This Demonstration shows impulse and magnitude responses for examples of linear-phase discrete filters. Such filters have constant group delay (i.e. all the frequency components are delayed by the same amount), a property desirable in many applications. The impulse response of a linear-phase discrete filter is either symmetric or antisymmetric.

A discrete filter is said to have linear phase when its frequency response can be written in the form

.

Its impulse response is either symmetric,

,

or antisymmetric,

,

where is the length of the filter. In particular, an odd-length, antisymmetric filter must be 0 in the middle.

References

[1] M. Vetterli, J. Kovačević, and V. K. Goyal, Foundations of Signal Processing, Cambridge: Cambridge University Press, 2014. www.fourierandwavelets.org.