Bessel Filters

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Bessel filters are all-pole filters with maximally flat pass-bands, maximally flat group delays, and poor "out-of-band" or stop-band attenuation compared to Butterworth, Chebyshev, and Elliptic filters of the same order. Since the group delays are relatively constant in the pass-band, Bessel filters exhibit minimal phase distortion, and hence very little overshoot in its step response.

The Low-Pass Bessel Filter

The transfer function of the low-pass Bessel filter is given by:

 

 

 

 

(1)

Where is the filter order, is the cut-off frequnecy, and is the reverse Bessel polynomial, and is equal to:

 

 

 

 

(2)

Where:

 

 

 

 

(3)

For . The low-pass Bessel filter characteristics are shown in Figs. 1-4.

Figure 1: The Bessel low-pass filter pole-zero plot for .
Figure 2: The Bessel low-pass filter magnitude response for .
Figure 3: The Bessel low-pass filter phase response for .
Figure 3: The Bessel low-pass filter group delay for .