Bi-quad filters realization on AIC Codecs

Transcription

1 pplition Report pril Bi-qud filter reliztion on IC Code HP Softwre BSTRCT Thi pplition report provide informtion regrding filter eqution nd o-effiient formt repreenttion tht n e ued to relize digitl filter on the IC3xxx minidsp pltform. It lo explin wy to updte the filter oeffiient on the fly uing hot proeor. Content Stndrd Bi-qud filter eqution.... ll P (Phe hift) filter.... Equliztion filter Noth ilter...5. Trele Shelf B Shelf ilter Seond order Linkwitz Riley....7 Seond Order Vrile Q ilter Seond order Butterworth ilter from Vrile Q Seond order Beel ilter from Vrile Q...5. irt Order Butterworth ilter...5. Seond order Cheyhev...7 Numer repreenttion formt for filter oeffiient.... ilter oeffiient normliztion... 3 Updting the ode filter oeffiient...3 ppendix. Biqud oeffiient omputtion exmple...5 igure igure. Phe hift filter phe repone ( Hz, BW3Hz)... igure. EQ filter with khz, BWHz,G6dB... igure 3. Noth filter mitude repone with khz,bwhz...6 igure. Trele helf filter mitude repone ( khz, G-6dB)...8 igure 5. B helf filter mitude repone( 5Hz,G6dB)... igure 6. Seond order Linkwitz Riley ( 5Hz, HLhigh)... igure 7. Seond order vrile Q filter( Hz,Q,HLlow)... igure 8. irt order Butterworth( Hz, HLlow)...6 igure 9. Seond order Cheyhev ( 6Hz, typhigh, rip3db)...9 igure. Normlizing filter repone...3 Tle Tle. EQ ilter oeffiient tle in hot ontroller for enhned ode...

2 Stndrd Bi-qud filter eqution. ll P (Phe hift) filter ilter prmeter BW Bndwidth in Hz Center frequeny in Hz Smple frequeny in Hz Error Cheking BW 9K igure. Phe hift filter phe repone ( Hz, BW3Hz) Eqution Bi-qud filter reliztion on IC Code

3 Bi-qud filter reliztion on IC Code 3 d BW BW o tn tn ilter Coeffiient [ ] [ ] B d. Equliztion filter ilter Prmeter BW ilter Bndwidth in Hz ilter Center requeny in Hz Smple rte in Hz G ilter Gin in db Error Cheking 8 9 G K BW

4 igure. EQ filter with khz, BWHz,G6dB Eqution Bi-qud filter reliztion on IC Code

5 Bi-qud filter reliztion on IC Code 5 < if G BW BW tn tn ele tn tn BW BW d H o ilter Coeffiient [ ] ] [ B H d H.3 Noth ilter ilter Prmeter BW Noth Bndwidth in Hz Noth Center frequeny in Hz Smple rte in Hz Error Cheking

6 BW 9K igure 3. Noth filter mitude repone with khz,bwhz Eqution 6 Bi-qud filter reliztion on IC Code

7 Bi-qud filter reliztion on IC Code 7 d BW BW o tn tn d ilter Coeffiient [ ] [ ] B B B.5. Trele Shelf ilter Prmeter Trele Shelf Corner frequeny in Hz Smple rte in Hz G Trele Shelf Gin in db Error Cheking 9 G K

8 igure. Trele helf filter mitude repone ( khz, G-6dB) Eqution g G qrt ρ ϕ g G log 8 Bi-qud filter reliztion on IC Code

9 Bi-qud filter reliztion on IC Code 9 If G > -6 & G < 6 qrt eleif > qrt ele qrt() end qrt tn ) ( ilter Coeffiient [ ] [ ] B.5 B Shelf ilter ilter Prmeter B Shelf Corner frequeny in Hz Smple rte in Hz G B Shelf Gin in db Error Cheking

10 9K G igure 5. B helf filter mitude repone( 5Hz,G6dB) Eqution Bi-qud filter reliztion on IC Code

11 Bi-qud filter reliztion on IC Code G g qrt g G log ϕ ρ If G > -6 & G < 6 qrt eleif > qrt ele qrt() end qrt tn ) ( ilter Coeffiient

12 B [ ] [ ].6 Seond order Linkwitz Riley ilter Prmeter Smple rte in Hz Cut frequeny in Hz HLLR ilter type (high, low) Error Cheking 9K HL ( high, low) igure 6. Seond order Linkwitz Riley ( 5Hz, HLhigh) Eqution Bi-qud filter reliztion on IC Code

13 w if HL(: 3) ' low' ele end B B B [ w ] [ w w ] [ ] [ w w ] k tn [ B k B( 3) B k, B k B( 3 ), B k B k B( 3) ] k ( 3) k, k ( 3 ), k k ( 3) [ ] ilter Coeffiient B B.7 Seond Order Vrile Q ilter ilter Prmeter Smple rte in Hz Cut frequeny in Hz HLLR ilter type (high, low) Qilter Q Error Cheking 9K HL ( high, low) Q w w Q Bi-qud filter reliztion on IC Code 3

14 igure 7. Seond order vrile Q filter( Hz,Q,HLlow) Eqution Bi-qud filter reliztion on IC Code

15 w if HL(:3) ' low' ele end B B B [ w ] w Q [ ] w Q w w k tn [ B k B( 3) B k, B k B( 3 ), B k B k B( 3) ] k ( 3) k, k ( 3 ), k k ( 3) [ ] ilter Coeffiient B B.8 Seond order Butterworth ilter from Vrile Q Seond order Butterworth filter n e relized y uing vrile Q filter with Q.77.9 Seond order Beel ilter from Vrile Q Seond order Beel filter n e relized y uing vrile Q filter with Q.5. irt Order Butterworth ilter ilter Prmeter Smple rte in Hz Cut frequeny in Hz HLLR ilter type (high, low) Error Cheking Bi-qud filter reliztion on IC Code 5

16 9K HL ( high, low) igure 8. irt order Butterworth( Hz, HLlow) Eqution 6 Bi-qud filter reliztion on IC Code

17 k tn W If HL ( : 3) W k W W k W ele k k W k k W end W k k W ' low' ilter Coeffiient B [ ] [ ]. Seond order Cheyhev ilter Prmeter Smple rte in Hz ripripple peifition in db typilter type (high,low,top) Bi-qud filter reliztion on IC Code 7

18 if typ(:3) to Stop nd Input Lower nd upper frequenie [f,f] Ele Cutoff frequeny in Hz If Sle pek to db Nrm If Sle PB to db Nrm - End if end nrm Error Cheking 9K rip Nrm, rip rip HL ( high, low, top) 8 Bi-qud filter reliztion on IC Code

19 igure 9. Seond order Cheyhev ( 6Hz, typhigh, rip3db) Eqution If typ(:3) to Cll hey(ord,rip, ele End Cll ochbi(,, rip,hl),hl) untion ochbi(,, rip,hl) If i(rip)> Sf Ele Sf End Bi-qud filter reliztion on IC Code 9

20 R rip If R B [ ] [ ] ele w ε R inh ε α β 3 β 5 inh inh rel rel if end if f HL Ele ( α) o( β) oh( α) in( β) ( α) o( β ) oh( α) in( β ) ( ) ( ) ε ( : 3) ' low' B B [ w ] [ w w ] w w i i End Bi-qud filter reliztion on IC Code

21 End k tn B B [ B k B( 3) B k, B k B( 3 ), B k B k B( 3) ] k ( 3) k, k ( 3), k k ( 3) [ ] B Numer repreenttion formt for filter oeffiient IC ode ome in two flvor. The tndrd verion of the MiniDSP ue 6 it oeffiient nd it dt word for minidsp_ nd 8 it dt word for minidsp_d while the enhned verion of the MiniDSP ue it oeffiient nd 3 it dt word. The IC35 nd IC3 re enhned devie. The TSC7, IC36, C3, IC3, nd IC3 re tndrd devie. ll of the IC ode devie ue 3.x dt formt (3. for the tndrd devie nd 3.9 for the enhned devie). Thi permit only two mitude it of hedroom for il tht re greter then. To redue the hne of lipping the il in the IC devie, the overll gin of the filter i moderted y ling the numertor vlue ed upon the vlue of the term. The oeffiient ize in the IC ode fmily i 6 it.5 formt for the tndrd devie nd it.3 formt for the enhned IC devie. With thee formt the MiniDSP oeffiient re le to repreent mximum poitive gin of - -5 for 6 it oeffiient nd - -3 for it oeffiient. When filter oeffiient re omputed for n IC ode, the gin of the filter repone i led to permit the vlue to e repreented in.3 or.5 formt. One we hve omputed the filter eqution from ove we then mut perform ouple of tep prior to loding the oeffiient into the ode. In the IC ode ue peifi iqud implementtion to ommodte the.5 nd.3 oeffiient dt formt. y ( n) x( n) x( n) x( n ) y( n) y( n ) Bi-qud filter reliztion on IC Code

22 . or formt we firt mut le the term y the vlue. The,, nd term re multiplied y ling vlue to limit the overll gin of the filter. If i greter thn, then the defult vlue for the ling vlue i /, otherwie it i The ling ftor i then pplied to the,, nd term of the filter. Thi defult vlue i omputed nd diplyed in uer modifile field when the filter oeffiient re omputed. The uer i permitted to hnge thi vlue to mller vlue. However if they ttempt it et it to lrger vlue thn the defult ling vlue then the vlue will np to the defult ling vlue.. Then oth the numertor nd denomintor oeffiient re led y ontnt vlue If the oeffiient re eing omputed for tndrd devie then The,,,, nd term re multiplied y 5 nd rounded to integer If the oeffiient re eing omputed for n enhned devie then The,,,, nd term re multiplied y 3 nd rounded to integer. 3. Then we le the nd term y.5. ppendix illutrte the genertion of oeffiient uing the ove proedure.. ilter oeffiient normliztion ilter oeffiient normliztion i performed to limit the ize of the oeffiient vlue, deried ove, nd to limit the mximum gin of the filter to void lipping. There re two ple where lipping n our.. Internl il level nd lipping The minidsp i le to internlly repreent dt vlue uing 3.9 or 3. formt. Thi permit il level lrge db to e repreented. However, the intermedite gin inide of filter n e higher thn the il level tht re viile t the output of omponent. To ount for thi, filter gin re typilly led to reerve prt or ll of thi db hedroom for internl omputtion.. Output il level nd lipping The mximum il level tht n e output without lipping y the IS output or the DC interpoltor i dt vlue repreented y.9 or. vlue (.99 nd -.). Thi orrepond to il level of db. Coeffiient ling n e ued to void lipping during internl opertion nd when the il i ent to the I S or interpoltor output. Bi-qud filter reliztion on IC Code

23 or exmple, we wih to ue n EQ filter tht h gin of 5 db t 5 Hz. Thi filter repone i hown the lue urve in igure. To void overflow for our internl repreenttion, we normlized the filter oeffiient o tht the il tht i output doe not exeed 5 db. In thi exmple, the filter gin i led y db (multiplying the oeffiient y ). The led filter repone i hown y the red urve in igure. Similrly to void lipping when the il w output, the filter gin hould e led o tht it doe not exeed db. In thi exmple, the filter gin i led y 5 db (multiplying the oeffiient y.77879).. Thi i hown y the green urve in igure. 5 5 d B req igure. Normlizing filter repone 3 Updting the ode filter oeffiient hot ontroller need to provide the filter oeffiient vlue over IC to the IC ode. On the ontroller, the oeffiient vlue need to e pre omputed nd tored in tle. The hot ontroller will red the vlue from the tle nd downlod the oeffiient vlue in equene tht trt t the urrent iqud filter etting to the deired new vlue when n updte i requeted. The hnge of gin mut e in inrement/derement of ¼ db to void pop nd lik. or intne, if n EQ filter t Hz need to e operted etween rnge of -8dB to 8dB, the hot ontroller need to mintin tle of,,, nd term through -8d, dB, -7.5dB 7dB, 7.5dB, 7.5dB, 7.75dB, 8dB. Bi-qud filter reliztion on IC Code 3

24 Tle. EQ ilter oeffiient tle in hot ontroller for enhned ode -8dB x759 x8c5 x7e69bc x7ed3b x db -7.5dB -7.5dB db x7 7.5dB 7.75dB 8dB x7666 x8c73 x7d35 x77e7 x8e89c Bi-qud filter reliztion on IC Code

25 ppendix. Biqud oeffiient omputtion exmple Thi ppendix illutrte the omputtion iqud oeffiient nd onverting them into formt required to lod in IC ode.. ilter Speifition: EQ filter with 5 Hz, Gin 6dB nd Q.87 (BW7Hz) on IC35. pplying the eqution in etion. we get the iqud oeffiient Before writing thee oeffiient to ode memory, ouple of normliztion tep mut e performed ed on their vlue ording to etion.. Sine >, we need to le the numertor oeffiient y le ftor Sle the nd y Sine the oeffiient re to e omputed for enhned devie, we need to le it y nd rounded to neret integer. Hene the finl oeffiient hexdeiml vlue tht h to e loded onto the IC35 re x79 x8e5 x6e5bc x76 x88bd Bi-qud filter reliztion on IC Code 5