Difference: ClicNaff (3 vs. 4)

Revision 403 Nov 2014 - JackTowler

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META TOPICPARENT name="ClicBpm"

Numerical Analysis of the Fundamental Frequencies

This is a method of measuring the frequency with higher resolution than with just a standard discrete fourier transform:

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%BEGINLATEX%\begin{equation*}
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%BEGINLATEX% \begin{displaymath}
 X(k/N)=\sum_{n=0}^N x(n)\exp\left( j\frac{2\pi k}{N} n \right)
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\end{equation*}%ENDLATEX%
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\end{displaymath} %ENDLATEX%
  which is at maximum amplitude for resonant frequency $k_{max}/N$. Numerical analysis can be performed about the resonant frequencies measured by the fourier transform:
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%BEGINLATEX%\begin{equation*}
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%BEGINLATEX% \begin{displaymath}
 X(f)=\sum_{n=0}^N x(n)\exp(j 2\pi f n)
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\end{equation*}%ENDLATEX%
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\end{displaymath} %ENDLATEX%
  where f is in the range $k_{max}/N\pm1/N$. The frequency for which, this is a maximum is a more precise measure of the resonant frequency than with the fourier transform alone.
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