I am taking a look to digital filters used on sigma-delta ADCs, my doubt is about sinc filters.
Here an example about sinc filters I've found on datasheet:
Sinc1:
- 4th order, decimate by 2, 5 taps (1 4 6 4 1)
$H(z) = \left(\frac{1-Z^{-2}}{1-Z^{-1}}\right)^4$
Sinc2:
- 5th order, decimate by 2, 6 taps (1 5 10 10 5 1)
$H(z) = \left(\frac{1-Z^{-2}}{1-Z^{-1}}\right)^5 $
Both used for decimation by 2.
Ok, for now don't take care sum of kernel/taps should give me 1...
For Sinc1 $H(z)$ equals to $(z+1)^4 = z^4+4z^3+6z^2+4z+1$ (then 1 4 6 4 1 taps)
The same for Sinc2.
- why $H(z)$ written in first way? It looks IIR transfer function instead FIR...
- why sometimes using even number of taps and sometimes odd ones?
- how can I get transfer functions above starting from sinc function as $$\text{sinc}(n) = \frac{\sin(2 \pi \frac{Fc}{Fs}n)}{\pi n}$$ where $F_c$ and $F_s$ are cut-off frequency and sampling frequency?
Thanks.