Linear-Phase Discrete Filters

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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.

Contributed by: Jelena Kovacevic (June 2012)
Open content licensed under CC BY-NC-SA



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.


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

[2] Wikipedia. "Linear Phase." (Jun 12, 2012)

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