why bandpass is designed in symmetrical?

[elvis0206]

In DSP, I have encountered various types of filters.
Among them, I'm most interested in the bandpass filter. I wonder why it is designed in symmetrical about the y-axis?

That's the central frequency of the passbands of a bandpass filter is at frequency(doesn't matter it is normalized or not) v1 and -v1 on the positive and the negative x-axis respectively, but no other frequency, let say v1 on positive and -v2 on negative x-axis?

what is the objective for such design?
what effect it gives to the final result of the output?

I have found some books but found no answers about these....hope you guys can help

 

[FvM]

If you refer to standard filter prototypes (e.g. Butterworth, Chebyshev), they aren't symmetrical in a linear frequency scale rather than a logarithmic scale, which can be easily understood by the nature of there transmission function.

P.S.: I guess, FIR filters designed with a symmetrical impulse response tend to have a symmetrical frequency response in a linear scale.

 

[Communications_Engineer]

it is not a rule that bandpass filter should be symmetric, examples are given by FvM.


Usually FIR filters are designed to be symmetrical so that they have a linear phase response.

 

[elvis0206]

it is not a rule that bandpass filter should be symmetric, examples are given by FvM.


Usually FIR filters are designed to be symmetrical so that they have a linear phase response.

In other words, the symmetrical of the filter will give no distortion to the signal.
However, is the distortion-free signal is the final result of the output?
Will there any other specific results to be given?

 

[FvM]

In other words, the symmetrical of the filter will give no distortion to the signal.

The statement is about linear phase respectively symmetry in time domain. In my opinion, it's not more than a guess, that it's related to some kind of symmetry in frequency domain. Referring to your original question, you are guessing about a property of filter designs not explicitely stated or derived my the authors. What do you expect from this analysis?

Firstly, symmetry in frequency domain can only exist for band pass or -stop filters. So there's obviously no exact relation between linear phase and frequency domain behaviour. Secondly, the said filters aren't strictly symmetrical in frequency domain, particularly in the stop band.

Can you falsify this contradicting guess: A filter can be designed with arbitrary frequency response (e.g. non-sysmmetrical) and linear phase.