Difference: ClicNaff (3 vs. 4)
Revision 403 Nov 2014 - JackTowler
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Numerical Analysis of the Fundamental FrequenciesThis 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*} | ||||||||
| > > | %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% | ||||||||
| > > | \end{displaymath} %ENDLATEX% | ||||||||
which is at maximum amplitude for resonant frequency  . Numerical analysis can be performed about the resonant frequencies measured by the fourier transform: | |||||||||
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| < < | %BEGINLATEX%\begin{equation*} | ||||||||
| > > | %BEGINLATEX% \begin{displaymath} | ||||||||
| X(f)=\sum_{n=0}^N x(n)\exp(j 2\pi f n) | |||||||||
| Changed: | |||||||||
| < < | \end{equation*}%ENDLATEX% | ||||||||
| > > | \end{displaymath} %ENDLATEX% | ||||||||
where f is in the range  . 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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