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If you consider the electric chain with arbitrary elements, you may be wondered by the obvious question: what are the necessary and enough conditions in order to prevent signal's distortion when passing through the chain?
The answer is that this chain must have constant amplitude-frequency response and linear phase response for all the frequncy range. That's why linear phase characteristic is so important and desirable.
constant amplitude-frequency response means that the plot of Magnitude vs frequency of the impulse response of the system is flat, at least in the band of interest. If not so the system will produce distortion by attenuating/amplifying the frequency components of the input signal in a selective manner (e.g. some harmonic components will be reduced and other will be enhanced).
In DSP context,an FIR filter is a linear phase filter.It is a simple tap delay filter whose output is weighted average of current and previous input samples.Phase linearity is particularly important for image processing systems as eye is very scensitive to phase change.
A linear phase filter is a filter for which the phase shift is a linear function of frequency. For example, if the phase shift is X degrees at frequency F, then the phase shift will be nX degrees at a frequency of nF. It is possible to achieve exact linear phase with a FIR filter. However, not all FIR filters have the linear phase property. Certain symmetry or anti-symmetry requirements of the filter coefficients are required for linear phase response. For example, for a filter with an odd number of taps (coefficients), if the coefficients are symmetrical with respect to the center tap, then the filter will have linear phase. Meeting this requirement does not, however, guarantee that the amplitude response with respect to frequency will be desireable. For a concise description of coefficient symmetry/anti-symmetry requirements, see
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For a practical method of linear filter design, search for "Parks-McClellan"