Linear phase
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Linear phase is a property of a filter, where the phase response of the filter is a linear function of frequency, excluding the possibility of wraps at 
. Perfect linear phase is equivalent to a symmetrical impulse response; therefore, it can only be achieved by a (digital) FIR filter.
Since the group delay of a filter that has linear phase (or generalized linear phase) property is constant, all frequency components have equal delay times. So the distortion due to the frequency selective delays are not present which is mostly a desired feature. However, a filter with non-linear phase has a group delay that varies with frequency, resulting in phase distortion.
Some examples of filters having linear and non-linear phases are given below for comparison purposes. 
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