基于短时分数阶傅里叶变换的含噪信号特征提取

Feature Extraction of Noisy Signals Based on Short-Time Fractional Fourier Transform

摘要:

通过对比噪声背景下短时傅里叶变换和短时分数阶傅里叶变换的时频分辨能力,进一步明确了短时分数阶傅里叶变换对频率时变信号的独特优势。研究了短时分数阶傅里叶变换的窗口滑动方式对瞬时频率估计的影响,可以发现:首先,在调频率较大或是变化剧烈时,短时分数阶傅里叶变换具有更好的鲁棒性；其次,在基于短时分数阶傅里叶变换的瞬时频率估计,实际应用中应主要采用以第一采样时刻作为估计值的逐点滑动方式。

Abstract:

By comparing the time-frequency resolution of short-time Fourier transform with that of short-time fractionalFourier transform under noise background, the unique advantages of short-time fractional Fourier transform for frequencytime-varying signals were further clarified. Then the influence of window sliding mode of short-time fractional Fouriertransform on instantaneous frequency estimation was studied. It can be found that, firstly, the frequency modulation islarge or the change is dramatic. Short-time fractional Fourier transform has better robustness in severe time. Secondly, inthe practical application of instantaneous frequency estimation based on short-time fractional Fourier transform, point-bypoint sliding method with the first sampling time as the estimation value shouldbeadopted.