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<p>Since published in 1988, the FFT Accumulation Method (FAM) has been used extensively to compute the Spectral Correlation Function (SCF) and the Spectral Coherence Function (SCoF) to obtain or detect cyclic features of cyclostationary signals. When the input is a Gaussian random variable (r.v.), the SCF (or SCoF) estimates are also random variables with some probability density function (pdf). Although the FAM is considered the most computationally efficient method, there has been no in-depth statistical analysis of the algorithm. This paper analyzes the statistics of spectral estimates of the SCF using the FAM algorithm by obtaining the pdf for the points covering the frequency and cycle frequency <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13634_2025_1241_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(\left(f;\alpha\right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>f</mi> <mo>;</mo> <mi>α</mi> </mfenced> </math></EquationSource> </InlineEquation> plane, and application examples with simulation results are provided. The method proposed in the paper can be extended to other algorithms, provided they can be given by a quadratic form.</p>

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The probability density function of spectral correlation function estimates

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月30日

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  • Miguel Tavares,
  • José Gerald,
  • João Goes

摘要

Since published in 1988, the FFT Accumulation Method (FAM) has been used extensively to compute the Spectral Correlation Function (SCF) and the Spectral Coherence Function (SCoF) to obtain or detect cyclic features of cyclostationary signals. When the input is a Gaussian random variable (r.v.), the SCF (or SCoF) estimates are also random variables with some probability density function (pdf). Although the FAM is considered the most computationally efficient method, there has been no in-depth statistical analysis of the algorithm. This paper analyzes the statistics of spectral estimates of the SCF using the FAM algorithm by obtaining the pdf for the points covering the frequency and cycle frequency \(\left(f;\alpha\right)\) f ; α plane, and application examples with simulation results are provided. The method proposed in the paper can be extended to other algorithms, provided they can be given by a quadratic form.