subject: Bessel Filter: An Over-all View Of Its Functions [print this page] Bessel Filter: An Over-all View Of Its Functions
A Bessel filter is used in signal and electronics processing. It is a linear filter which is used in crossover systems and usually has a group delay which is flat. The filtered signals of the group delay can maintain their wave shape in the pass band.
It is named after the German mathematician Friedrich Bessel. He created the mathematical theory which is used by the filters today. They are also called Thomson or Bessel-Thomson filters as W.E. Thomson was also involved in it. He became the first person to use the Bessel functions for creating a functional filter.
When it is used, the roll-off rate gain on either positions of the -3dB frequency is traded off. Here the gain decreases as a function of frequency. It is gentler than the Butterworth Filter for a specific n-order filter. This allows it to preserve the stages of the various elements within the input signal.
The best way to find the effective use of it is to compare it with Butterworth Filter of order n. The result will be readily apparent. Most filters are straightforward circuits but we need to know their good points and bad points while using them.
It employs the standard low-pass to high-pass transformation when a crossover is constructed using it. For best polar response and magnitude, several frequency normalizations can be chosen even though at higher frequencies the linear phase approximation is not maintained in the low-pass of the pass band.
It was not originally created to be used in a crossover and needs a minor modification to work properly. The purpose of it is to get approximately linear phase, which is the same to a time delay. It is the best phase response when we do not want to change an existing phase shift from an audible standpoint.
They are either low-pass or all-pass. However, a crossover needs a high-pass separately and this has to be obtained from the low-pass. Many ways are there to obtain a high-pass from a low-pass. The advantages of using it is it has the best step response and has very little overshoot. The disadvantage of using it is the slower initial rate of attenuation more than the pass-band in Butterworth.
Thus it has excellent pulse response with its ringing and minimal overshoot. A higher-order Bessel filter gives the same response as a Butterworth filter but the fidelity of the pulse response makes its complexity worth using. appnection between the two b
