Bessel Filter: calculate group delay

[pavel47]

Hello,

Bessel filters is know by its good phase characteristics: in passband phase is proportional to frequency, so group delay (which is derivative of phase with respect to frequency) is constant.
But is there some formula that calculates exactly the group delay based on filter parameters:

• cut-off frequency
• filter order

Thanks in advance

Pavel

 

[FvM]

I believe group delay is derived from Bessel polynomial in this Wikipedia article https://en.wikipedia.org/wiki/Bessel_filter

 

[pavel47]

Thanks,
In the formula for group delay omega is normalized frequency, i.e. omega = omega' / omega_cut_off.
where omega' - is angular frequency, i.e. omega' = 2*Pi*F. Correct ?
When calculating delay at zero frequency (F = 0), I obtain group delay = 1.

But at zero frequency group delay should be 1/omega_cut_off ?

Where I've been mistaken with my considerations.

Thanks

 

[zorro]

Hi Pavel,

When using normalized frequencies you obtain group_delay=1 because in normalized values omega_cut_off =1 . So, you have group_delay=1/omega_cut_off as you expected.

Note that when using non-normalized values time has dimensions of seconds and omega has dimensions of 1/time (i.e. 1/s).
In normalized values, all (i.e. time as well as frequency) is adimensional (just numeric values refering to normalization values).
Regards

Z