Talk:Coherent sampling

The standard FFT equation which relates sampling frequency $fs$, number of samples, $N$ and time period of the FFT $T$ is:

$T={\frac {N}{f_{s}}}$

This equation is used in:

• http://www.maximintegrated.com/app-notes/index.mvp/id/3190
• http://enpub.fulton.asu.edu/jalali/EEE598_Fall07/EEE%20598,%20Week%201,Lecture2.pdf (slide 3)
• "Digital Signal Processing", Mulgrew, Grant and Thompson, 2nd ed, ISBN 0-333-96356-3, page 251
• "Numerical Recipes in C" Press, Teukolsky, Vetterling, Flannery, 2nd ed, ISBN 0-521-43108-5, page 550

For coherent sampling we want to have some number of cycles, M, of our sinewave within the period $T$, so if we have a sinewave frequency of $f_{in}$, then the sinewave duration is ${\frac {1}{fin}}$, and we can write

$T=M{\frac {1}{f_{in}}}$

Now equating $T$, we get:

${\frac {N}{f_{s}}}=M{\frac {1}{f_{in}}}$

and so we get:

${\frac {f_{in}}{f_{s}}}={\frac {M}{N}}$

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