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Bessel and Linear Phase Filters


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The Bessel Filter's and Linear Phase filter's distinguishing characteristic is the near constant group delay throughout the pass band of the low pass filter.

Filter Solutions normalizes Bessel and Linear Phase filters such that the prototype high frequency attenuation matches the Butterworth filter. The pass band attenuation of the Bessel filter increases with the order of the filter when this normalization is applied. However, Filter Solutions allows the user the option of selecting the desired pass band attenuation in dB's.  3dB attenuation is a popular choice for some.

Bessel filters modified for equiripple group delay are frequently referred to as Linear Phase filters.  The equiripple group delay had added efficiency in that the group delay remains flat farther into the stop band.  See the description of Delay Filters for more on the equiripple group delay.  Bessel and Linear Phase filters may be further modified to have a stop band with transmission zeros.

Below is an examples of Bessel and Linear Phase low pass and step responses.


 

Bessel Low Pass filter, 10Hz Pass Band Frequency
Bessel Low Pass filter, 10KR/S Pass Band Frequency
Bessel Modified With Equiripple Group Delay, Period=2.0
Linear Phase With Equiripple Group Delay, Period=2.0
Bessel Modified With Equiripple Group Delay, Period=2.6
Linear Phase With Equiripple Group Delay, Period=2.6
Bessel Modified With Stop Band
Bessel Modified With Stop Band
Bessel Modified With Stop Band and Equiripple Group Delay
Linear Phase With Stop Band and Equiripple Group Delay
Bessel Low Pass Filter Step Response
Bessel Low Pass Filter Step Response