If the zeros were on the imaginary axis, it sure would have been a NOTCH filter.
But, since the complex conjugate zeros are on the left of the jW axis, the transfer function has second order terms in both numerator and denominator.
I tried the Bode plot of the transfer function and ended up getting a high pass filter by assuming zeros at z1,z2= -1+i , -1 -i and poles at p1= -3 and p2= -5.
But does the asymptotic approximations end up with correct results?
How can i identify the type of filter if the transfer function is not in any of the standard forms ,for example , in case of a notch filter :
edit: i agree with the fact that there are many other filters apart from the 5 basic ones,but is there any way of predicting the behavior (approximating) given any pole-zero plot like the one above.