[sdiy] Digital filtering question

[Thomas Strathmann]

Am 8/21/10 20:30 , schrieb 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!

To understand the ideal lowpass filter it's easier to look at the 
frequency domain representation which is just a rectangle centered 
around f=0 that extends to the positive and negative cutoff frequency.
Thus, if f_c is the cutoff frequency you get H(f) = 1 if |f| <= f_c and 
0 otherwise. The fourier transform (i.e. impulse response )of this 
rectangle function then is h(t) = 2*f_c * sinc(2*pi*f_c*t).

I would suggest you get a good book about system theory to get down the 
basics which are common to both analog and digital signal processing and 
then look for a text which deals with digital filter design. I cannot 
name any examples here because all the books I have on these subjects 
are in German although the one by Alfred Mertins is also available in 
English, but rather academic which may or may not be what you are 
looking for.

	Thomas