# Impulse coefficient when it does not match the bin index

Assume that I have a N=10 samples with Fs=10. assume in the time domain an unit impulse event happens which should be placed at 3.425 index in time domain. Assume that I could not change Fs or increase N How could i register such unit impulse inside a vector with 10 elements when it does not match to my bin index? I somehow understood it is related to Sinc function but still did not get how could I know the coefficients of the bins in the mentioned example settings.

For example it should be something like [0 0 .3 .52 .6 .43 .3 .2 0 0] but I have no idea how determine the numbers. Thanks

## 1 Answer

You need to design a fractional delay. That's not a trivial problem and requires a fair bit of math and requirements management. A really good resource is http://users.spa.aalto.fi/vpv/publications/vesan_vaitos/ch3_pt1_fir.pdf

• Thank you. Do you mean in order to know the coefficients of my example (vector of 10 elements) I need to go that much in depth ? I am not sure if I even put a lot of time I could connect that PDF to the solution of my problem by myself. Could you please let me know the answer at least if you know the method? I just know I need to use Sinc function. Thanks Oct 1 '19 at 19:22
• I think in my case it does not work as FD used when you want to have smooth transition between to samples and not when a unit impulse happens ( rapid change) between two samples Oct 3 '19 at 5:40