourier变换的信号能量积累方式及变换基函数的时频表示, 提出利用时频平面上的多项式调频曲线族代替Fourier变换和分数阶Fourier 变换的调频直线族, 将变换的适用范围扩展到非线性调频信号. 采用粒子群智能优化算法搜索调频曲线族的最优多项式参数, 使混合信号中的某一分量在多项式调频Fourier域上能量谱集中. 最后对能量谱集中的分量进行窄带滤波, 并利用多项式调频逆Fourier变换重构信号分量. 仿真实验结果表明, 该方法不仅能够提取混合信号中的线性调频分量, 还能够实现非线性调频分量的能量谱集中、信号分离和时频特征提取.

Signal component extraction method based on polynomial chirp Fourier transform

As frequency modulated (FM) signals widely exist in the natural world as well as in different artificial applications, it is of great practical significance to explore the ways to extract such signal components in the complex and noisy environment. To extract one component from the noisy multicomponent signal effectively, a component extraction method based on polynomial chirp Fourier transform (PCFT) is presented in this paper. First, the physical meanings of Fourier transform (FT) and fractional Fourier transform (FRFT) are analyzed and their internal relations are expounded from the perspective of signal energy accumulation. Essentially, the FT accumulates signal energy along the time-frequency beelines parallel to the time axis and obtains an energy-concentrated spectrum from the narrow-band stationary signals whose frequency does not change, whereas it fails to process non-stationary signals with changeable frequencies. By rotating the time-frequency axis, the FRFT changes the energy accumulation mode of the signal in the old time-frequency plane and achieves a more concentrated spectrum for the linear frequency modulated (LFM) signal, but with larger error or even invalidation when dealing with nonlinear frequency modulated (NLFM) signal. Using FT and FRFT, in this paper we attempt to improve the energy accumulation mode of the conventional transform method and propose the PCFT. In this transform, the beeline families in the traditional transform, independent of time (or v) axes, are replaced by a family of polynomial chirping curves in the time-frequency plane. These polynomial chirping curves are capable of approaching more closely to the instantaneous frequency curve of FM signal so as to obtain a more concentrated transform spectrum and thereby extend the application of PCFT from LFM signal to NLFM signal. When selecting the polynomial chirping curve, we build up a nonlinear optimization model guided by the principle of energy spectrum concentration and in this way convert the problem of determining the polynomial curve families into the one of optimizing the polynomial parameters. Then particle swarm optimization algorithm is employed to search for the optimal polynomial parameters so as to concentrate the energy of one component in the new transform domain, i.e., the polynomial chirp Fourier domain. After doing that, each component is separated into its concentrated spectrum with a narrow-band filter and reconstructed with the inverse PCFT. Moreover, to extract components from a noisy multicomponent signal successfully, an iteration involving parameter estimation, PCFT, filter and recovery is introduced. To verify the effectiveness of the PCFT-based method, a series of examples, including simulated and real-world signals, is chosen for simulations and experiments. The experimental results indicate that compared with FT and FRFT, the proposed method overcomes the shortcoming of distributed energy spectrum for NLFM components in the traditional transforms and obtains a concentrated energy spectrum in the polynomial chirp Fourier domain, therefore realizing component separation and time-frequency characteristic extraction. The PCFT-based method not only has the capability of dealing with the extraction of LFM components, but also performs well in the separation of crossed NLFM components, and with little extraction error.