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Linear-Phase Discrete Filters

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.

Details

A discrete filter is said to have linear phase when its frequency response can be written in the form
H(
jω
e
)=r(ω)
jαω
e
.
Its impulse response is either symmetric,
h
n
=
h
L-1-n
,
or antisymmetric,
h
n
=-
h
L-1-n
,
where
L
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.
[2] Wikipedia. "Linear Phase." (Jun 12, 2012) en.wikipedia.org/wiki/Linear_phase.

External Links

Permanent Citation

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