Type of Filter from pole-zero plot

active-filterfilterfrequency responsepole-zeroplot

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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 :

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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.

Best Answer

Certainly, it is not one of the classical response types - but a mixture. To desribe the response in words:

In your pn-diagram, the two real poles have larger pole frequecies than the zero frequency of the pair of zeros. From this it can be concluded that the frequency response has, in principle, a highpass-notch behaviour. However, because the zeros have a small real part the notch depth is finite.

The corresponding transfer function contains a second-order polynominal in both, numerator and denominator. The pole Q is very low (Q<0.5) and the zero-Q is rather high.

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