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# URGENT : Group Delay Chebyshev Filter

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#### Heidi.Eissa

##### Newbie level 4
I'm designing an analog chebyshev filter of order =10 and i want to know the formula of group delay , i know it's -1*derivative of phase of frequency response but i wonder if there is a clearer formula for the chebyshev filter relating the group delay with the filter order .. if you know i'd be very thankful for your help !

thank !

I don't know, if the formula that is available will be "clearer", but I can give you some background information to that expression.
There are in principle two alternatives:
1.) You can split the 10th order function into 5 separat transfer functions - each of 2nd order. For each of this functions you can use a delay formula that is available (expressed in terms of pole frequency and damping resp. pole Q). The final delay function then is the sum of the 5 delay functions.
2.) There is another formula based on the pole location of the 5 pole pairs. Thus, the delay formula consists of the sum of 5 expressions - each containing the real part of the respective pole and the squared magnitude of the difference (w-Sn), with Sn=pole location.
______________
As you will see, it's relatively complicated and I doubt if it really helps.
Nevertheless, if you are interested I can give you details (tell me if to 1) or 2)).

LvW

Heidi.Eissa

### Heidi.Eissa

Points: 2
I don't know, if the formula that is available will be "clearer", but I can give you some background information to that expression.
There are in principle two alternatives:
1.) You can split the 10th order function into 5 separat transfer functions - each of 2nd order. For each of this functions you can use a delay formula that is available (expressed in terms of pole frequency and damping resp. pole Q). The final delay function then is the sum of the 5 delay functions.
2.) There is another formula based on the pole location of the 5 pole pairs. Thus, the delay formula consists of the sum of 5 expressions - each containing the real part of the respective pole and the squared magnitude of the difference (w-Sn), with Sn=pole location.

As you will see, it's relatively complicated and I doubt if it really helps.
Nevertheless, if you are interested I can give you details (tell me if to 1) or 2)).

LvW

______________

thank you so much for your quick reply .. dunno , i feel that the first one is less complicated , so can you provide me with more details about it ?

OK, see the attachement for details.
Remember, at first you have to split the transfer functions into sepate bandpass functions Hi - each of 2nd order (of course).
Then you have to follow the group delay definition and to sum all components.
But I am afraid, it is a rather cumbersome procedure.
Good luck.
LvW

#### Attachments

• Group delay band pass.pdf
60.6 KB · Views: 81

Sorry, I just have realized that I have mixed your posting with another posting dealing with a high-order bandpass.
In your case, it is a lowpass - that's a bit more easy. Wait some minutes for my revised pdf-attachement.
LvW

Last edited:

See the attachement for the low pass case.
I hope there is no typing error.
Regards

CORRECTION (typing error) : In the pdf-attachement, the last expression (group delay of a standard 2nd order lowpass) has to be multiplied by 1/wp

#### Attachments

• Group delay low pass.pdf
63 KB · Views: 75
Last edited:

See the attachement for the low pass case.
I hope there is no typing error.
Regards

thank you so much .. but i have another question now 'if u don't mind :\$' when i plot the BER versus the OSNR for the chebyshev low pass filter of order =10 , when i use number of zero padding subcarriers=0 'since i'm using this filter in coherent optical OFDM system' and i found it don't decrease smoothly .. so can you tell me if you know why is that happening ?

thanks : )

Sorry, I can't. Perhaps another forum member has corresponding experience?

Hi Heidi,

there was a typing error in the pdf-attachement and I have corrected it, see my posting yesterday 14:11.
I am sorry.
LvW

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