Anti-symmetrical and symmetrical impulse

For what kind of application, the anti-symmetrical impulse and the symmetrical impulse response may be used?

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The anti- symmetrical impulse response may be used in order to develop Hilbert transforms and differentiators.
The impulse response that is symmetric with odd number of the samples may be used in order to design all the types of filters, like, high pass, low pass, band pass and the band reject. The symmetric impulse response with the even number of samples may be used in order to develop the band pass and low pass filter.

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