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BAHAN AJAR
Digital Signal Processing [Sistem Pemrosesan Sinyal]
Rahmad Hidayat Email : [email protected]
Jurusan Teknik Elektro SEKOLAH TINGGI TEKNOLOGI MANDALA Jalan Soekarno Hatta 597 Bandung
SISTEM PENILAIAN
•Tugas • UTS • UAS • Presensi Selasa 17.00 17 00
2
: : : :
20 % 30 % 40 % 10 %
MATERI
•BAB I •BAB II •BAB BAB III •BAB IV •BAB V
: : : : :
Pendahuluan Sinyal & Sistem Diskrit T Transformasi f iZ Filter DFT-FFT
• Latihan Aplikasi DSP dengan MATLAB •Tugas Membuat GUI MATLAB untuk beberapa aplikasi DSP
Catatan : beberapa p materi ((suplemen) p ) di-share melalui g google g drive
3
BAB II. PENDAHULUAN
LATAR BELAKANG Pemrosesan Sinyal Analog
Prosesor Analog Sederhana
ekivalen dengan sebuah FILTER ANALOG 5
LATAR BELAKANG Contoh Filter Analog
6
Fungsi Filter
Based on slides by Haris Balzakis –Lecture 5 DSP
7
Sistem Pemrosesan Sinyal (DSP) dari Sinyal Analog
(Blok ekivalen dari Prosesor Analog)
8
Sistem Pemrosesan Sinyal (DSP) dari Sinyal Analog
(Blok ekivalen dari Filter Analog)
9
Analog to Digital Converter
10
Jadi untuk apa sinyal diubah ?
11
BAB II II. SINYAL & SISTEM DISKRIT
Based on slides by Kenneth E. Barner, Univ.of Delaware
Tentang Sinyal
www.complextorial.com
13
Tentang Sinyal
Signals are functions of time that curry information relative to the state and/or the behavior of a system. Categorization: Depending on whether they are defined for continuous time intervals or for specific time instances: •) Continuous time signals. •) Discrete Di t titime signals. i l Depending on the values they take: •) Analog signals •) Digital signals.
Based on slides by Haris Balzakis –Lecture 5 DSP
14
Tipe Sinyal
Based on slides by Haris Balzakis –Lecture 5 DSP
15
Tipe Sinyal
Based on slides by Haris Balzakis –Lecture 5 DSP
16
Contoh Sinyal
17
Contoh Sinyal
18
Contoh Sinyal
19
Contoh Sinyal
20
Sinyal Waktu Diskrit
21
Sinyal Diskrit
22
Sinyal Diskrit
23
Sinyal Waktu Diskrit
See Oppenheim and Schafer , second edition pages 8-93, or first edition pages 8-79
24
Sinyal Waktu Diskrit
See Oppenheim and Schafer , second edition pages 8-93, or first edition pages 8-79
25
Sinyal Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
26
Sinyal Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
27
Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
28
Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
29
Sistem Waktu Diskrit (Contoh-1)
Based on slides by Kenneth E. Barner, Univ.of Delaware
30
Sistem Waktu Diskrit (Contoh-2)
Based on slides by Kenneth E. Barner, Univ.of Delaware
31
Klasifikasi Sistem Waktu Diskrit
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
32
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
33
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
34
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
35
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
36
Analisis Sistem LTI
(Linear Time Invariant )
Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
37
Analisis Sistem LTI
(Linear Time Invariant )
Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
38
Based on slides by Kenneth E. Barner, Univ.of Delaware
39
Based on slides by Kenneth E. Barner, Univ.of Delaware
40
Based on slides by Kenneth E. Barner, Univ.of Delaware
41
Properti Konvolusi
Based on slides by Kenneth E. Barner, Univ.of Delaware
42
Properti Konvolusi
See Oppenheim and Schafer, Second Edition pages 8–93, or First Edition pages 8–79.
43
Sistem LTI - KAUSAL
Based on slides by Kenneth E. Barner, Univ.of Delaware
44
Sistem LTI - KAUSAL A system is causal if the output at n depends only on the input at n and earlier inputs. For example, the backward difference system : is causal, but the forward difference system : is not.
See Oppenheim and Schafer, Second Edition pages 8–93, or First Edition pages 8–79.
45
Sistem LTI - STABIL
Based on slides by Kenneth E. Barner, Univ.of Delaware
46
Sistem LTI - STABIL The ideal delay system A system is stable if every bounded input sequence produces a bounded output sequence:
For example, example the accumulator is an example of an unbounded system, since its response to the unit step u[n] is
which has no finite upper bound bound. See Oppenheim and Schafer, Second Edition pages 8–93, or First Edition pages 8–79.
47
Based on slides by Kenneth E. Barner, Univ.of Delaware
48
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
49
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
50
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
51
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
52
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
53
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
54
Based on slides by Kenneth E. Barner, Univ.of Delaware
55
Difference Equation (Persamaan Beda)
Based on slides by Kenneth E. Barner, Univ.of Delaware
56
Realisasi Direct Form-I
Based on slides by Kenneth E. Barner, Univ.of Delaware
57
Realisasi Direct Form-II
Based on slides by Kenneth E. Barner, Univ.of Delaware
58
Realisasi :
Based on slides by Kenneth E. Barner, Univ.of Delaware
59
Persamaan Beda (Difference Equation)
60
Persamaan Beda (Difference Equation)
B.A Shenoi, “Introduction to DSP and Filter Design”, John Wiley & Sons,Inc., 2006
61
BAB III. TRANSFORMASI Z
Transformasi Z
Based on slides by EECS, University of Tennessee,2010
63
Transformasi Z
Based on slides by EECS, University of Tennessee,2010
64
Transformasi Z
Based on slides by EECS, University of Tennessee,2010
65
Transformasi Z dari Filter FIR
Based on slides by EECS, University of Tennessee,2010
66
Fungsi sistem dari Sistem LTI
Based on slides by EECS, University of Tennessee,2010
67
Kelengkapan Transformasi Z
Based on slides by EECS, University of Tennessee,2010
68
Transformasi Z sebagai operator
Based on slides by EECS, University of Tennessee,2010
69
Konvolusi & Transformasi Z
Based on slides by EECS, University of Tennessee,2010
70
Sistem Kaskade pd Transformasi Z
Based on slides by EECS, University of Tennessee,2010
71
Faktorisasi Polinomial Z
Based on slides by EECS, University of Tennessee,2010
72
Domain
Based on slides by EECS, University of Tennessee,2010
73
Bidang Z , plot Pole-Zero
Based on slides by EECS, University of Tennessee,2010
74
Signifikansi Zero dari H(z)
Based on slides by EECS, University of Tennessee,2010
75
Signifikansi Zero dari H(z)
Based on slides by EECS, University of Tennessee,2010
76
Filter Nulling
Based on slides by EECS, University of Tennessee,2010
77
Plot pole-zero & respon frekuensi
Based on slides by EECS, University of Tennessee,2010
78
Sum filter dengan running L-poin
Based on slides by EECS, University of Tennessee,2010
79
Bandpass filter Kompleks
Based on slides by EECS, University of Tennessee,2010
80
Bandpass filter dengan Kompleks
Based on slides by EECS, University of Tennessee,2010
81
Bandpass filter dg koefisien Real
Based on slides by EECS, University of Tennessee,2010
82
ROC (region of convergence)
Based on slides by EECS, University of Tennessee,2010
83
ROC (region of convergence)
Based on slides by EECS, University of Tennessee,2010
84
ROC (region of convergence)
Based on slides by EECS, University of Tennessee,2010
85
Contoh-1 (Penentuan Transformasi Z) (a) x[n] = [1, 2, 5, 7, 0, 1] Solution: X(z) = 1 + 2z-1+ 5z-2 + 7z-3 + z-5, ROC: entire z plane except z = 0 (b) y[n] [n] = [1, [1 2, 2 5, 5 7, 7 0, 0 1] Solution: Y(z) = z2 + 2z + 5 + 7z-1 + z-3 ROC: entire zz-plane plane except z = 0 and z = ∞. ∞ ( ) z[n] (c) [ ] = [[0,, 0,, 1,, 2,, 5,, 7,, 0,, 1]] Solution: Y(z) = z-2 + 2z-3 + 5z-4 + 7z-5 + z-7, ROC: all z except z=0 Based on slides by Dileep Kumar
86
Transformasi Z (d) p[n] = δ[n] S l ti Solution: P( P(z)) = 1 1, ROC ROC: entire ti z-plane. l (e) q[n] = δ[n – k], k] k > 0 Solution: Q(z) = z-k, entire z-plane except z=0. (f) r[n] = δ[n+k], k > 0 Solution: R(z) = zk, ROC: entire z-plane except z = ∞.
Based on slides by Dileep Kumar
87
Contoh-2 (Penentuan Transformasi Z) Determine the z-transform of x[n] = (1/2)nu[n] Solution:
X (z ) =
∞
∑
x [ n ]z − n
n
∞
n = −∞ ∞
⎛1⎞ = ∑ ⎜ ⎟ z −n = n=0 ⎝ 2 ⎠
⎛ 1 −1 ⎞ ⎜ z ⎟ ∑ ⎠ n=0 ⎝ 2
1 −1 ⎛ 1 ⎞ z + ⎜ z⎟ 2 ⎝2 ⎠ 1 = 1 −1 1− z 2 = 1+
n
−2
+ .......
ROC: |1/2 z-1| < 1, or equivalently |z| > 1/2 Based on slides by Dileep Kumar
88
Contoh-3 (Penentuan Transformasi Z) Determine the z-transform of the signal x[n] = anu[n] Solusi : X( z ) =
∞
n −n a ∑ z = n=0
= 1 + az
−1
(
+ az
)
−1 2
∑ (az ) ∞
n
−1
n=0
+ .......
1 = 1 − az − 1 ROC :| z |>| a | Based on slides by Dileep Kumar
89
Invers Transformasi Z In general, the inverse z-transform may be found by using any of the following methods: Power series method Partial fraction method
Based on slides by Dileep Kumar
90
Contoh Penentuan Invers Transformasi Z Example 1: Determine the z-transform of
X( z ) =
1 1 − 1 .5 z
−1
+ 0 .5 z
−2
With power series method and by dividing the numerator of X(z) by its denominator, we obtain the power series 1 1 − 32 z −1 + 12 z − 2
31 − 4 = 1 + 32 z −1 + 74 z − 2 + 158 z − 3 + 16 z + ...
∴ x[n] = [1, 3/2, 7/4, 15/8, 31/16,…. ] Based on slides by Dileep Kumar
91
Contoh Penentuan Invers Transformasi Z Example 2: Determine the z-transform of −1
4−z X( z ) = −1 −2 2 − 2z + z With power series method and by dividing the numerator of X(z) by its denominator, we obtain the power series
∴ x[n] = [2, [2 1.5, 1 5 0.5, 0 5 0.25, 0 25 …..]]
Based on slides by Dileep Kumar
92
LATIHAN SOAL TZ 1) Desainlah realisasi Direct Form-I dan II jika diberikan fungsi transfer dari filter digital sbb :
Solusi :
(di (direct fform-1) 1) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
93
LATIHAN SOAL TZ
(direct form form-2) 2) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
94
LATIHAN SOAL TZ 2).
95
Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
LATIHAN SOAL TZ 3).
96
LATIHAN SOAL TZ 4).
97
LATIHAN SOAL TZ 5).
98
LATIHAN SOAL TZ 6).
99
Kondisi STABIL
100
Kondisi STABIL
101
Kondisi STABIL
John W.Leis, “DSP using Matlab for Students & Reseachers”, John Wiley & Sons, Inc., 2011
102
LATIHAN SOAL
https://sttmandalabdg.academia.edu/rahmadhidayat/
103
LATIHAN SOAL
https://sttmandalabdg.academia.edu/rahmadhidayat/
104
LATIHAN SOAL 1) Dengan Matlab, lakukan plot diagram Pole zero rho = 0 0.9 9; theta = pi/8 ; a = [ 12*rho*cos(theta ) rho^2] ; b = [ 12 1 ] ; p = roots ( a ) z = roots (b) ( ) zplane (b , a ) a2 = poly (p) b2 = poly ( z ) Catat juga hasilnya !
105
LATIHAN SOAL 2) Dengan Matlab, lakukan plot diagram Pole zero
Catat juga hasilnya !
106
LATIHAN SOAL 2) Dengan Matlab, lakukan plot diagram Pole zero
Catat juga hasilnya !
107
Persamaan Beda (Difference Equation)
LATIHAN SOAL SOAL-SOAL SOAL PERSAMAAN BEDA ((Lihat materi suplemen) p )
108
Persamaan Beda (Difference Equation)
LATIHAN SOAL SOAL-SOAL SOAL PERSAMAAN BEDA ((Lihat materi suplemen) p )
109
BAB IV. FILTER
PERANCANGAN SISTEM DISKRIT (Filter)
111
PERANCANGAN SISTEM DISKRIT (Filter)
112
PERANCANGAN SISTEM DISKRIT (Filter)
113
PERANCANGAN SISTEM DISKRIT (Filter)
114
LATIHAN SOAL TZ 1) Desainlah realisasi Direct Form-I dan II jika diberikan fungsi transfer dari filter digital sbb :
Solusi :
(di (direct fform-1) 1) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
115
LATIHAN SOAL TZ
(direct form form-2) 2) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
116
PERANCANGAN SISTEM DISKRIT (IIR Filter)
117
PERANCANGAN SISTEM DISKRIT (IIR Filter)
118
PERANCANGAN SISTEM DISKRIT (IIR Filter)
119
PERANCANGAN SISTEM DISKRIT (IIR Filter)
120
PERANCANGAN SISTEM DISKRIT (IIR Filter)
121
PERANCANGAN SISTEM DISKRIT (IIR Filter)
122
PERANCANGAN SISTEM DISKRIT (IIR Filter)
123
PERANCANGAN SISTEM DISKRIT (IIR Filter)
Gambar juga direct form-1 form 1 dan direct form-2 form 2 nya !
124
PERANCANGAN SISTEM DISKRIT (IIR Filter)
125
PERANCANGAN SISTEM DISKRIT (IIR Filter)
126
PERANCANGAN SISTEM DISKRIT (IIR Filter)
127
PERANCANGAN SISTEM DISKRIT (IIR Filter) Cek kebenaran form kaskade : hitung 8 sampel pertama dari impuls respon
128
HASIL SIMULASI
129
BAB V. DFT- FFT
CONTOH APLIKASI
131
REFERENSI
REFERENSI
• Understanding Digital Signal Processor, R.G Lyons, Prentice Hall, 2004. • Digital Di it l Si Signall P Processing i – a practice ti guide id ffor engineers i and d scientists, SW.Smith, Newness, 2003. • Digital g Signal g Processing, g S.Mitra, Mc.Graw Hill,3rd Edition, 2005
133
Terimakasih ! Rahmad Hidayat [email protected]
STT MANDALA Copyright 2018
Digital Signal Processing [Sistem Pemrosesan Sinyal]
Rahmad Hidayat Email : [email protected]
Jurusan Teknik Elektro SEKOLAH TINGGI TEKNOLOGI MANDALA Jalan Soekarno Hatta 597 Bandung
SISTEM PENILAIAN
•Tugas • UTS • UAS • Presensi Selasa 17.00 17 00
2
: : : :
20 % 30 % 40 % 10 %
MATERI
•BAB I •BAB II •BAB BAB III •BAB IV •BAB V
: : : : :
Pendahuluan Sinyal & Sistem Diskrit T Transformasi f iZ Filter DFT-FFT
• Latihan Aplikasi DSP dengan MATLAB •Tugas Membuat GUI MATLAB untuk beberapa aplikasi DSP
Catatan : beberapa p materi ((suplemen) p ) di-share melalui g google g drive
3
BAB II. PENDAHULUAN
LATAR BELAKANG Pemrosesan Sinyal Analog
Prosesor Analog Sederhana
ekivalen dengan sebuah FILTER ANALOG 5
LATAR BELAKANG Contoh Filter Analog
6
Fungsi Filter
Based on slides by Haris Balzakis –Lecture 5 DSP
7
Sistem Pemrosesan Sinyal (DSP) dari Sinyal Analog
(Blok ekivalen dari Prosesor Analog)
8
Sistem Pemrosesan Sinyal (DSP) dari Sinyal Analog
(Blok ekivalen dari Filter Analog)
9
Analog to Digital Converter
10
Jadi untuk apa sinyal diubah ?
11
BAB II II. SINYAL & SISTEM DISKRIT
Based on slides by Kenneth E. Barner, Univ.of Delaware
Tentang Sinyal
www.complextorial.com
13
Tentang Sinyal
Signals are functions of time that curry information relative to the state and/or the behavior of a system. Categorization: Depending on whether they are defined for continuous time intervals or for specific time instances: •) Continuous time signals. •) Discrete Di t titime signals. i l Depending on the values they take: •) Analog signals •) Digital signals.
Based on slides by Haris Balzakis –Lecture 5 DSP
14
Tipe Sinyal
Based on slides by Haris Balzakis –Lecture 5 DSP
15
Tipe Sinyal
Based on slides by Haris Balzakis –Lecture 5 DSP
16
Contoh Sinyal
17
Contoh Sinyal
18
Contoh Sinyal
19
Contoh Sinyal
20
Sinyal Waktu Diskrit
21
Sinyal Diskrit
22
Sinyal Diskrit
23
Sinyal Waktu Diskrit
See Oppenheim and Schafer , second edition pages 8-93, or first edition pages 8-79
24
Sinyal Waktu Diskrit
See Oppenheim and Schafer , second edition pages 8-93, or first edition pages 8-79
25
Sinyal Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
26
Sinyal Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
27
Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
28
Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
29
Sistem Waktu Diskrit (Contoh-1)
Based on slides by Kenneth E. Barner, Univ.of Delaware
30
Sistem Waktu Diskrit (Contoh-2)
Based on slides by Kenneth E. Barner, Univ.of Delaware
31
Klasifikasi Sistem Waktu Diskrit
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
32
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
33
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
34
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
35
Klasifikasi Sistem Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
36
Analisis Sistem LTI
(Linear Time Invariant )
Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
37
Analisis Sistem LTI
(Linear Time Invariant )
Waktu Diskrit
Based on slides by Kenneth E. Barner, Univ.of Delaware
38
Based on slides by Kenneth E. Barner, Univ.of Delaware
39
Based on slides by Kenneth E. Barner, Univ.of Delaware
40
Based on slides by Kenneth E. Barner, Univ.of Delaware
41
Properti Konvolusi
Based on slides by Kenneth E. Barner, Univ.of Delaware
42
Properti Konvolusi
See Oppenheim and Schafer, Second Edition pages 8–93, or First Edition pages 8–79.
43
Sistem LTI - KAUSAL
Based on slides by Kenneth E. Barner, Univ.of Delaware
44
Sistem LTI - KAUSAL A system is causal if the output at n depends only on the input at n and earlier inputs. For example, the backward difference system : is causal, but the forward difference system : is not.
See Oppenheim and Schafer, Second Edition pages 8–93, or First Edition pages 8–79.
45
Sistem LTI - STABIL
Based on slides by Kenneth E. Barner, Univ.of Delaware
46
Sistem LTI - STABIL The ideal delay system A system is stable if every bounded input sequence produces a bounded output sequence:
For example, example the accumulator is an example of an unbounded system, since its response to the unit step u[n] is
which has no finite upper bound bound. See Oppenheim and Schafer, Second Edition pages 8–93, or First Edition pages 8–79.
47
Based on slides by Kenneth E. Barner, Univ.of Delaware
48
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
49
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
50
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
51
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
52
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
53
Based on slides of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, August 31, 2010
54
Based on slides by Kenneth E. Barner, Univ.of Delaware
55
Difference Equation (Persamaan Beda)
Based on slides by Kenneth E. Barner, Univ.of Delaware
56
Realisasi Direct Form-I
Based on slides by Kenneth E. Barner, Univ.of Delaware
57
Realisasi Direct Form-II
Based on slides by Kenneth E. Barner, Univ.of Delaware
58
Realisasi :
Based on slides by Kenneth E. Barner, Univ.of Delaware
59
Persamaan Beda (Difference Equation)
60
Persamaan Beda (Difference Equation)
B.A Shenoi, “Introduction to DSP and Filter Design”, John Wiley & Sons,Inc., 2006
61
BAB III. TRANSFORMASI Z
Transformasi Z
Based on slides by EECS, University of Tennessee,2010
63
Transformasi Z
Based on slides by EECS, University of Tennessee,2010
64
Transformasi Z
Based on slides by EECS, University of Tennessee,2010
65
Transformasi Z dari Filter FIR
Based on slides by EECS, University of Tennessee,2010
66
Fungsi sistem dari Sistem LTI
Based on slides by EECS, University of Tennessee,2010
67
Kelengkapan Transformasi Z
Based on slides by EECS, University of Tennessee,2010
68
Transformasi Z sebagai operator
Based on slides by EECS, University of Tennessee,2010
69
Konvolusi & Transformasi Z
Based on slides by EECS, University of Tennessee,2010
70
Sistem Kaskade pd Transformasi Z
Based on slides by EECS, University of Tennessee,2010
71
Faktorisasi Polinomial Z
Based on slides by EECS, University of Tennessee,2010
72
Domain
Based on slides by EECS, University of Tennessee,2010
73
Bidang Z , plot Pole-Zero
Based on slides by EECS, University of Tennessee,2010
74
Signifikansi Zero dari H(z)
Based on slides by EECS, University of Tennessee,2010
75
Signifikansi Zero dari H(z)
Based on slides by EECS, University of Tennessee,2010
76
Filter Nulling
Based on slides by EECS, University of Tennessee,2010
77
Plot pole-zero & respon frekuensi
Based on slides by EECS, University of Tennessee,2010
78
Sum filter dengan running L-poin
Based on slides by EECS, University of Tennessee,2010
79
Bandpass filter Kompleks
Based on slides by EECS, University of Tennessee,2010
80
Bandpass filter dengan Kompleks
Based on slides by EECS, University of Tennessee,2010
81
Bandpass filter dg koefisien Real
Based on slides by EECS, University of Tennessee,2010
82
ROC (region of convergence)
Based on slides by EECS, University of Tennessee,2010
83
ROC (region of convergence)
Based on slides by EECS, University of Tennessee,2010
84
ROC (region of convergence)
Based on slides by EECS, University of Tennessee,2010
85
Contoh-1 (Penentuan Transformasi Z) (a) x[n] = [1, 2, 5, 7, 0, 1] Solution: X(z) = 1 + 2z-1+ 5z-2 + 7z-3 + z-5, ROC: entire z plane except z = 0 (b) y[n] [n] = [1, [1 2, 2 5, 5 7, 7 0, 0 1] Solution: Y(z) = z2 + 2z + 5 + 7z-1 + z-3 ROC: entire zz-plane plane except z = 0 and z = ∞. ∞ ( ) z[n] (c) [ ] = [[0,, 0,, 1,, 2,, 5,, 7,, 0,, 1]] Solution: Y(z) = z-2 + 2z-3 + 5z-4 + 7z-5 + z-7, ROC: all z except z=0 Based on slides by Dileep Kumar
86
Transformasi Z (d) p[n] = δ[n] S l ti Solution: P( P(z)) = 1 1, ROC ROC: entire ti z-plane. l (e) q[n] = δ[n – k], k] k > 0 Solution: Q(z) = z-k, entire z-plane except z=0. (f) r[n] = δ[n+k], k > 0 Solution: R(z) = zk, ROC: entire z-plane except z = ∞.
Based on slides by Dileep Kumar
87
Contoh-2 (Penentuan Transformasi Z) Determine the z-transform of x[n] = (1/2)nu[n] Solution:
X (z ) =
∞
∑
x [ n ]z − n
n
∞
n = −∞ ∞
⎛1⎞ = ∑ ⎜ ⎟ z −n = n=0 ⎝ 2 ⎠
⎛ 1 −1 ⎞ ⎜ z ⎟ ∑ ⎠ n=0 ⎝ 2
1 −1 ⎛ 1 ⎞ z + ⎜ z⎟ 2 ⎝2 ⎠ 1 = 1 −1 1− z 2 = 1+
n
−2
+ .......
ROC: |1/2 z-1| < 1, or equivalently |z| > 1/2 Based on slides by Dileep Kumar
88
Contoh-3 (Penentuan Transformasi Z) Determine the z-transform of the signal x[n] = anu[n] Solusi : X( z ) =
∞
n −n a ∑ z = n=0
= 1 + az
−1
(
+ az
)
−1 2
∑ (az ) ∞
n
−1
n=0
+ .......
1 = 1 − az − 1 ROC :| z |>| a | Based on slides by Dileep Kumar
89
Invers Transformasi Z In general, the inverse z-transform may be found by using any of the following methods: Power series method Partial fraction method
Based on slides by Dileep Kumar
90
Contoh Penentuan Invers Transformasi Z Example 1: Determine the z-transform of
X( z ) =
1 1 − 1 .5 z
−1
+ 0 .5 z
−2
With power series method and by dividing the numerator of X(z) by its denominator, we obtain the power series 1 1 − 32 z −1 + 12 z − 2
31 − 4 = 1 + 32 z −1 + 74 z − 2 + 158 z − 3 + 16 z + ...
∴ x[n] = [1, 3/2, 7/4, 15/8, 31/16,…. ] Based on slides by Dileep Kumar
91
Contoh Penentuan Invers Transformasi Z Example 2: Determine the z-transform of −1
4−z X( z ) = −1 −2 2 − 2z + z With power series method and by dividing the numerator of X(z) by its denominator, we obtain the power series
∴ x[n] = [2, [2 1.5, 1 5 0.5, 0 5 0.25, 0 25 …..]]
Based on slides by Dileep Kumar
92
LATIHAN SOAL TZ 1) Desainlah realisasi Direct Form-I dan II jika diberikan fungsi transfer dari filter digital sbb :
Solusi :
(di (direct fform-1) 1) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
93
LATIHAN SOAL TZ
(direct form form-2) 2) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
94
LATIHAN SOAL TZ 2).
95
Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
LATIHAN SOAL TZ 3).
96
LATIHAN SOAL TZ 4).
97
LATIHAN SOAL TZ 5).
98
LATIHAN SOAL TZ 6).
99
Kondisi STABIL
100
Kondisi STABIL
101
Kondisi STABIL
John W.Leis, “DSP using Matlab for Students & Reseachers”, John Wiley & Sons, Inc., 2011
102
LATIHAN SOAL
https://sttmandalabdg.academia.edu/rahmadhidayat/
103
LATIHAN SOAL
https://sttmandalabdg.academia.edu/rahmadhidayat/
104
LATIHAN SOAL 1) Dengan Matlab, lakukan plot diagram Pole zero rho = 0 0.9 9; theta = pi/8 ; a = [ 12*rho*cos(theta ) rho^2] ; b = [ 12 1 ] ; p = roots ( a ) z = roots (b) ( ) zplane (b , a ) a2 = poly (p) b2 = poly ( z ) Catat juga hasilnya !
105
LATIHAN SOAL 2) Dengan Matlab, lakukan plot diagram Pole zero
Catat juga hasilnya !
106
LATIHAN SOAL 2) Dengan Matlab, lakukan plot diagram Pole zero
Catat juga hasilnya !
107
Persamaan Beda (Difference Equation)
LATIHAN SOAL SOAL-SOAL SOAL PERSAMAAN BEDA ((Lihat materi suplemen) p )
108
Persamaan Beda (Difference Equation)
LATIHAN SOAL SOAL-SOAL SOAL PERSAMAAN BEDA ((Lihat materi suplemen) p )
109
BAB IV. FILTER
PERANCANGAN SISTEM DISKRIT (Filter)
111
PERANCANGAN SISTEM DISKRIT (Filter)
112
PERANCANGAN SISTEM DISKRIT (Filter)
113
PERANCANGAN SISTEM DISKRIT (Filter)
114
LATIHAN SOAL TZ 1) Desainlah realisasi Direct Form-I dan II jika diberikan fungsi transfer dari filter digital sbb :
Solusi :
(di (direct fform-1) 1) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
115
LATIHAN SOAL TZ
(direct form form-2) 2) Edmund Lai, “Practical DSP for Engineers and Technicians”, Newnes, 2003
116
PERANCANGAN SISTEM DISKRIT (IIR Filter)
117
PERANCANGAN SISTEM DISKRIT (IIR Filter)
118
PERANCANGAN SISTEM DISKRIT (IIR Filter)
119
PERANCANGAN SISTEM DISKRIT (IIR Filter)
120
PERANCANGAN SISTEM DISKRIT (IIR Filter)
121
PERANCANGAN SISTEM DISKRIT (IIR Filter)
122
PERANCANGAN SISTEM DISKRIT (IIR Filter)
123
PERANCANGAN SISTEM DISKRIT (IIR Filter)
Gambar juga direct form-1 form 1 dan direct form-2 form 2 nya !
124
PERANCANGAN SISTEM DISKRIT (IIR Filter)
125
PERANCANGAN SISTEM DISKRIT (IIR Filter)
126
PERANCANGAN SISTEM DISKRIT (IIR Filter)
127
PERANCANGAN SISTEM DISKRIT (IIR Filter) Cek kebenaran form kaskade : hitung 8 sampel pertama dari impuls respon
128
HASIL SIMULASI
129
BAB V. DFT- FFT
CONTOH APLIKASI
131
REFERENSI
REFERENSI
• Understanding Digital Signal Processor, R.G Lyons, Prentice Hall, 2004. • Digital Di it l Si Signall P Processing i – a practice ti guide id ffor engineers i and d scientists, SW.Smith, Newness, 2003. • Digital g Signal g Processing, g S.Mitra, Mc.Graw Hill,3rd Edition, 2005
133
Terimakasih ! Rahmad Hidayat [email protected]
STT MANDALA Copyright 2018
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