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Properties of Linear-phase FIR Filters 309
is constant, which is the group delay. Therefore α is called a constant
group delay. Inthis case, as a group, frequencies are delayed at a constant
rate. But some frequencies may get delayed more and others delayed less.
For this type of linear phase one can show that
h (n) =−h(M −1−n), 0 ≤ n ≤ (M −1); α = M − 1 ,β= ± π 2 2
(7.4)
This means that the impulse response h(n) isantisymmetric. The index
of symmetry is still α =(M − 1)/2. Once again we have two possible
types, one for M odd and one for M even.
• M odd: In this case α = (M − 1)/2 isaninteger and the impulse
response is as shown.
Antisymmetric Impulse Response: M odd
h(n)
0
0 (M – 1)/2 M – 1
n
Note that the sample h(α) atα =(M − 1)/2 must necessarily be equal
to zero, i.e., h((M − 1)/2) = 0.
• M even: In this case α =(M − 1)/2 isnot an integer and the impulse
response is as shown.
Antisymmetric Impulse Response: M even
h(n)
0
0 M/2+1 M/2 M – 1
n
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