2.2 - jadval.
Funksiya
|
O'tish kengligi (normallashgan)
|
O'tkazish
oralig'idagi
tekissizlik
|
Tushish
oralig'idagi
pasaytirish
|
Formula
|
To'g'riburchakli
|
0.9/
IN
|
0.7416
|
21
|
1
|
Xenning
|
3A/n
|
0.0546
|
44
|
2nn
0.5 + 0.5 cos (——)
y J
|
Xemming
|
3-3/n
|
0.0194
|
53
|
2nn
0.54 + 0.46cos(——-)
y J
|
Blekman
|
5-5/n
|
0.0017
|
75
|
( 2nn \ ( 4nn \
0.4 2 + 0.5 со s ( ) + 0.0 8 со s ( )
\N - 1/ \N - 1)
|
- jadvaldan ko'rinib turibdiki tushirish oralig'idagi pasaytirishni Xemming va Blekman funksiyalari qanoatlantiradi. Soddalik uchun Xemming
funksiyasini olamiz. U holda Af = 0.3 / 8 = 0.0375, bundan N = 3.3 / 0.0375 = 88. Koeffitsientlar soni toq bo'ladigan qilib 89 ta qiymat olamiz.
hD(n)w(n), -44 < n < 44
hD(ri) = 2 fc
sin(nwc)
nwr
hD(n) = 2 fC ,
w (n) = 0.54 + 0.46с о s ( 2 пп/%д) ,
n Ф 0 n = 0
-44 < n < 44.
bu
yerda
Yuqoridagi formuladan bizga nomalum koeffitsientlardan faqatgina fc va wc lar qoldi. Bular diskretlash chastotasiga nisbatan normallashgan chastotalar.
300 1150
fc = 1000 + — = 1150 Hz -> —— = 0.14375 Jc 2 8000
Shunday ekan h(n) simmetrik funksiya bo'lgani uchun faqatgina h(0), h(1) ... h(44) ni hisoblash kifoya, qolganlarini simmetriklik shartidan hosil qilish mumkin.
n = 0: ho(0) = 2 ■ 0.143 75 = 0.2875, w(0) = 0.54 + 0.46 cos(0) = 1, h(0) = hD(0) ■ w(0) = 0.2875.
n = 1: hD(1) = 2- 0.143 75 -sin ( 2 n' 0'143 7 5} = 0.2499,
w(1) = 0.54 + 0.46 cos( 2 tt/89) = 0.9975, h(1) = hD(1) ■ w(1) = 0.2499 - 0.9975 = 0.2493.
n = 44: hD(44) = 2 - 0.143 75 - s 1 n (4 4 - 2 ”- 0 ■ 14375) = 0.0064,
w(44) = 0.54 + 0.46 cos(2 t - 44 - /89) = 0.08, h(44) = hD(44) ■ w(44) = 0.0064- 0.08= 0.0005.
Ushbu qiymatlar yuqoridagi talab qilingan past chastotali filtrning h(n) keffitsientlaridir. Koeffitsientlarning qolgan qismini h(n) funksiyasining simmetriklik shartidan kelib chiqib hisoblash mumkin.
Past chastotali filtr h(n) koeffitsientlari. (N = 89, Xemming, f
c=1 kHz, Af=0.3 kHz)
h(0)
|
0.0005
|
h(88)
|
h(1)
|
0.0006
|
h(87)
|
h(2)
|
0.0002
|
h(86)
|
h(3)
|
-0.0005
|
h(85)
|
h(4)
|
-0.0008
|
h(84)
|
h(5)
|
-0.0006
|
h(83)
|
h(6)
|
0.00025
|
h(82)
|
h(7)
|
0.0011
|
h(81)
|
h(8)
|
0.0012
|
h(80)
|
h(9)
|
0.0003
|
h(79)
|
h(10)
|
-0.0012
|
h(78)
|
h(11)
|
-0.0021
|
h(77)
|
h(12)
|
-0.0014
|
h(76)
|
h(13)
|
0.0007
|
h(75)
|
h(14)
|
0.0029
|
h(74)
|
h(15)
|
0.0031
|
h(73)
|
h(16)
|
0.0006
|
h(72)
|
h(17)
|
-0.0031
|
h(71)
|
h(18)
|
-0.0051
|
h(70)
|
h(19)
|
-0.0032
|
h(69)
|
h(20)
|
0.002
|
h(79)
|
h(21)
|
0.0066
|
h(67)
|
h(22)
|
0.0067
|
h(69)
|
h(23)
|
0.0010
|
h(65)
|
h(24)
|
-0.0068
|
h(64)
|
h(25)
|
-0.0107
|
h(63)
|
h(26)
|
-0.0062
|
h(62)
|
h(27)
|
0.0045
|
h(68)
|
h(28)
|
0.0139
|
h(60)
|
h(29)
|
0.0135
|
h(59)
|
h(30)
|
0.0014
|
h(58)
|
h(31)
|
-0.0147
|
h(57)
|
h(32)
|
-0.0221
|
h(56)
|
h(33)
|
-0.0123
|
h(55)
|
h(34)
|
0.0108
|
h(54)
|
h(35)
|
0.0309
|
h(53)
|
h(36)
|
0.0298
|
h(52)
|
h(37)
|
0.0017
|
h(51)
|
h(38)
|
-0.0387
|
h(50)
|
h(39)
|
-0.0606
|
h(49)
|
h(40)
|
-0.0354
|
h(48)
|
h(41)
|
0.0439
|
h(47)
|
h(43)
|
0.154
|
h(46)
|
h(43)
|
0.2496
|
h(45)
|
h(44)
|
0.2875
|
h(44)
|
Mos keluvchi strukturali filtrni tasvirlash
KIX filtri quyidagi H(z) tavsiflovchi funksiya orqali xarakterlanadi.
JV-l
H(z) = Z
h(n)z~n
n= 0
Strukturali filtrni tasvirlash bu tavsiflovchi funksiyaning blok-sxema korinishi yozishning bir usuludir. Ko'p hollarda bunday strukturalar ko'paytuvchilar, summatorlar va kechiktiruvchi elementlarning o'zoro bir biri bilan bog'lanishidan tashkil topadi. Bular ichidan eng ko'p foydalaniladiganlaridan biri transversal struktura hisoblanadi. Transversal struktura 2.1 - rasm tasvirlangan