filter -pass filter figure the wave digital ow-pass filter is s... The valunsformation of thepass filter presen cheme of the band -A52*N14; N14-A51*N14; N10=N9;N12=N11log10absh ging in t
Trang 1he program for th
llows, and the fr
ogram for comp
ructure in the figu
G A
G C G
A
G C G
A
0 1 1
2 2
0 1
0 1 2
3
2 3 4
ure 4
wave digital low276524;A3=0.18280; N8=0; N10=0; X
.
R L R
B
R L G
A
G C
3 3
4 4
1 2
1 2 3
4
3 4 5
52 4
2 447408
026493
Fig
5
Asfilt
A3chahigpro
for i=1:1:200 XN1=A1*XN XN3=N6-A BN4=XN4 BN3=XN3 BN2=XN2 BN1=XN1 N1=XN*A N5=BN3-A N9=N10-A YN(i)=2*N N2=N1;N4=
end [h,w]=freqz(YN Plot(w,20*log10
g 5 Frequency re
Design of the
s a second exampter for n=5, Amax
=0.182, B4=0.192anging the valuegh-pass filter in ogram we also ha
N-A1*N2+N2;
A3*XN2-A3*N6;
4-A51*XN4+2*N13-B4*XN4-B4*BN42-A3*XN2+BN3+N-BN2*XN2-B2*BNA1-A1*N2+BN1;
A3*XN2-A3*N6;
A51*XN4-A51*N1N10-A51*XN4-A5
=N3;N6=N5;N8=NN,1,200)
XN2=XN1+N4 XN4=XN3+N0-A51*N10-A52*N4;
N6-A3*N6;
N2;
N3=BN1+BN2 N7=BN3+BN410-A52*N10;
hebychev wave
DF A1=0.223, B2=MATLAB programhebychev low-pailter from the prN7; N10= -N9
digital
=0.226,
m and
ss and evious
Trang 2v low-pass and hi
Cauer WDF
rder ladder LC retained from table
dB and Ωs=2.0000
filter -pass filter figurethe wave digital
ow-pass filter is s 114, 1979) (C 05
ed by digital strfilter of the 5th o
shown
550 for
ructure rder is
Fig
Fig WiwapreinpC(1C(2N1R(3R(5K(4A(
A(
for
g 8 Discrete reali
g 9 Structure of tith the assistanceave digital filter esented in Figureput data of the L1)=2.235878; C(3)2)=0.096443; C(4)14=0; G(1)=1; G(23)=R(2)+1/(C(2)+
5)=R(4)+1/(C(4)+
4)=(L(4)*C(4)-1)/
(3)=G(3)/(G(3)+C(51)=2*G(5)/(G(5)
r i=1:1:200 XN2=A(1)*XN1+
XN4=N8-A(3)*X BN5=XN5-A(51) BN4 =XN4-B(4)*
BN3 =XN3-A(3)*
BN2 =XN2-B(2)*
N1 =A(1)*XN1-A N5=-K(2)*N3+K N9=BN4+BN5;
el and serial LC ci
ass filter n=5
g MATLAB progrand A52 The atte
m was obtained ined from the cat
=2.092084; L(2)=0
=1; N2=0; N4=0; N
=1/G(2);
G(3)=1/R(3); GG(5)=1/R(5);
A(1)=G(1)/G(2);
4)=R(4)/R(5);
(52)=2/(G(5)+C(5 XN3=XN2+N XN5=XN4+N12;
51)*N14-A(52)*NA(3)*N8;
N3=BN2*BN3;
N7=BN4-A(3)*XN1=N10-N9*K(4)+N
ircuit
ram we can calcuenuation of the lofrom the structualogue of the Cau981174; L(4)=0.88N6=0; N8=0; N10G(4)=G(3)+C(3);
K(2)=(L(2)*C(2)-1 B(2)=R(2)/R(3);
5)+1);
N6;
; 14*;
N3-A(3)*N8;
N12*K(4);
ulate coefficientsow-pass Cauer fure in the Figure uer filter (Saal 19789139;
=0; N12=0;
R(4)=1/G(4);
1)/(L(2)*C(2)+1);
of the ilter is
9 The 79.)
Trang 3v low-pass and hi
Cauer WDF
rder ladder LC retained from table
dB and Ωs=2.0000
filter -pass filter figure
the wave digital
ow-pass filter is s 114, 1979) (C 05
ed by digital strfilter of the 5th o
shown
550 for
ructure rder is
Fig
Fig WiwapreinpC(1C(2N1R(3R(5K(4A(
A(
for
g 8 Discrete reali
g 9 Structure of tith the assistanceave digital filter esented in Figureput data of the L1)=2.235878; C(3)2)=0.096443; C(4)14=0; G(1)=1; G(23)=R(2)+1/(C(2)+
5)=R(4)+1/(C(4)+
4)=(L(4)*C(4)-1)/
(3)=G(3)/(G(3)+C(51)=2*G(5)/(G(5)
r i=1:1:200 XN2=A(1)*XN1+
XN4=N8-A(3)*X BN5=XN5-A(51) BN4 =XN4-B(4)*
BN3 =XN3-A(3)*
BN2 =XN2-B(2)*
N1 =A(1)*XN1-A N5=-K(2)*N3+K N9=BN4+BN5;
el and serial LC ci
ass filter n=5
g MATLAB progrand A52 The atte
m was obtained ined from the cat
=2.092084; L(2)=0
=1; N2=0; N4=0; N
=1/G(2);
G(3)=1/R(3); GG(5)=1/R(5);
A(1)=G(1)/G(2);
4)=R(4)/R(5);
(52)=2/(G(5)+C(5 XN3=XN2+N XN5=XN4+N12;
51)*N14-A(52)*NA(3)*N8;
N3=BN2*BN3;
N7=BN4-A(3)*XN1=N10-N9*K(4)+N
ircuit
ram we can calcuenuation of the lofrom the structualogue of the Cau981174; L(4)=0.88N6=0; N8=0; N10G(4)=G(3)+C(3);
K(2)=(L(2)*C(2)-1 B(2)=R(2)/R(3);
5)+1);
N6;
; 14*;
N3-A(3)*N8;
N12*K(4);
ulate coefficientsow-pass Cauer fure in the Figure uer filter (Saal 19789139;
=0; N12=0;
R(4)=1/G(4);
1)/(L(2)*C(2)+1);
of the ilter is
9 The 79.)
Trang 4Cauer filter (Saa
A With the tran
lues of the band-p
g 11.Tolerance sc
51)*XN5-A(52)*NN6=N5;N8=N7;N200); plot(w,20*lbtained by chang11; N14=-N13 In
*XN5-A(51)*N14-response of the C
Cauer band-pa
and-pass filter thnormalized low-p
l 1979) The valunsformation of thepass filter presen
cheme of the band
-A(52)*N14;
N14-A(51)*N14;
N10=N9;N12=N11log10(abs(h))) ging in the progra
n Figure 10 the
Cauer low-pass an
ass filter
hat accomplish thpass filter for C03ues of the normali
e low-pass filter nted in Figure 12B
to the band-pass
B
=0;
=-N3; N6=-N5; N8ow-pass and hig
ve digital filter
me given in Figuobtained from theter are shown in
FigaftSertra
Figpa
g 12 A) LC lowter impedance trarial-parallel resoansformed into p
g 13 Impedancerallel resonant cir
w-pass Cauer filteansformation
onant circuit in parallel-parallel re
e transformation rcuit
a
er, B) LC band-p
the longitudinaesonant circuit, fi
u 14
C aC
allel resonant LC
A
L
A A L A
c c
1
2
1 2 2
4
LA LA
2 1
C A
C A
1 2
u
2
u
2
C) LC band-pas
e figure 12B) ctions (5) up to (11
C circuit to the pa
s filter
can be 1)
arallel-(5)
(6)
(7) (8) (9)
Trang 5Cauer filter (Saa
A With the tran
lues of the band-p
g 11.Tolerance sc
51)*XN5-A(52)*N
*XN5-A(51)*N14-N6=N5;N8=N7;N200); plot(w,20*lbtained by chang11; N14=-N13 In
response of the C
Cauer band-pa
and-pass filter thnormalized low-p
l 1979) The valunsformation of the
pass filter presen
cheme of the band
-A(52)*N14;
N14-A(51)*N14;
N10=N9;N12=N11log10(abs(h)))
ging in the progra
n Figure 10 the
Cauer low-pass an
ass filter
hat accomplish thpass filter for C03ues of the normali
e low-pass filter nted in Figure 12B
to the band-pass
B
=0;
=-N3; N6=-N5; N8ow-pass and hig
ve digital filter
me given in Figuobtained from theter are shown in
FigaftSertra
Figpa
g 12 A) LC lowter impedance trarial-parallel resoansformed into p
g 13 Impedancerallel resonant cir
w-pass Cauer filteansformation
onant circuit in parallel-parallel re
e transformation rcuit
a
er, B) LC band-p
the longitudinaesonant circuit, fi
u 14
C aC
allel resonant LC
A
L
A A L A
c c
1
2
1 2 2
4
LA LA
2 1
C A
C A
1 2
u
2
u
2
C) LC band-pas
e figure 12B) ctions (5) up to (11
C circuit to the pa
s filter
can be 1)
arallel-(5)
(6)
(7) (8) (9)
Trang 6gure 8 The coeffi
gure 8 can be obta
K1=0
K3=0
and-pass filter afittances Yi and im
G1=G0-+Y
R
R3=R2+1/
s of the parallel autput of the band
he load resistor R
G
G G
A R B
R Z R B
G A
G Y G A
1 1 2
1 2 2 3
2 3 3 41
3 4 42
3 4
22
L C i i
L C i
K
0.543105 K2=0.870278 K4=
fter the impedancmpedances Ri we
Y1=4.39611
R2=R1+1/Y2=0.46/Y3=0.581104 and serial adaptod-pass filter the pa
1 7208 3
v
1 2
v
1 2
R1=0.227432
63853
G3=1.720862 ors of the wave darallel dependent
.
.
.
of the
of each nted in nted in
ave digital filte
ucture of the Butt
structure of the wction of the paral end of the struct
ad resistance RL=dent adaptor
er
terworth wave di
wave digital filterllel and serial adture must be conn
=1 In case of n e
gital filter
r The daptors nected even at
Trang 7gure 8 The coeffi
gure 8 can be obta
resonant circuit icients Ki i=(1, 2,
ained by followin
K1=0
K3=0
and-pass filter afittances Yi and im
G1=G0-+Y
R
R3=R2+1/
s of the parallel autput of the band
he load resistor R
G
G G
A R
B
R Z R
B
G A
G Y G
1 1
2
1 2 2
3
2 3 3
41
3 4 42
3 4
22
L C i i
L C i
K
0.543105 K2=0.870278 K4=
fter the impedancmpedances Ri we
Y1=4.39611
R2=R1+1/Y2=0.46/Y3=0.581104 and serial adaptod-pass filter the pa
4 4
1 7208 3
v
1
2
v
1
R1=0.227432
63853
G3=1.720862 ors of the wave d
arallel dependent
.
.
.
of the
of each nted in nted in
ave digital filte
ucture of the Butt
structure of the wction of the paral end of the struct
ad resistance RL=dent adaptor
er
terworth wave di
wave digital filterllel and serial adture must be conn
=1 In case of n e
gital filter
r The daptors nected even at
Trang 8In tables 1-5 are the elements of the Butterworth wave digital filters for various attenuation
Amax in the pass-band and n=3, 4, 5, 6 and 7 The tables was designed for sampling
frequency fs=0.5
Table 1 Elements of the Butterworth WDF N=3, Amax in dB
Table 2 Elements of the Butterworth WDF N=4, Amax in dB
Table 3 Elements of the Butterworth WDF N=5, Amax in dB
0.1 0.6764 0.3694 0.3210 0.5690 0.9679 0.2 0.6568 0.3424 0.2924 0.5385 0.9599 0.3 0.6449 0.3268 0.2760 0.5200 0.9545 0.4 0.6364 0.3157 0.2645 0.5067 0.9503 0.5 0.6295 0.3071 0.2556 0.4961 0.9468 0.6 0.6239 0.3000 0.2484 0.4874 0.9437 0.7 0.6190 0.2941 0.2423 0.4798 0.9409 0.8 0.6147 0.2889 0.2369 0.4732 0.9385 0.9 0.6109 0.2843 0.2326 0.4673 0.9362 1.0 0.6074 0.2802 0.2281 0.4620 0.9431
Amax A1 B2 A3 B4 A51 A52 0.1 0.7022 0.3784 0.2876 0.3188 0.6021 0.9815 0.2 0.6872 0.3658 0.2655 0.2951 0.5781 0.9722 0.3 0.6782 0.3531 0.2532 0.2813 0.5636 0.9742 0.4 0.6716 0.3441 0.2446 0.2717 0.5530 0.9718 0.5 0.6664 0.3371 0.2380 0.2642 0.5446 0.9699 0.6 0.6621 0.3313 0.2325 0.2580 0.5376 0.9682 0.7 0.6584 0.3264 0.2280 0.2529 0.5317 0.9667 0.8 0.6551 0.3222 0.2240 0.2484 0.5264 0.9653 0.9 0.6522 0.3184 0.2205 0.2444 0.5217 0.9641 1.0 0.6495 0.3149 0.2173 0.2408 0.5174 0.9629
able 4 Elements o
Amax A1 0.1 0.74 0.2 0.76 0.3 0.73 0.4 0.72 0.5 0.72 0.6 0.72 0.7 0.72 0.8 0.71 0.9 0.71 1.0 0.71
of Chebychev WD
0.2468 0.2229 0.2422 0.2184 0.2384 0.2145 0.2350 0.2112 0.2321 0.2083 0.2294 0.2056
arious attenuatiompling frequency f
filter
n Amax
fs=0.5
Trang 9In tables 1-5 are the elements of the Butterworth wave digital filters for various attenuation
Amax in the pass-band and n=3, 4, 5, 6 and 7 The tables was designed for sampling
frequency fs=0.5
Table 1 Elements of the Butterworth WDF N=3, Amax in dB
Table 2 Elements of the Butterworth WDF N=4, Amax in dB
Table 3 Elements of the Butterworth WDF N=5, Amax in dB
0.4 0.5962 0.3056 0.4682 0.9133 0.5 0.5867 0.2941 0.4545 0.9068 0.6 0.5789 0.2846 0.4331 0.9012 0.7 0.5721 0.2767 0.4334 0.8963 0.8 0.5662 0.2698 0.4249 0.8918 0.9 0.5609 0.2637 0.4174 0.8876 1.0 0.5561 0.2583 0.4105 0.8838
0.1 0.6764 0.3694 0.3210 0.5690 0.9679 0.2 0.6568 0.3424 0.2924 0.5385 0.9599 0.3 0.6449 0.3268 0.2760 0.5200 0.9545 0.4 0.6364 0.3157 0.2645 0.5067 0.9503 0.5 0.6295 0.3071 0.2556 0.4961 0.9468 0.6 0.6239 0.3000 0.2484 0.4874 0.9437 0.7 0.6190 0.2941 0.2423 0.4798 0.9409 0.8 0.6147 0.2889 0.2369 0.4732 0.9385 0.9 0.6109 0.2843 0.2326 0.4673 0.9362 1.0 0.6074 0.2802 0.2281 0.4620 0.9431
Amax A1 B2 A3 B4 A51 A52 0.1 0.7022 0.3784 0.2876 0.3188 0.6021 0.9815
0.2 0.6872 0.3658 0.2655 0.2951 0.5781 0.9722 0.3 0.6782 0.3531 0.2532 0.2813 0.5636 0.9742 0.4 0.6716 0.3441 0.2446 0.2717 0.5530 0.9718 0.5 0.6664 0.3371 0.2380 0.2642 0.5446 0.9699 0.6 0.6621 0.3313 0.2325 0.2580 0.5376 0.9682 0.7 0.6584 0.3264 0.2280 0.2529 0.5317 0.9667 0.8 0.6551 0.3222 0.2240 0.2484 0.5264 0.9653 0.9 0.6522 0.3184 0.2205 0.2444 0.5217 0.9641 1.0 0.6495 0.3149 0.2173 0.2408 0.5174 0.9629
able 4 Elements o
Amax A1 0.1 0.74 0.2 0.76 0.3 0.73 0.4 0.72 0.5 0.72 0.6 0.72 0.7 0.72 0.8 0.71 0.9 0.71 1.0 0.71
of Chebychev WD
0.2468 0.2229 0.2422 0.2184 0.2384 0.2145 0.2350 0.2112 0.2321 0.2083 0.2294 0.2056
arious attenuatiompling frequency f
filter
n Amax
fs=0.5
Trang 10Amax A1 B2 A3 B4 A51 A52
Table 7 Elements of Chebychev WDF N=5, Amax in dB
Table 8.Elements of Chebychev WDF N=7, Amax in dB
Table 9.Elements of Chebychev WDF N=9, Amax in dB
11 Tables of Cauer wave digital filter
In tables 10-12 are the elements of Cauer wave digital filters for various attenuation Amax in
the pass-band and N=3, 5 and 7 The tables was designed for sampling frequency fs=0.5
g 18 Frequency r
C 0.0004 0.0017 0.0039 0.0109 0.0279 0.0436 0.0988 0.1773 0.2803 1.2494
able 10 Elements
Amax 0.0017 0.0039 0.0109 0.0279 0.0436 0.0988 0.1773 0.2803 1.2494
able 11 Elements
Amax As 0.0004 43.5 0.6 0.0017 49.5 0.6 0.0039 53.0 0.6 0.0109 57.5 0.5
response and stru
N=3, Ωs=4.8097, K2 B2 A3 0.399 0.330 0.373 0.311 0.343 0.290 0.318 0.272 0.306 0.264 0.288 0.251 0.277 0.243 0.270 0.237 0.256 0.221
N=5, Ωs=2.000, K2
0.3521 0.4838 0.3240 0.4464 0.3093 0.4274 0.2924 0.4064
A32 0.9629 0.9374 0.9160 0.8803 0.8365 0.8114 0.7573 0.7110 0.6699 0.4999
Trang 11Amax A1 B2 A3 B4 A51 A52
Table 7 Elements of Chebychev WDF N=5, Amax in dB
Table 8.Elements of Chebychev WDF N=7, Amax in dB
Table 9.Elements of Chebychev WDF N=9, Amax in dB
11 Tables of Cauer wave digital filter
In tables 10-12 are the elements of Cauer wave digital filters for various attenuation Amax in
the pass-band and N=3, 5 and 7 The tables was designed for sampling frequency fs=0.5
g 18 Frequency r
C 0.0004 0.0017 0.0039 0.0109 0.0279 0.0436 0.0988 0.1773 0.2803 1.2494
able 10 Elements
Amax 0.0017 0.0039 0.0109 0.0279 0.0436 0.0988 0.1773 0.2803 1.2494
able 11 Elements
Amax As 0.0004 43.5 0.6 0.0017 49.5 0.6 0.0039 53.0 0.6 0.0109 57.5 0.5
response and stru
N=3, Ωs=4.8097, K2 B2 A3 0.399 0.330 0.373 0.311 0.343 0.290 0.318 0.272 0.306 0.264 0.288 0.251 0.277 0.243 0.270 0.237 0.256 0.221
N=5, Ωs=2.000, K2
0.3521 0.4838 0.3240 0.4464 0.3093 0.4274 0.2924 0.4064
A32 0.9629 0.9374 0.9160 0.8803 0.8365 0.8114 0.7573 0.7110 0.6699 0.4999
Trang 12Fig 20 Parallel and serial adaptors deposited in simulink browse library
The simulink model of the fifth order filter in the figure 4 corresponds to the realization of a wave digital filter application on TMS320C6711 DSK using Embedded Target for Texas Instruments TMS320C6000 DSP Platform The model of the filter, figure 21, was created by means of serial and parallel block that were added to the window simulink library browser
In the output and input of WDF were added ADC and DAC convertors of the TMS320C6711 that are in the simulink library browser, Embedded Target for TI C6000 DSP and C6711DSK board support
Fig 21 Realization of fifth order wave digital filter by TMS320C6711 simulink
This project created in code composer studio can be seen in figure 22 and can run on the DSPC6711
Trang 13Fig 20 Parallel and serial adaptors deposited in simulink browse library
The simulink model of the fifth order filter in the figure 4 corresponds to the realization of a wave digital filter application on TMS320C6711 DSK using Embedded Target for Texas Instruments TMS320C6000 DSP Platform The model of the filter, figure 21, was created by means of serial and parallel block that were added to the window simulink library browser
In the output and input of WDF were added ADC and DAC convertors of the TMS320C6711 that are in the simulink library browser, Embedded Target for TI C6000 DSP and C6711DSK board support
Fig 21 Realization of fifth order wave digital filter by TMS320C6711 simulink
This project created in code composer studio can be seen in figure 22 and can run on the DSPC6711