Introduction to Digital Signal

Processing (DSP)

Mata Kuliah: Pengolahan Sinyal Digital

Nanang Ismail
 What is Digital Signal Processing?

Digital: operating by the use of discrete signals to

represent data in the form of numbers

Signal: a parameter (electrical quantity or effect) that can

be varied in such a way as to convey information

Processing: a series operations performed according to

programmed instructions

changing or analysing information

which is measured as discrete
sequences of numbers
 The Journey

“Learning digital signal processing is not something

you accomplish; it’s a journey you take”.

R.G Lyons, Understanding Digital Signal processing

 Applications of DSP - Radar

Radar and Sonar:

Examples

1)target detection – position and

velocity estimation

2) tracking
 Applications of DSP - Biomedical

Biomedical: analysis of biomedical signals,

diagnosis, patient monitoring,
preventive health care, artificial
organs
Examples:

1)electrocardiogram (ECG) signal – provides

doctor with information about the condition of
the patient’s heart

2)electroencephalogram (EEG) signal – provides

Information about the activity of the brain
 Applications of DSP - Speech

Speech applications:

Examples
1) noise reduction – reducing background noise
in the sequence produced by a sensing device (microphone)

2)speech recognition – differentiating

between various speech sounds

3) synthesis of artificial speech – text to speech

systems for blind
 Applications of DSP - Communications

Communications:

Examples
1) telephony – transmission of information in digital form via
telephone lines, modem technology, mobile phones

2) encoding and decoding of the information

sent over a physical channel (to optimise
transmission or to detect or correct errors in
transmission)
 Applications of DSP – Image Processing

Image Processing:

Examples
1)content based image retrieval – browsing,
searching and retrieving images from database

2) image enhancement

2) compression - reducing the redundancy in

the image data to optimise transmission /
storage
 Applications of DSP – Music

Music Applications:

Examples:

1) Recording

2) Playback

3) Manipulation (mixing, special effects)

 Applications of DSP - Multimedia

Multimedia:
generation storage and
transmission of sound, still
images, motion pictures

Examples:
1) digital TV

2) video conferencing
 DSP Implementation - Operations

To implement DSP we must be able to:

Input Digital Digital

Signal Signal
DSP
Output

1) perform numerical operations including, for

example, additions, multiplications, data transfers
and logical operations
either using computer or special-purpose hardware
 DSP chips

• Introduction of the microprocessor in the late 1970's and

early 1980's meant DSP techniques could be used in a
much wider range of applications.
DSP chip – a programmable
device, with its own native
instruction code

designed specifically to meet

numerically-intensive
requirements of DSP

capable of carrying out

millions of floating point
Bluetooth Household Home theatre
headset appliances system operations per second
 DSP Implementation – Digital/Analog Conversion

To implement DSP we must be able to:

Digital Digital Analog

Signal Signal Signal
DSP Reconstruction

2) convert the digital information, after being processed

back to an analog signal
- involves digital-to-analog conversion & reconstruction
(recall from 1B Signal and Data Analysis)
e.g. text-to-speech signal (characters are used to generate artificial
sound)
 DSP Implementation –Analog/Digital Conversion

To implement DSP we must be able to:

Analog Digital Digital

Signal Signal Signal
Sampling DSP

3) convert analog signals into the digital information

- sampling & involves analog-to-digital conversion
(recall from 1B Signal and Data Analysis)
e.g. Touch-Tone system of telephone dialling (when button is
pushed two sinusoid signals are generated (tones) and
transmitted, a digital system determines the frequences and
uniquely identifies the button – digital (1 to 12) output
 DSP Implementation

To implement DSP we must be able to:

Analog Digital Digital Analog

Signal Signal Signal Signal
Sampling DSP Reconstruction

perform both A/D and D/A conversions

e.g. digital recording and playback of music (signal is sensed by

microphones, amplified, converted to digital, processed, and
converted back to analog to be played
17
 Limitations of DSP - Aliasing

Most signals are analog in nature, and have to be sampled

loss of information
• we only take samples of the signals at intervals and
don’t know what happens in between
aliasing
cannot distinguish between
higher and lower frequencies
(recall from 1B Signal
and Data Analysis)

Sampling theorem: to avoid

aliasing, sampling rate must be
at least twice the maximum
frequency component
(`bandwidth’) of the signa1l8
Gjendemsjø, A. Aliasing Applet, Connexions, http://cnx.org/content/m11448/1.14
 Limitations of DSP - Antialias Filter

• Sampling theorem says there is enough information to

reconstruct the signal, which does not mean sampled signal looks
like original one
correct reconstruction is not just connecting
samples with straight lines

needs antialias filter (to filter out all high frequency

components before sampling) and the same for
reconstruction – it does remove information though

Each sample
is taken at a
slightly earlier (recall from 1B Signal
part of a cycle and Data Analysis)
19
 Limitations of DSP – Frequency Resolution

Most signals are analog in nature, and have to be sampled

loss of information

• we only take samples for a limited period of time

limited frequency
resolution

does not pick up “relatively”

slow changes

(recall from 1B Signal

and Data Analysis) 20
 Limitations of DSP – Quantisation Error

Most signals are analog in nature, and have to be sampled

loss of information
• limited (by the number of bits available) precision in data
storage and arithmetic

quantisation error

smoothly varying signal

represented by “stepped”
waveform

(recall from 1B Signal

and Data Analysis) 21
 Advantages of Digital over Analog Signal Processing

Why still do it?

• Digital system can be simply reprogrammed for other

applications / ported to different hardware / duplicated
(Reconfiguring analog system means hadware redesign, testing, verification)
• DSP provides better control of accuracy requirements
(Analog system depends on strict components tolerance, response may drift with
temperature)
• Digital signals can be easily stored without deterioration
(Analog signals are not easily transportable and often can’t be processed off-line)
• More sophisticated signal processing algorithms can be
implemented
(Difficult to perform precise mathematical operations in analog form)
22
Keuntungan Pemrosesan sinyal secara digital

 Untuk menyimpan hasil pengolahan, sinyal digital lebih mudah dibandingkan sinyal analog.
 Untuk media penyimpan digital dapat digunakan elemen memori: flash memory, CD/DVD, hard disk.
 Untuk menyimpan sinyal analog dapat digunakan pita tape magnetik.
 Sinyal digital kebal terhadap noise, karena bekerja pada level tegangan logika “1” dan “0”
 Lebih kebal terhadap perubahan temperatur.
 Lebih mudah memprosesnya, secara teori tidak ada batasannya, tergantung dari kreativitas dan inovasi
perancang.

Kelemahan sinyal digital

 Dapat Terjadi kehilangan informasi akibat pembulatan saat kuantisasi dan filtering saat pembalikan kembali
ke sinyal analog.

 Diperlukan waktu proses yang lebih lama dibandingkan sinyal analog, perlu waktu sampling dan rekonstruksi
ulang
Perbandingan pengolahan sinyal
 SINYAL, SISTEM DAN PEMROSESAN SINYAL

 Sinyal
 Besaran-besaran yang tergantung pada waktu dan ruang
 Besaran fisis/non fisis (variabel tak bebas)
 Waktu dan ruang (variabel bebas)

s1 (t )  5 t
s2 (t )  20 t 2

s3 ( x, y )  3 x  2 xy  10 y 2

Sinyal-sinyal dengan hubungan matematis yang jelas

 Suara pembicaraan (speech signals)

Sinyal –sinyal dengan hubungan matematis yang tidak jelas

 Suatu segmen dari suara pembicaraan dapat
direpresentasikan sebagai :
 Sejumlah sinyal sinusoidal dengan amplituda,
frekuensi dan fasa yang berbeda

N
s( t )   A i ( t ) sin [2 Fi ( t ) t  i ( t )]
i 1

 Informasi yang terkandung di dalam suatu sinyal

ditentukan dengan mengukur :
 Amplituda(A)
 Frekuensi(F)
 Fasa()
 Sinyal electrocardiogram (ECG)
 Sinyal elektronik yang berasal dari aktivitas jantung
 Informasi mengenai kondisi dari jantung pasien

 Sinyal electroencephalogram (EEG)

 Sinyal elektronik yang berasal dar aktivitas otak
 Sinyal-sinyal , ,  dan 

 Sinyal-sinyal dengan satu variabel bebas (waktu)

 Suara pembicaraan, ECG dan EEG

 Sinyal dengan dua variabel bebas (ruang)

 Gambar (image signal)
 Sistem
 Alat fisik yang melakukan suatu operasi pada suatu sinyal
 Filter
 Mereduksi (mengurangi) derau (noise)
 Alat non fisik
 Software (perangkat lunak)
 Melakukan sejumlah operasi-operasi matematik
 Algoritma

 Pemrosesan sinyal (Signal processing)

 Operasi-operasi yang dilakukan pada suatu sinyal

 ELEMEN-ELEMEN DASAR DARI Pemrosesan Sinyal
 Sistem pemrosesan sinyal analog

Sinyal Pemroses Sinyal

input sinyal output
analog analog analog

 Sistem pemrosesan sinyal digital

Sinyal A/D Pemroses D/A Sinyal

input sinyal output
analog Converter digital Converter analog

Sinyal input digital Sinyal output digital

SIMBOL OPERASI
PENGOLAHAN SINYAL
Pembagian Sinyal

Sinyal dibagi berdasarkan beberapa kriteria:

1. Kanal dan Dimensi
2. Periodisitas
3. Keacakan
4. Sinyal Ganjil dan Genap
5. Energi dan Daya
6. Amplitudo (nilai) dan Waktu
 KLASIFIKASI SINYAL
 Single-channel signal
 Hanya terdiri dari satu sinyal (variabel tak bebas)
 Nilainya bisa real atau kompleks
 Monitor TV monochrome : sinyal 1 kanal

s1 ( t )  A sin(3t )
j3t
s 2 ( t )  Ae  A cos(3t )  jA sin(3t )
 Multi-channel signal
 Lebih dari satu sinyal (variabel tak bebas)
 Gelombang gempa (3 channels)
 ECG (3 channels/12 channels)
 Monitor TV color: sinyal 3 kanal, RGB
 Gelombang gempa :
 Primary wave (Longitudinal)
 Secondary wave (Transversal)
 Surface wave (Permukaan)

Vektor

S1 ( t ) 
S( t )  S2 ( t )
S3 ( t ) 

3 komponen kecepatan permukaan

 Sinyal satu dimensi
 Hanya fungsi dari satu variabel bebas

 Multi-dimensional signal
 Fungsi lebih dari satu variabel bebas

S  I(x, y)

Sinyal dua dimensi

 Sinyal tiga dimensi
 Gambar televisi hitam-putih
S  I(x, y, t )

 Multichannel multidimensional signal

 Gambar televisi berwarna

I r ( x, y, t ) 
 
I( x, y, t )  I g ( x, y, t )
I ( x, y, t )
 b 

Gambar diam (still image) : sinyal 2 dimensi

Gambar bergerak : sinyal 3 dimensi : x, y, t
 Sinyal waktu kontinu
 Speech signal
 Sinyal waktu diskrit
 Hanya ada pada waktu-waktu tertentu saja

0,8n n  0
x (n )  
0 lainnya

0,8
0,64
 Sinyal bernilai kontinu (Continuous-valued signal)
 Dapat berharga berapa saja

Sinyal bernilai kontinu dan waktu diskrit

 Sinyal bernilai diskrit (Discrete-valued signal)
 Bernilai pada beberapa kemungkinan saja
 Sinyal digital
 Waktu diskrit
 Harga diskrit

Sinyal Analog Vs Sinyal Digital

 Sinyal deterministik
 Nilainya dapat diprediksi

 Sinyal acak (random signal)

 Nilainya tidak dapat diprediksi
 keberadaanya bersifat probabilistik
Sinyal riil dan sinyal kompleks

 Sinyal riil merupakan sinyal yang bersifat riil untuk semua variabel.

 Sinyal kompleks merupakan sinyal yang mempunyai nilai yang kompleks, ada faktor
nilai imajiner.
Sinyal Riil : Sinyal Komplek :
XR (n) = 2n Cost n x(n) = 2n ejn
Sinyal ganjil dan sinyal genap

• Sinyal x(t) atau sinyal x(n) dikatakan sebagai sinyal genap jika :
x(-t) = x(t)
x(-n) = x(n)
• Sinyal x(t) atau sinyal x(n) dikatakan sebagai sinyal ganjil jika :
x(-t) = -x(t)
x(-n) = -x(n)

Sinyal Kontinu Genap dan Sinyal Diskrit Genap Sinyal Kontinu Ganjil dan Sinyal Diskrit Ganjil
Sinyal periodik dan sinyal non-periodik

• Sinyal periodik yaitu sinyal yang mengalami pengulangan bentuk yang

sama pada selang waktu tertentu. Secara matematis, sinyal waktu
kontinyu dinyatakan periodik jika dan hanya jika :
x(t+kT) = x(t) untuk = - < t < 
dimana : k adalah bilangan bulat, T adalah perioda sinyal.
• Sinyal waktu diskrit dinyatakan periodik jika dan hanya jika :
X(n+kN) = x(n) untuk = - < n < 
dimana : k adalah bilangan bulat, N adalah perioda sinyal

Sinyal Periodik Sinyal Non-Periodik

Terimakasih