Bessel-Filter
A Bessel filter is a frequency filter in the draft of the following (equivalent) properties were pursued:
- Optimal " transfer response rectangle ", i.e., a wave form, the frequency components falling within the passband of the filter, will (except for a delay ) unchanged at the output;
- Constant group delay in the passband;
- Linear phase response in the passband.
It is accepted that the amplitude curve bends not as sharp as with Butterworth filter or Chebyshev filters.
In the digital signal processing Bessel filter ( recursive filter structure ) can be realized by selecting the appropriate filter coefficients in the IIR filters.
The filter is named Friedrich Bessel (1784-1846) after the German mathematician.
Transfer function
The transfer function is optimized to make the group delay of the frequency independent.
Having the transfer function for a filter of order n
With
Can be used for the coefficients of the recursion formula
Determine.
Properties
The Bessel filter has the following properties:
- Smooth frequency response in the passband
- Low slope of the amplitude response (low even when compared with Butterworth filter ) to the cutoff frequency
- Small overshoot in the step response, decreases with the order
- Constant group delay in the passband