I have an analog filter with its frequency response curve in dB described by the following expression:
$$
N_{dB}=20log_{10}\omega t_1 \sqrt{\frac{1+(\omega t_2)^2}{1+(\omega t_1)^2}}
$$
This expression is derived from the series connection of two lowpass filters each associated with the following RC circuit:
where, for each circuit, the time constant $t_i=RC$ and of course $\omega = 2\pi f$, where $f$ is the frequency (this is actually the equalization curve for magnetic tape recording/playback, see Annex B, page 14 of this document).
I would like to obtain an approximation of this frequency response using a digital filter. I don't know if there is a method to exploit our knowledge of the analog frequency response or if I should design the filter myself from scratch. The end goal is to obtain the impulse response and save it as a a .wav file (I know how to do this last part). I just took a basic DSP course at my Uni but we didn't work with analog filters so I am a little bit lost.