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:

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