How to convert passband and stopband frequencies to poles and zeros

I have a NI 9229 digitizer with the following datasheet.

The datasheet mentions:

a passband frequency of $$0.453f_s$$ with a flatness of $$\le0.1\,\text{dB}$$ a stopband frequency of $$0.547f_s$$ with rejection of $$\ge100\,\text{dB}$$

I want to convert those numbers into poles/zeros to be able to establish the device frequency response.

I want to convert those numbers into poles/zeros

That is impossible. These are just two points out of the frequency response, and you need the full frequency response for that. There's almost certainly an analog filter with many-poles/zeros involved here as anti-aliasing filter. You can't even with a perfect model of that filter get all these coefficients from just two points!

to be able to establish the device frequency response.

You're trying to calculate the frequency response from something that needs to be calculated from the frequency response.

However, they do tell you that if your signal is bandlimited to less than $$0.453f_s$$, then you can assume the system is essentially flat. There you go – your frequency response below $$0.453f_s$$ is just $$H(f)=\text{const.}$$.

• Ok, I understand your explanation, but still can't obtain the values of poles and zeros.