TTHalfbandLinear33 is a 33-Pole Halfband filter built up from a 2-path allpass structure.
Same magnitude response with respect to frequency as TTHalfband9, but with nearly linear phase response.
The coefficients can be calculated using the "lineardesign_2.m" Matlab script. To generate the particular set of coefficients currently hard-coded into this filter, choose the following settings (yields a roughly -60dB stopband attenuation):
- iterations: 100 (iterations bring the filter toward equiripple in the stopband)
- wc = 0.2895 (this is the normalized frequency of the start of the stopband)
- number of paths = 2
- number of coefficients = 8
The result is:
Roots =
-0.832302165608369 -0.338171398434493 + 0.342959068350197i -0.338171398434493 - 0.342959068350197i -0.001794835916660 + 0.437771696086791i -0.001794835916660 - 0.437771696086791i 0.421285425003053 0.298484480776670 + 0.301855022798834i 0.298484480776670 - 0.301855022798834i
branch 1 - type1 coefficient 0.8323021656083688 -0.4212854250030528
branch 1 - type2 1st coefficient 0.6763427968689864 0.003589671833320152 -0.59696896155334
branch 1 - type2 2nd coefficient 0.2319808172827758 0.1916472793306732 0.1802094400534031
The ordering of the coefficients may not be at first obvious. The first line of coefficients are the two alpha coefficients for the first two (first-order) allpass filters, F0 and F1.
@ The second and third lines together provide the coefficient pairs for the remaining (second-order) filters. Thus, 0.6763427968689864 and 0.2319808172827758 are the coefficient pair for the first filter 0.003589671833320152 and 0.1916472793306732 are the coefficient pair for the second filter, and so on.
- Authors
- Timothy Place, Trond Lossius
- Copyright
- Copyright © 2010, Timothy Place
This code is licensed under the terms of the "New BSD License"
http://creativecommons.org/licenses/BSD/
Definition in file TTHalfbandLinear33.h.