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:

 \begin{displaymath} X(k/N)=\sum_{n=0}^N x(n)\exp\left( j\frac{2\pi k}{N} n \right) \end{displaymath}

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:

 \begin{displaymath} X(f)=\sum_{n=0}^N x(n)\exp(j 2\pi f n) \end{displaymath}

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.


This topic: PP/JAI > BeamPosition > ClicBpm > ClicNaff
Topic revision: r4 - 03 Nov 2014 - JackTowler
 
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