Multiplierless QMF filter-bank coefficients found by DLM (April 1999) Ref: B. W. Wah, Y. Shang, and Z. Wu, "Discrete {L}agrangian Method for Optimizing the Design of Multiplierless QMF Filter Banks," IEEE Transactions on Circuits and Systems, Part II, (accepted to appear) 1999. --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 16a Filter len=16 Due to symmetrcity, only 8 coefficients are presented. Scaling Factor= 0.9747 Next are continuous coefficients 0.481024710131851 0.097780236466990 -0.090391143989817 -0.009658802126791 0.027616879897716 -0.002578159252827 -0.005057741828340 0.001056947450803 Next are discrete coefficients in binary form +2**(- 1) -2**(- 5) +2**(-13) -2**(-16) -2**(-19) -2**(-23) = 0.46885478 = 0.48102471 * 0.9747 +2**(- 3) -2**(- 5) +2**(- 9) -2**(-11) +2**(-13) -2**(-15) = 0.09530640 = 0.09778024 * 0.9747 -2**(- 4) -2**(- 6) -2**(- 7) -2**(- 9) -2**(-12) +2**(-15) = -0.08810425 = -0.09039114 * 0.9747 -2**(- 7) -2**(- 9) +2**(-11) -2**(-13) -2**(-16) +2**(-22) = -0.00941443 = -0.00965880 * 0.9747 +2**(- 5) -2**(- 8) -2**(-11) +2**(-14) +2**(-19) -2**(-22) = 0.02691817 = 0.02761688 * 0.9747 -2**(- 9) -2**(-11) -2**(-14) -2**(-16) +2**(-18) +2**(-20) = -0.00251293 = -0.00257816 * 0.9747 -2**(- 8) -2**(-10) -2**(-14) +2**(-16) -2**(-20) -2**(-22) = -0.00492978 = -0.00505774 * 0.9747 +2**(-10) +2**(-14) -2**(-17) +2**(-22) = 0.00103021 = 0.00105695 * 0.9747 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 16b Filter len=16 Due to symmetrcity, only 8 coefficients are presented. Scaling Factor= 0.8524 Next are continuous coefficients 0.477383137868078 0.106698747309985 -0.095268976291207 -0.016076192224826 0.035935922834807 -0.001960173983464 -0.009867841231885 0.002897719943093 Next are discrete coefficients in binary form +2**(- 1) -2**(- 3) +2**(- 5) +2**(-10) -2**(-12) -2**(-14) = 0.40692139 = 0.47738314 * 0.8524 +2**(- 3) -2**(- 5) -2**(- 8) +2**(-10) +2**(-13) +2**(-17) = 0.09095001 = 0.10669875 * 0.8524 -2**(- 4) -2**(- 6) -2**(- 8) +2**(-10) -2**(-13) -2**(-15) = -0.08120728 = -0.09526898 * 0.8524 -2**(- 6) +2**(- 9) -2**(-15) -2**(-20) = -0.01370335 = -0.01607619 * 0.8524 +2**(- 5) -2**(-11) -2**(-13) -2**(-17) -2**(-22) = 0.03063178 = 0.03593592 * 0.8524 -2**(- 9) +2**(-12) +2**(-15) +2**(-17) -2**(-26) = -0.00167085 = -0.00196017 * 0.8524 -2**(- 7) -2**(-11) -2**(-13) +2**(-16) -2**(-18) +2**(-24) = -0.00841135 = -0.00986784 * 0.8524 +2**(- 9) +2**(-11) +2**(-15) -2**(-19) = 0.00247002 = 0.00289772 * 0.8524 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 16c Filter len=16 Due to symmetrcity, only 8 coefficients are presented. Scaling Factor= 0.5967 Next are continuous coefficients 0.472569787284528 0.117426419429929 -0.099628361184553 -0.025769744024058 0.046528382618583 0.001719664424553 -0.020558857650079 0.006673932175391 Next are discrete coefficients in binary form +2**(- 2) +2**(- 5) +2**(-10) -2**(-12) -2**(-25) = 0.28198239 = 0.47256979 * 0.5967 +2**(- 4) +2**(- 7) -2**(-12) -2**(-26) = 0.07006834 = 0.11742642 * 0.5967 -2**(- 4) +2**(- 8) -2**(-10) +2**(-13) -2**(-30) = -0.05944824 = -0.09962836 * 0.5967 -2**(- 6) +2**(-12) +2**(-18) +2**(-22) = -0.01537681 = -0.02576974 * 0.5967 +2**(- 5) -2**(- 8) +2**(-11) -2**(-14) -2**(-17) +2**(-23) = 0.02776349 = 0.04652838 * 0.5967 +2**(-10) +2**(-14) -2**(-16) +2**(-18) -2**(-25) = 0.00102612 = 0.00171966 * 0.5967 -2**(- 6) +2**(- 8) -2**(-11) -2**(-14) +2**(-21) +2**(-23) = -0.01226747 = -0.02055886 * 0.5967 +2**(- 8) +2**(-14) +2**(-16) -2**(-22) +2**(-25) = 0.00398234 = 0.00667393 * 0.5967 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 24b Filter len=24 Due to symmetrcity, only 12 coefficients are presented. Scaling Factor= 0.9661 Next are continuous coefficients 0.473115646793487 0.116024287809880 -0.098294296714784 -0.025618213289903 0.044238603136058 0.003899936658257 -0.019014258029828 0.001434311957083 0.006487472940091 -0.001365212275737 -0.001413705444968 0.000402756284426 Next are discrete coefficients in binary form +2**(- 1) -2**(- 4) +2**(- 6) +2**(- 8) +2**(-14) -2**(-16) = 0.45707703 = 0.47311565 * 0.9661 +2**(- 3) -2**(- 6) +2**(- 9) +2**(-11) +2**(-12) +2**(-15) = 0.11209106 = 0.11602429 * 0.9661 -2**(- 3) +2**(- 5) -2**(-10) -2**(-12) +2**(-17) +2**(-20) = -0.09496212 = -0.09829430 * 0.9661 -2**(- 6) -2**(- 7) -2**(-10) -2**(-12) -2**(-14) -2**(-15) = -0.02474976 = -0.02561821 * 0.9661 +2**(- 4) -2**(- 6) -2**(- 8) -2**(-12) +2**(-16) -2**(-20) = 0.04273891 = 0.04423860 * 0.9661 +2**(- 8) -2**(-13) -2**(-16) -2**(-20) -2**(-22) = 0.00376773 = 0.00389994 * 0.9661 -2**(- 6) -2**(- 8) +2**(-10) +2**(-12) -2**(-14) +2**(-19) = -0.01836967 = -0.01901426 * 0.9661 +2**(- 9) -2**(-11) -2**(-14) -2**(-16) -2**(-18) +2**(-20) = 0.00138569 = 0.00143431 * 0.9661 +2**(- 7) -2**(- 9) +2**(-11) -2**(-14) -2**(-16) -2**(-18) = 0.00626755 = 0.00648747 * 0.9661 -2**(- 9) +2**(-11) +2**(-13) +2**(-15) -2**(-17) +2**(-20) = -0.00131893 = -0.00136521 * 0.9661 -2**(- 9) +2**(-11) +2**(-13) -2**(-15) +2**(-17) -2**(-23) = -0.00136578 = -0.00141371 * 0.9661 +2**(-11) -2**(-13) +2**(-15) -2**(-17) +2**(-28) = 0.00038910 = 0.00040276 * 0.9661 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 24c Filter len=24 Due to symmetrcity, only 12 coefficients are presented. Scaling Factor= 0.6413 Next are continuous coefficients 0.468684900909286 0.124606702511013 -0.099978914651970 -0.034500614596328 0.050845280761338 0.009968000846517 -0.027467024859820 -0.000577178924147 0.013363039774250 -0.002242551566695 -0.005112633454145 0.002432981110690 Next are discrete coefficients in binary form +2**(- 2) +2**(- 4) -2**(- 6) +2**(- 8) -2**(-12) +2**(-15) = 0.30056763 = 0.46868490 * 0.6413 +2**(- 4) +2**(- 6) +2**(- 9) -2**(-12) +2**(-14) +2**(-16) = 0.07991028 = 0.12460670 * 0.6413 -2**(- 4) -2**(- 9) +2**(-11) -2**(-13) -2**(-15) +2**(-20) = -0.06411648 = -0.09997891 * 0.6413 -2**(- 5) +2**(- 7) +2**(- 9) -2**(-11) -2**(-13) -2**(-15) = -0.02212524 = -0.03450061 * 0.6413 +2**(- 5) +2**(- 9) -2**(-11) -2**(-13) +2**(-16) -2**(-20) = 0.03260708 = 0.05084528 * 0.6413 +2**(- 7) -2**(- 9) +2**(-11) +2**(-14) -2**(-16) -2**(-20) = 0.00639248 = 0.00996800 * 0.6413 -2**(- 6) -2**(- 9) -2**(-15) -2**(-17) +2**(-19) -2**(-22) = -0.01761460 = -0.02746702 * 0.6413 -2**(-11) +2**(-13) -2**(-18) -2**(-23) = -0.00037014 = -0.00057718 * 0.6413 +2**(- 7) +2**(-10) -2**(-12) +2**(-15) -2**(-17) +2**(-19) = 0.00856972 = 0.01336304 * 0.6413 -2**(- 9) +2**(-11) +2**(-15) -2**(-18) -2**(-27) = -0.00143815 = -0.00224255 * 0.6413 -2**(- 8) +2**(-11) +2**(-13) +2**(-16) +2**(-19) +2**(-31) = -0.00327873 = -0.00511263 * 0.6413 +2**(- 9) -2**(-11) +2**(-13) -2**(-15) +2**(-18) +2**(-24) = 0.00156027 = 0.00243298 * 0.6413 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 24d Filter len=24 Due to symmetrcity, only 12 coefficients are presented. Scaling Factor= 0.5342 Next are continuous coefficients 0.465604438624637 0.129904652391646 -0.100089387026051 -0.040619527744649 0.054124855718466 0.015313774403094 -0.033078681034615 -0.003825765743277 0.019651791969965 -0.001572794969588 -0.010511483292774 0.004854955641083 Next are discrete coefficients in binary form +2**(- 2) -2**(-10) -2**(-12) -2**(-14) +2**(-17) = 0.24872589 = 0.46560444 * 0.5342 +2**(- 4) +2**(- 7) -2**(-10) +2**(-14) -2**(-19) = 0.06939507 = 0.12990465 * 0.5342 -2**(- 4) +2**(- 7) +2**(-10) +2**(-12) -2**(-20) = -0.05346775 = -0.10008939 * 0.5342 -2**(- 5) +2**(- 7) +2**(- 9) -2**(-12) +2**(-15) -2**(-20) = -0.02169895 = -0.04061953 * 0.5342 +2**(- 5) -2**(- 9) -2**(-11) +2**(-13) -2**(-16) -2**(-19) = 0.02891350 = 0.05412486 * 0.5342 +2**(- 7) +2**(-11) -2**(-13) +2**(-19) = 0.00818062 = 0.01531377 * 0.5342 -2**(- 6) -2**(- 9) -2**(-13) +2**(-15) -2**(-20) = -0.01767063 = -0.03307868 * 0.5342 -2**(- 9) -2**(-13) +2**(-15) +2**(-20) = -0.00204372 = -0.00382577 * 0.5342 +2**(- 6) -2**(- 8) -2**(-10) -2**(-12) -2**(-24) = 0.01049799 = 0.01965179 * 0.5342 -2**(-10) +2**(-13) +2**(-16) -2**(-20) = -0.00084019 = -0.00157279 * 0.5342 -2**(- 7) +2**(- 9) +2**(-12) = -0.00561523 = -0.01051148 * 0.5342 +2**(- 9) +2**(-11) +2**(-13) +2**(-15) -2**(-21) = 0.00259352 = 0.00485496 * 0.5342 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 32c Filter len=32 Due to symmetrcity, only 16 coefficients are presented. Scaling Factor= 0.5706 Next are continuous coefficients 0.466412926321902 0.128520399990142 -0.099803203872911 -0.039313525180837 0.052945554528034 0.014531374228364 -0.031212526917082 -0.004156865114251 0.017940413103662 -0.000143214104429 -0.009407944483712 0.001397643263115 0.004198433504245 -0.001232623218278 -0.001418038998994 0.000720379480428 Next are discrete coefficients in binary form +2**(- 2) +2**(- 6) +2**(-11) +2**(-15) -2**(-17) -2**(-20) = 0.26613522 = 0.46641293 * 0.5706 +2**(- 4) +2**(- 6) -2**(- 8) -2**(-10) +2**(-13) -2**(-15) = 0.07333374 = 0.12852040 * 0.5706 -2**(- 4) +2**(- 7) -2**(- 9) -2**(-12) -2**(-14) -2**(-19) = -0.05694771 = -0.09980320 * 0.5706 -2**(- 5) +2**(- 7) +2**(-10) +2**(-15) -2**(-19) +2**(-25) = -0.02243230 = -0.03931353 * 0.5706 +2**(- 5) -2**(-10) -2**(-14) -2**(-19) +2**(-22) = 0.03021073 = 0.05294555 * 0.5706 +2**(- 7) +2**(-11) -2**(-17) -2**(-19) +2**(-21) -2**(-23) = 0.00829160 = 0.01453137 * 0.5706 -2**(- 6) -2**(- 9) -2**(-12) +2**(-16) -2**(-18) +2**(-20) = -0.01780987 = -0.03121253 * 0.5706 -2**(- 9) -2**(-11) +2**(-14) +2**(-17) +2**(-20) -2**(-23) = -0.00237191 = -0.00415687 * 0.5706 +2**(- 7) +2**(- 9) +2**(-11) -2**(-16) -2**(-19) +2**(-24) = 0.01023680 = 0.01794041 * 0.5706 -2**(-13) +2**(-15) +2**(-17) +2**(-19) +2**(-22) +2**(-24) = -0.00008172 = -0.00014321 * 0.5706 -2**(- 7) +2**(- 9) +2**(-11) +2**(-18) -2**(-20) +2**(-24) = -0.00536817 = -0.00940794 * 0.5706 +2**(-10) -2**(-12) +2**(-14) +2**(-18) +2**(-22) -2**(-26) = 0.00079750 = 0.00139764 * 0.5706 +2**(- 9) +2**(-11) -2**(-14) +2**(-16) -2**(-28) = 0.00239563 = 0.00419843 * 0.5706 -2**(-10) +2**(-12) +2**(-15) -2**(-19) +2**(-21) = -0.00070333 = -0.00123262 * 0.5706 -2**(-10) +2**(-12) -2**(-14) -2**(-16) -2**(-21) +2**(-24) = -0.00080913 = -0.00141804 * 0.5706 +2**(-11) -2**(-14) -2**(-16) -2**(-20) +2**(-26) = 0.00041105 = 0.00072038 * 0.5706 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 32d Filter len=32 Due to symmetrcity, only 16 coefficients are presented. Scaling Factor= 0.6971 Next are continuous coefficients 0.463783133920886 0.132820798102042 -0.099381318377587 -0.044441414672869 0.054853630448975 0.019393569512341 -0.034934726067175 -0.007923790259711 0.022662590572985 0.002014489071969 -0.014118331864855 0.000877952219988 0.008053852109207 -0.002060296355165 -0.003748483183120 0.002346222138340 Next are discrete coefficients in binary form +2**(- 2) +2**(- 4) +2**(- 6) -2**(- 8) -2**(-10) +2**(-14) = 0.32330322 = 0.46378313 * 0.6971 +2**(- 3) -2**(- 5) -2**(-10) -2**(-12) +2**(-14) -2**(-20) = 0.09258938 = 0.13282080 * 0.6971 -2**(- 4) -2**(- 7) +2**(-10) +2**(-14) -2**(-18) = -0.06927872 = -0.09938132 * 0.6971 -2**(- 5) +2**(-12) +2**(-15) -2**(-18) -2**(-20) = -0.03098011 = -0.04444141 * 0.6971 +2**(- 5) +2**(- 7) -2**(-10) +2**(-13) +2**(-15) -2**(-24) = 0.03823847 = 0.05485363 * 0.6971 +2**(- 6) -2**(- 9) -2**(-13) -2**(-15) -2**(-25) = 0.01351926 = 0.01939357 * 0.6971 -2**(- 5) +2**(- 7) -2**(-10) +2**(-14) +2**(-25) = -0.02435300 = -0.03493473 * 0.6971 -2**(- 7) +2**(- 9) +2**(-11) -2**(-13) -2**(-15) +2**(-27) = -0.00552367 = -0.00792379 * 0.6971 +2**(- 6) +2**(-12) -2**(-14) -2**(-17) -2**(-19) -2**(-21) = 0.01579809 = 0.02266259 * 0.6971 +2**(- 9) -2**(-11) -2**(-14) +2**(-21) +2**(-26) = 0.00140430 = 0.00201449 * 0.6971 -2**(- 7) -2**(- 9) -2**(-14) -2**(-16) +2**(-25) = -0.00984189 = -0.01411833 * 0.6971 +2**(-11) +2**(-13) +2**(-19) -2**(-22) = 0.00061202 = 0.00087795 * 0.6971 +2**(- 7) -2**(- 9) -2**(-12) -2**(-20) +2**(-24) = 0.00561434 = 0.00805385 * 0.6971 -2**(- 9) +2**(-11) +2**(-15) -2**(-19) +2**(-30) = -0.00143623 = -0.00206030 * 0.6971 -2**(- 8) +2**(-10) +2**(-12) +2**(-14) +2**(-16) -2**(-18) = -0.00261307 = -0.00374848 * 0.6971 +2**(- 9) -2**(-12) -2**(-14) -2**(-16) +2**(-18) -2**(-20) = 0.00163555 = 0.00234622 * 0.6971 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 32e Filter len=32 Due to symmetrcity, only 16 coefficients are presented. Scaling Factor= 0.5019 Next are continuous coefficients 0.460165434779162 0.138221021714166 -0.098198681956958 -0.050771416634957 0.056183939080809 0.025932948934673 -0.038656206999340 -0.013901337515099 0.028334709055444 0.006779657224422 -0.021159352000241 -0.002105341985611 0.015634254384122 -0.001261685088850 -0.011130950678438 0.005481869700801 Next are discrete coefficients in binary form +2**(- 2) -2**(- 6) -2**(- 8) +2**(-11) +2**(-31) = 0.23095703 = 0.46016543 * 0.5019 +2**(- 4) +2**(- 7) -2**(-10) +2**(-15) +2**(-17) -2**(-20) = 0.06937313 = 0.13822102 * 0.5019 -2**(- 4) +2**(- 6) -2**(- 9) -2**(-11) +2**(-15) -2**(-25) = -0.04928592 = -0.09819868 * 0.5019 -2**(- 5) +2**(- 7) -2**(- 9) -2**(-13) +2**(-15) +2**(-28) = -0.02548217 = -0.05077142 * 0.5019 +2**(- 5) -2**(- 8) +2**(-10) -2**(-13) +2**(-21) = 0.02819872 = 0.05618394 * 0.5019 +2**(- 6) -2**(- 8) +2**(-10) +2**(-12) +2**(-14) +2**(-16) = 0.01301575 = 0.02593295 * 0.5019 -2**(- 6) -2**(- 8) +2**(-13) +2**(-17) = -0.01940155 = -0.03865621 * 0.5019 -2**(- 7) +2**(-10) -2**(-13) -2**(-16) -2**(-18) = -0.00697708 = -0.01390134 * 0.5019 +2**(- 6) -2**(- 9) +2**(-11) +2**(-14) -2**(-30) = 0.01422119 = 0.02833471 * 0.5019 +2**(- 8) -2**(-11) -2**(-16) = 0.00340271 = 0.00677966 * 0.5019 -2**(- 6) +2**(- 8) +2**(-10) +2**(-13) +2**(-22) = -0.01061988 = -0.02115935 * 0.5019 -2**(-10) -2**(-14) -2**(-16) -2**(-18) = -0.00105667 = -0.00210534 * 0.5019 +2**(- 7) +2**(-15) +2**(-18) = 0.00784683 = 0.01563425 * 0.5019 -2**(-11) -2**(-13) -2**(-15) +2**(-17) = -0.00063324 = -0.00126169 * 0.5019 -2**(- 7) +2**(- 9) +2**(-12) +2**(-15) -2**(-19) = -0.00558662 = -0.01113095 * 0.5019 +2**(- 8) -2**(-10) -2**(-12) +2**(-14) +2**(-18) +2**(-20) = 0.00275135 = 0.00548187 * 0.5019 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 48c Filter len=48 Due to symmetrcity, only 24 coefficients are presented. Scaling Factor= 0.7914 Next are continuous coefficients 0.464222724611843 0.132073167902609 -0.099385058846714 -0.043593785785080 0.054325935724320 0.018812932539143 -0.034086265014463 -0.007801475264612 0.021734230440616 0.002462513267519 -0.013439890890673 -0.000057844616923 0.007837626679184 -0.000756769611705 -0.004212844844777 0.000787535971814 0.002036529687549 -0.000527209305977 -0.000855282216413 0.000243946732913 0.000300641612465 -0.000054980276328 -0.000092166689895 -0.000012643580669 Next are discrete coefficients in binary form +2**(- 1) -2**(- 3) -2**(- 7) +2**(-12) -2**(-14) +2**(-16) = 0.36738586 = 0.46422272 * 0.7914 +2**(- 4) +2**(- 5) +2**(- 7) +2**(- 9) +2**(-10) +2**(-15) = 0.10452271 = 0.13207317 * 0.7914 -2**(- 4) -2**(- 6) -2**(-11) -2**(-15) -2**(-17) -2**(-19) = -0.07865334 = -0.09938506 * 0.7914 -2**(- 5) -2**(- 9) -2**(-10) -2**(-12) -2**(-14) -2**(-16) = -0.03450012 = -0.04359379 * 0.7914 +2**(- 4) -2**(- 6) -2**(- 8) +2**(-15) -2**(-17) +2**(-19) = 0.04299355 = 0.05432594 * 0.7914 +2**(- 6) -2**(-10) +2**(-12) -2**(-18) -2**(-22) +2**(-25) = 0.01488855 = 0.01881293 * 0.7914 -2**(- 5) +2**(- 8) +2**(-11) -2**(-13) +2**(-19) -2**(-22) = -0.02697587 = -0.03408627 * 0.7914 -2**(- 7) +2**(- 9) -2**(-12) -2**(-14) -2**(-17) -2**(-19) = -0.00617409 = -0.00780148 * 0.7914 +2**(- 6) +2**(- 9) -2**(-11) +2**(-13) -2**(-16) +2**(-18) = 0.01720047 = 0.02173423 * 0.7914 +2**(- 9) -2**(-18) -2**(-21) -2**(-31) = 0.00194883 = 0.00246251 * 0.7914 -2**(- 6) +2**(- 8) +2**(-10) +2**(-13) -2**(-16) -2**(-20) = -0.01063633 = -0.01343989 * 0.7914 -2**(-14) +2**(-16) -2**(-29) = -0.00004578 = -0.00005784 * 0.7914 +2**(- 8) +2**(- 9) +2**(-12) +2**(-14) +2**(-15) +2**(-17) = 0.00620270 = 0.00783763 * 0.7914 -2**(-11) -2**(-13) +2**(-16) -2**(-18) = -0.00059891 = -0.00075677 * 0.7914 -2**(- 9) -2**(-10) -2**(-12) -2**(-13) -2**(-15) -2**(-17) = -0.00333405 = -0.00421284 * 0.7914 +2**(-11) +2**(-13) +2**(-16) -2**(-19) -2**(-21) +2**(-25) = 0.00062326 = 0.00078754 * 0.7914 +2**(- 9) -2**(-11) +2**(-13) +2**(-15) -2**(-17) +2**(-19) = 0.00161171 = 0.00203653 * 0.7914 -2**(-11) +2**(-14) +2**(-17) +2**(-19) +2**(-21) -2**(-30) = -0.00041723 = -0.00052721 * 0.7914 -2**(-10) +2**(-12) +2**(-14) -2**(-17) +2**(-19) +2**(-22) = -0.00067687 = -0.00085528 * 0.7914 +2**(-12) -2**(-14) +2**(-17) +2**(-19) +2**(-21) -2**(-24) = 0.00019306 = 0.00024395 * 0.7914 +2**(-12) -2**(-17) +2**(-19) -2**(-21) -2**(-26) +2**(-30) = 0.00023793 = 0.00030064 * 0.7914 -2**(-14) +2**(-16) +2**(-19) +2**(-21) -2**(-23) = -0.00004351 = -0.00005498 * 0.7914 -2**(-14) -2**(-16) +2**(-18) -2**(-21) +2**(-26) +2**(-31) = -0.00007294 = -0.00009217 * 0.7914 -2**(-17) -2**(-19) -2**(-21) +2**(-27) = -0.00001001 = -0.00001264 * 0.7914 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 48d Filter len=48 Due to symmetrcity, only 24 coefficients are presented. Scaling Factor= 0.7138 Next are continuous coefficients 0.461392390624453 0.136384245192981 -0.098457721208918 -0.048693771554696 0.055384054742430 0.023986151586497 -0.036900435618975 -0.012381199061553 0.025791158593312 0.005992195725808 -0.018090151644915 -0.002340764082858 0.012435309190181 0.000324326758627 -0.008210710999544 0.000639301149342 0.005114075181597 -0.000948263303543 -0.002931633326947 0.000882796728167 0.001487026497843 -0.000646649438415 -0.000621264439800 0.000433549055301 Next are discrete coefficients in binary form +2**(- 2) +2**(- 4) +2**(- 6) +2**(-10) +2**(-12) -2**(-18) = 0.32934189 = 0.46139239 * 0.7138 +2**(- 4) +2**(- 5) +2**(- 8) -2**(-11) +2**(-13) +2**(-14) = 0.09735107 = 0.13638425 * 0.7138 -2**(- 4) -2**(- 7) +2**(-15) +2**(-18) -2**(-20) = -0.07027912 = -0.09845772 * 0.7138 -2**(- 5) -2**(- 8) +2**(-11) -2**(-13) +2**(-15) +2**(-19) = -0.03475761 = -0.04869377 * 0.7138 +2**(- 5) +2**(- 7) +2**(-11) -2**(-16) -2**(-19) -2**(-21) = 0.03953314 = 0.05538405 * 0.7138 +2**(- 6) +2**(- 9) -2**(-11) +2**(-15) +2**(-20) -2**(-27) = 0.01712131 = 0.02398614 * 0.7138 -2**(- 5) +2**(- 8) +2**(-10) +2**(-15) -2**(-18) +2**(-20) = -0.02633953 = -0.03690044 * 0.7138 -2**(- 7) -2**(-10) -2**(-14) +2**(-16) -2**(-18) +2**(-20) = -0.00883770 = -0.01238120 * 0.7138 +2**(- 6) +2**(- 8) -2**(-10) -2**(-13) -2**(-15) +2**(-17) = 0.01840973 = 0.02579116 * 0.7138 +2**(- 8) +2**(-11) -2**(-13) +2**(-18) +2**(-20) +2**(-24) = 0.00427729 = 0.00599228 * 0.7138 -2**(- 6) +2**(- 8) -2**(-10) -2**(-12) +2**(-15) -2**(-18) = -0.01291275 = -0.01809015 * 0.7138 -2**(- 9) +2**(-12) +2**(-15) +2**(-17) +2**(-24) = -0.00167078 = -0.00234068 * 0.7138 +2**(- 7) +2**(-10) +2**(-13) -2**(-15) -2**(-18) -2**(-21) = 0.00887632 = 0.01243531 * 0.7138 +2**(-12) -2**(-16) +2**(-18) -2**(-20) -2**(-22) = 0.00023150 = 0.00032433 * 0.7138 -2**(- 7) +2**(- 9) -2**(-19) +2**(-21) = -0.00586081 = -0.00821071 * 0.7138 +2**(-11) -2**(-15) -2**(-19) +2**(-21) +2**(-23) = 0.00045645 = 0.00063947 * 0.7138 +2**(- 8) -2**(-12) -2**(-16) +2**(-18) -2**(-22) +2**(-25) = 0.00365046 = 0.00511412 * 0.7138 -2**(-10) +2**(-12) +2**(-14) -2**(-17) +2**(-19) +2**(-22) = -0.00067687 = -0.00094826 * 0.7138 -2**(- 9) -2**(-13) -2**(-16) -2**(-19) -2**(-22) = -0.00209260 = -0.00293163 * 0.7138 +2**(-11) +2**(-13) +2**(-16) +2**(-18) +2**(-20) -2**(-22) = 0.00063014 = 0.00088280 * 0.7138 +2**(-10) +2**(-13) -2**(-15) -2**(-17) +2**(-20) +2**(-25) = 0.00106147 = 0.00148707 * 0.7138 -2**(-11) +2**(-15) -2**(-18) = -0.00046158 = -0.00064665 * 0.7138 -2**(-11) +2**(-14) -2**(-16) -2**(-20) -2**(-24) = -0.00044352 = -0.00062135 * 0.7138 +2**(-12) +2**(-14) +2**(-18) +2**(-21) +2**(-23) = 0.00030959 = 0.00043372 * 0.7138 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 48e Filter len=48 Due to symmetrcity, only 24 coefficients are presented. Scaling Factor= 0.5793 Next are continuous coefficients 0.458339860396909 0.140774379672935 -0.096881984326787 -0.053904905604016 0.055446621463354 0.029593454048503 -0.038611215979617 -0.017858551673356 0.028842351153871 0.010956636307340 -0.022310019568337 -0.006525746573855 0.017279070645607 0.003648096470147 -0.013591052542156 -0.001475042616088 0.010272618219187 0.000289740513875 -0.007902014014759 0.001060186880314 0.005557749857047 -0.001817463223395 -0.003476886166494 0.002625773406988 Next are discrete coefficients in binary form +2**(- 2) +2**(- 6) -2**(-13) +2**(-16) -2**(-19) = 0.26551628 = 0.45833986 * 0.5793 +2**(- 4) +2**(- 6) +2**(- 8) -2**(-11) +2**(-17) = 0.08155060 = 0.14077438 * 0.5793 -2**(- 4) +2**(- 7) -2**(- 9) +2**(-11) +2**(-15) -2**(-19) = -0.05612373 = -0.09688198 * 0.5793 -2**(- 5) +2**(-15) -2**(-17) = -0.03122711 = -0.05390491 * 0.5793 +2**(- 5) +2**(-10) -2**(-13) +2**(-16) +2**(-21) = 0.03212023 = 0.05544662 * 0.5793 +2**(- 6) +2**(- 9) -2**(-11) +2**(-14) -2**(-17) +2**(-22) = 0.01714349 = 0.02959345 * 0.5793 -2**(- 5) +2**(- 7) +2**(-10) +2**(-13) -2**(-15) +2**(-19) = -0.02236748 = -0.03861122 * 0.5793 -2**(- 7) -2**(- 9) -2**(-11) -2**(-13) +2**(-15) = -0.01034546 = -0.01785855 * 0.5793 +2**(- 6) +2**(-10) +2**(-13) -2**(-16) = 0.01670837 = 0.02884235 * 0.5793 +2**(- 7) -2**(- 9) +2**(-11) -2**(-21) = 0.00634718 = 0.01095664 * 0.5793 -2**(- 6) +2**(- 8) -2**(-10) -2**(-12) +2**(-16) = -0.01292419 = -0.02231002 * 0.5793 -2**(- 8) +2**(-13) +2**(-18) = -0.00378036 = -0.00652575 * 0.5793 +2**(- 7) +2**(- 9) +2**(-12) = 0.01000977 = 0.01727907 * 0.5793 +2**(- 9) +2**(-13) +2**(-15) +2**(-17) = 0.00211334 = 0.00364810 * 0.5793 -2**(- 7) -2**(-14) +2**(-22) = -0.00787330 = -0.01359105 * 0.5793 -2**(-10) +2**(-13) = -0.00085449 = -0.00147504 * 0.5793 +2**(- 7) -2**(- 9) +2**(-13) -2**(-15) = 0.00595093 = 0.01027262 * 0.5793 +2**(-12) -2**(-14) -2**(-16) = 0.00016785 = 0.00028974 * 0.5793 -2**(- 8) -2**(-10) +2**(-12) +2**(-14) = -0.00457764 = -0.00790201 * 0.5793 +2**(-11) +2**(-13) +2**(-18) = 0.00061417 = 0.00106019 * 0.5793 +2**(- 8) -2**(-10) +2**(-12) +2**(-14) -2**(-16) = 0.00321960 = 0.00555775 * 0.5793 -2**(-10) -2**(-14) -2**(-16) = -0.00105286 = -0.00181746 * 0.5793 -2**(- 9) -2**(-14) = -0.00201416 = -0.00347689 * 0.5793 +2**(- 9) -2**(-11) +2**(-14) -2**(-18) -2**(-20) = 0.00152111 = 0.00262577 * 0.5793 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 64d Filter len=64 Due to symmetrcity, only 32 coefficients are presented. Scaling Factor= 0.9955 Next are continuous coefficients 0.460093492003076 0.138225775756529 -0.097791134323204 -0.050941883529747 0.055429924677988 0.026440392900866 -0.037641156444233 -0.014848771375487 0.027149301985890 0.008288428509193 -0.019931841112153 -0.004321471462892 0.014584382414997 0.001907947373594 -0.010499518340344 -0.000499832546334 0.007368824414306 -0.000246920698196 -0.004996731316007 0.000563296262551 0.003246133019731 -0.000614068545270 -0.002001710179941 0.000527879809806 0.001153414241038 -0.000379481907169 -0.000611194589520 0.000230395452633 0.000290748523385 -0.000109210318504 -0.000128370023504 0.000049815233002 Next are discrete coefficients in binary form +2**(- 1) -2**(- 4) +2**(- 6) +2**(- 8) +2**(-10) +2**(-16) = 0.45802307 = 0.46009349 * 0.9955 +2**(- 3) +2**(- 7) +2**(- 8) +2**(-10) -2**(-13) +2**(-15) = 0.13760376 = 0.13822578 * 0.9955 -2**(- 4) -2**(- 5) -2**(- 8) +2**(-11) -2**(-13) -2**(-14) = -0.09735107 = -0.09779113 * 0.9955 -2**(- 4) +2**(- 6) -2**(- 8) +2**(-14) +2**(-17) -2**(-24) = -0.05071265 = -0.05094188 * 0.9955 +2**(- 4) -2**(- 7) +2**(-11) +2**(-18) +2**(-20) -2**(-24) = 0.05518049 = 0.05542992 * 0.9955 +2**(- 6) +2**(- 7) +2**(- 9) +2**(-10) -2**(-14) +2**(-16) = 0.02632141 = 0.02644039 * 0.9955 -2**(- 5) -2**(- 7) +2**(- 9) -2**(-11) +2**(-13) +2**(-18) = -0.03747177 = -0.03764116 * 0.9955 -2**(- 6) +2**(-10) -2**(-13) -2**(-16) +2**(-18) = -0.01478195 = -0.01484877 * 0.9955 +2**(- 5) -2**(- 8) -2**(-12) -2**(-14) -2**(-16) +2**(-18) = 0.02702713 = 0.02714930 * 0.9955 +2**(- 7) +2**(-11) -2**(-14) +2**(-16) -2**(-18) -2**(-24) = 0.00825113 = 0.00828843 * 0.9955 -2**(- 6) -2**(- 8) -2**(-12) -2**(-14) -2**(-17) +2**(-19) = -0.01984215 = -0.01993184 * 0.9955 -2**(- 8) -2**(-11) +2**(-13) -2**(-15) +2**(-20) = -0.00430202 = -0.00432147 * 0.9955 +2**(- 6) -2**(-10) -2**(-13) -2**(-17) +2**(-26) = 0.01451875 = 0.01458438 * 0.9955 +2**(- 9) -2**(-14) +2**(-17) -2**(-21) +2**(-23) = 0.00189936 = 0.00190795 * 0.9955 -2**(- 7) -2**(- 9) -2**(-11) -2**(-13) -2**(-14) -2**(-16) = -0.01045227 = -0.01049952 * 0.9955 -2**(-11) -2**(-17) -2**(-19) +2**(-22) -2**(-28) = -0.00049758 = -0.00049983 * 0.9955 +2**(- 7) -2**(-11) +2**(-16) -2**(-18) +2**(-29) = 0.00733566 = 0.00736882 * 0.9955 -2**(-12) -2**(-19) +2**(-22) = -0.00024581 = -0.00024692 * 0.9955 -2**(- 8) -2**(-10) -2**(-13) +2**(-15) +2**(-23) = -0.00497425 = -0.00499673 * 0.9955 +2**(-11) +2**(-14) +2**(-16) -2**(-18) +2**(-30) = 0.00056076 = 0.00056330 * 0.9955 +2**(- 8) -2**(-10) +2**(-12) +2**(-14) -2**(-18) +2**(-21) = 0.00323153 = 0.00324613 * 0.9955 -2**(-11) -2**(-13) -2**(-20) = -0.00061131 = -0.00061407 * 0.9955 -2**(- 9) -2**(-15) -2**(-17) -2**(-19) +2**(-21) = -0.00199270 = -0.00200171 * 0.9955 +2**(-11) +2**(-15) +2**(-17) -2**(-20) +2**(-25) = 0.00052550 = 0.00052788 * 0.9955 +2**(-10) +2**(-12) -2**(-14) -2**(-16) +2**(-18) = 0.00114822 = 0.00115341 * 0.9955 -2**(-11) +2**(-13) -2**(-16) +2**(-18) -2**(-23) = -0.00037777 = -0.00037948 * 0.9955 -2**(-11) -2**(-13) +2**(-19) = -0.00060844 = -0.00061119 * 0.9955 +2**(-12) -2**(-16) +2**(-21) = 0.00022936 = 0.00023040 * 0.9955 +2**(-12) +2**(-14) -2**(-16) -2**(-21) = 0.00028944 = 0.00029075 * 0.9955 -2**(-13) +2**(-16) -2**(-19) = -0.00010872 = -0.00010921 * 0.9955 -2**(-13) -2**(-17) +2**(-19) = -0.00012779 = -0.00012837 * 0.9955 +2**(-14) -2**(-16) +2**(-18) = 0.00004959 = 0.00004982 * 0.9955 End of all binary coefficients --------------------------------------------------------------------------------------------------- Johnston's QMF Filter Bank 64e Filter len=64 Due to symmetrcity, only 32 coefficients are presented. Scaling Factor= 0.8026 Next are continuous coefficients 0.457288379417284 0.141979362968789 -0.096160872987224 -0.055326418540379 0.054981831508535 0.031250479094797 -0.038460684244454 -0.019727013457484 0.029127110039953 0.012946892283725 -0.022885331839004 -0.008541005465148 0.018294266623034 0.005513392509500 -0.014734140453629 -0.003346058902317 0.011845327748523 0.001768069376590 -0.009410196547196 -0.000675212347742 0.007371748886945 -0.000077829139951 -0.005645880282089 0.000558468637816 0.004219483057816 -0.000879291046774 -0.002984827351398 0.001031421765466 0.001957016694644 -0.001081290341303 -0.001027857072033 0.001029008170954 Next are discrete coefficients in binary form +2**(- 1) -2**(- 3) -2**(- 7) -2**(-12) +2**(-14) +2**(-16) = 0.36701965 = 0.45728838 * 0.8026 +2**(- 3) -2**(- 6) +2**(- 8) +2**(-10) -2**(-12) -2**(-14) = 0.11395264 = 0.14197936 * 0.8026 -2**(- 4) -2**(- 6) +2**(-10) -2**(-15) +2**(-22) = -0.07717872 = -0.09616087 * 0.8026 -2**(- 4) +2**(- 6) +2**(- 9) +2**(-11) +2**(-15) -2**(-19) = -0.04440498 = -0.05532642 * 0.8026 +2**(- 4) -2**(- 6) -2**(- 8) +2**(-10) +2**(-12) -2**(-14) = 0.04412842 = 0.05498183 * 0.8026 +2**(- 5) -2**(- 7) +2**(- 9) -2**(-12) -2**(-14) -2**(-18) = 0.02508163 = 0.03125048 * 0.8026 -2**(- 5) +2**(-11) -2**(-13) +2**(-16) -2**(-26) = -0.03086855 = -0.03846068 * 0.8026 -2**(- 6) -2**(-12) +2**(-15) +2**(-17) -2**(-19) = -0.01583290 = -0.01972701 * 0.8026 +2**(- 5) -2**(- 7) -2**(-14) +2**(-20) = 0.02337742 = 0.02912711 * 0.8026 +2**(- 7) +2**(- 9) +2**(-11) +2**(-13) +2**(-16) -2**(-24) = 0.01039118 = 0.01294689 * 0.8026 -2**(- 6) -2**(- 8) +2**(-10) +2**(-12) -2**(-14) +2**(-18) = -0.01836777 = -0.02288533 * 0.8026 -2**(- 7) +2**(-10) -2**(-16) -2**(-18) = -0.00685501 = -0.00854101 * 0.8026 +2**(- 6) -2**(-10) +2**(-15) +2**(-18) +2**(-22) -2**(-25) = 0.01468298 = 0.01829427 * 0.8026 +2**(- 8) +2**(-11) +2**(-15) = 0.00442505 = 0.00551339 * 0.8026 -2**(- 6) +2**(- 8) -2**(-13) +2**(-16) -2**(-24) = -0.01182562 = -0.01473414 * 0.8026 -2**(- 8) +2**(-10) +2**(-12) = -0.00268555 = -0.00334606 * 0.8026 +2**(- 7) +2**(- 9) -2**(-12) -2**(-16) +2**(-20) -2**(-23) = 0.00950706 = 0.01184533 * 0.8026 +2**(- 9) -2**(-11) -2**(-14) +2**(-16) -2**(-26) = 0.00141905 = 0.00176807 * 0.8026 -2**(- 7) +2**(-12) +2**(-16) +2**(-21) = -0.00755262 = -0.00941020 * 0.8026 -2**(-11) -2**(-14) +2**(-17) -2**(-22) = -0.00054193 = -0.00067521 * 0.8026 +2**(- 7) -2**(- 9) +2**(-14) -2**(-18) -2**(-25) = 0.00591657 = 0.00737175 * 0.8026 -2**(-14) -2**(-19) +2**(-21) = -0.00006247 = -0.00007783 * 0.8026 -2**(- 8) -2**(-11) -2**(-13) -2**(-16) +2**(-21) = -0.00453138 = -0.00564588 * 0.8026 +2**(-11) -2**(-15) -2**(-17) -2**(-19) = 0.00044823 = 0.00055847 * 0.8026 +2**(- 8) -2**(-11) -2**(-15) -2**(-20) +2**(-24) = 0.00338656 = 0.00421948 * 0.8026 -2**(-10) +2**(-12) +2**(-15) -2**(-18) = -0.00070572 = -0.00087929 * 0.8026 -2**(- 9) -2**(-11) +2**(-14) -2**(-16) +2**(-27) = -0.00239562 = -0.00298483 * 0.8026 +2**(-10) -2**(-13) -2**(-15) +2**(-18) +2**(-25) = 0.00082782 = 0.00103142 * 0.8026 +2**(- 9) -2**(-11) +2**(-13) -2**(-16) -2**(-20) = 0.00157070 = 0.00195702 * 0.8026 -2**(-10) +2**(-13) -2**(-16) +2**(-19) = -0.00086784 = -0.00108129 * 0.8026 -2**(-10) +2**(-13) +2**(-15) -2**(-20) -2**(-25) = -0.00082496 = -0.00102786 * 0.8026 +2**(-10) -2**(-13) -2**(-15) +2**(-19) = 0.00082588 = 0.00102901 * 0.8026 End of all binary coefficients ---------------------------------------------------------------------------------------------------