[sdiy] Digital filtering question

[Tom Wiltshire]

Hi all,

All the textbooks tell me that the ideal digital lowpass filter has a filter kernel that is the Sinc function, Sin(x)/x. This function needs windowing for practical use since it continues to infinity in both directions, but that's just an implementation detail!

My question is: What's the cutoff frequency?

I can change it by altering x, but what's the relationship between the variable x and the cutoff? I understand that digital filters are usually specified as some fraction of the sample rate, so if "0" were be 0Hz, and "1" was the sample rate, what's the relation to the "x" in the Sinc function.

Any pointers to places where I can learn more of this stuff appreciated, but I've read the obvious places and still don't get it!

Thanks,
Tom