High pass filter design

How to improve the out band rejection,especially lower than the band frequency,and the insertion loss is less than 3 dB?Thanks in advance!

Use an Eliptical type topology.

Could you please post some reference for that?

Thanks a lot!

Chebyshev has best out-of-band attenuation, Eliptic has steepest slope and smaller attenuation for the same filter order.
Specify cutoff frequency, minimum out-of-band attenuation at specified frequency, alowed passband ripple and how cutoff frequency is defined by ripple or 3dB attenuation.