# Difference: ClicNaff (1 vs. 4)

#### Revision 403 Nov 2014 - JackTowler

Line: 1 to 1

 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:

Changed:
<
<
%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)
Changed:
<
<
\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:
Changed:
<
<
%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.
Line: 22 to 26

-->
>
>
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#### Revision 308 May 2013 - StewartBoogert

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Numerical Analysis of the Fundamental Frequencies

Line: 22 to 22

-->
Deleted:
<
<
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#### Revision 212 Feb 2013 - webmanip_5foldt2nt_2esh

Line: 1 to 1

 META TOPICPARENT name="ClicBpm"

# Numerical Analysis of the Fundamental Frequencies

Line: 23 to 23

• Set MYTITLE = - CTF3 BPM Prototype Overview
-->
Changed:
<
<
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>
>
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#### Revision 112 Feb 2013 - FrancisCullinan

Line: 1 to 1
>
>
 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:

which is at maximum amplitude for resonant frequency . Numerical analysis can be performed about the resonant frequencies measured by the fourier transform:

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.

<--
Set STYLESIDEBAR = off
Set MYTITLE = - CTF3 BPM Prototype Overview

-->

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Latex rendering error!! dvi file was not created.

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