Electronic – What are the series inductors used for in this filter

A capacitor's complex impedance is given by

$$ \frac{1}{j \omega C} \Omega $$

where \$\omega\$ is the frequency, and \$C\$ the capacitance. For a low-frequency signal, you can see that the impedance will be relatively high. Conversely, you can see that for a high frequency signal, the impedance will be quite low.

A high-frequency signal will see the capacitor connected to ground, and travel through it, since it is a low impedance path, but a low frequency signal will not be affected by it. The capacitors to ground form a low-pass filter for the lines they're connected to, as they remove high-frequency signals from the line by giving those signals a low-impedance path to GND.

See this question.

You have drawn a differential choke not a common-mode choke - a CM choke has dots at the same end and doesn't easily saturate because current flowing sets up cancelling flux thus nearly entirely preventing saturation. The differential choke in your circuit very easily saturates because the fluxes from the two coils are additive.

The CM choke blocks only common mode currents i.e. currents of the same direction trying to enter and pass through the choke - this is a good example of transformer action. For differential currents (as per the signal you want to pass) the windings are in effect anti-phase and have a low impedance: -

impedance = \$j\omega (L - M)\$ where L is the inductance of a winding and M is the mutual inductance between windings. M is usually very close in value to L therefore the net inductance for differential signals is lower than for common mode signals. For common-mode currents, the impedance is \$j\omega (L + M)\$ i.e. significantly more than for differential currents.

I get the feeling that you are expecting a CM choke to deal with high frequency differential currents differently to low frequency currents. This is theoretically not the case but, in reality, because leakage inductances exist (not all the flux is shared between the two coils), there is a tendency for higher frequencies to receive more attenuation.

For more info read this on page 6