Fourier變換的基本格式與PSD非參數(shù)估計(jì)

Basic forms of Fourier transformation and PSD nonparametric estimation

摘要: 以傳統(tǒng)Fourier變換為基礎(chǔ)的非參數(shù)估計(jì)方法是振動工程研究中PSD估計(jì)的重要方法。文章以周期圖法為例，研究Fourier變換基本格式的不同對PSD非參數(shù)估計(jì)結(jié)果的影響。首先介紹了Fourier變換常見的幾種基本格式及其對應(yīng)的PSD非參數(shù)估計(jì)計(jì)算公式；然后基于PSD的物理內(nèi)涵，分析、證明多種不同形式的PSD估計(jì)公式的同時存在是一種人為誤解，只有惟一的一種PSD估計(jì)結(jié)果才是具有典型物理意義的；最后給出了Fourier變換的一種通用格式及其PSD估計(jì)計(jì)算公式。

Abstract: Nonparametric estimation of power spectrum density (PSD) in vibration engineering, including the major approach as well as the periodogram method, is based on classical Fourier transformation (FT), but takes quite different forms. This paper discusses the influences of the FT forms on PSD estimation using non-parameter methods such as the periodogram method. First, several FT forms and PSD non-parameter methods are discussed. Then, it is shown that among different forms for PSD estimation only one has physical meaning consistent with the PSD concept. Finally, a general formula for FT and PSD estimation is proposed.