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How can I determine by looking at the following tranfer function, that is this the transfer function of a band-pass filter:

$$\frac{1}{as^3+bs^2+cs+1}$$

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  • \$\begingroup\$ That is not a bandpass filter, and the order has something to do with the polynomial in the denominator. \$\endgroup\$ – a concerned citizen Apr 17 '18 at 6:13
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You could guess the form of the frequency response of the filter if you knew the poles and the zeroes of any TF. Then drawing the poles and the zeroes in the complex plane you could tell something about that.

In your case there is no zero (numerator is constant). So you have a denominator which is a 3rd order polynomial. To find the poles you must find the roots of that polynomial, which are a function of the coefficients a,b,c.

For algebraic equations up to the 4th order there are general formulas to find those roots. See here for 3rd order and here for 4th order.

Anyway, a 3rd order equation with real coefficients (assuming a,b,c are real) will have at least a real root and either another two real roots or a couple of complex conjugate roots.

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    \$\begingroup\$ I'd like to congratulate you on doing his homework. :-) \$\endgroup\$ – a concerned citizen Apr 17 '18 at 6:29
  • \$\begingroup\$ @aconcernedcitizen I'm not doing his homework. I'm giving him hints to do it himself. \$\endgroup\$ – Lorenzo Donati supports Monica Apr 17 '18 at 6:30

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