Talk:Coherent sampling

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

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

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 ${\displaystyle T}$, so if we have a sinewave frequency of ${\displaystyle f_{in}}$, then the sinewave duration is ${\displaystyle {\frac {1}{fin}}}$, and we can write

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

Now equating ${\displaystyle T}$, we get:

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

and so we get:

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