# General transfer function for a bandpass filter

Is there a general form of transfer function (with peak frequency $\omega_m$ and quality factor $Q$) relevant for any type of bandpass filter ?

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a bandpass filter has two cutoff frequencies! –  stevenvh May 14 '12 at 12:00
well I meant the peak frequency, the frequency at which the gain is maximum –  snickers May 14 '12 at 12:02
Some bandpass filters have multiple peaks, like a Chebychev for example. –  Olin Lathrop May 14 '12 at 12:04
@snickers - even without the multiple peaks (Olin's comment) the center frequency isn't enough to know the bandwidth. –  stevenvh May 14 '12 at 12:06
@snickers - example of the frequency response of a Chebychev filter: cnx.org/content/m16895/latest/c92.png –  stevenvh May 14 '12 at 12:09
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## 1 Answer

No. Whilst a standard second-order bandpass section can be defined in this way ...

$H(s) = \dfrac{\dfrac{\omega_m}{Q}s}{s^2+\dfrac{\omega_m}{Q}s+\omega_m^2}$

... it is also possible to have a second-order bandpass filter with the same characteristic frequency and Q but with a different transfer function. This previous question which addresses a filter with a stop-band attenuation of 1 is a case-in-point.

Furthermore, higher-order filters will require more than just these two parameters to define them since there are more coefficients.

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