INTRODUCTION TO DIGITAL SIGNAL
PROCESSING
LUTFI A. AREBI
Feb, 2021
Department of Computer Engineering
University of Tripoli
Digital Signal Processing
 Text books:
1.
Digital Signal Processing, Principles, Algorithms, and Applications: John G.
Proakis, Dimitris G.Manolakis, 4th edtion.
2.
Discrete Time Signal Processing – A. V. Oppenheim and R.W. Schaffer, with
john buck, 2nd edition.
 Course evaluation system
» Test 1:
15%
» Test 2:
15%
» Home works:
10%
» Mini projects or special report
10%
» Final
50%
Slide 2
Digital Signal Processing
Systems
Linear
Continuous
Non-Linear
Sampling
Discrete
Time domain:
• differential equ.
• Convolution integral
• State variable
Frequency domain
• Fourier series
• Fourier transform
Complex domain
Laplace transform
s=r+jIm
Time domain:
• Difference equ.
• Convolution sum
• State variable
Frequency domain
• Fourier analysis
• FFT
Complex domain
Z-transform
𝑧 = 𝑟e𝑗ѳ
Slide 3
What is signal ?

A signal is anything you can see, hear, observe or measure using some machine.
• Examples: Speech, audio, light, radio, TV, radar, supersonic, temperature, ECG, EEG, etc.

A signal is defined as any physical quantity that varies with time, space or another independent
variable.

A signal is the carrier of information.
.ECG contains information related to sickness. medical diagnosis
.Voice contains information about who is speaking and what is spoken
.Speech recognition•

.Speaker recognition
Representation of signals
– Mathematic representations of signals
Continuous-time signal or analog signal
– x(t)
• Discrete-time signal or sequence
– x(n) or x(nT) or xn
• Digital signal
– Discrete value of x(n)
Slide 4
Classification of signals
 Analog signal
Continuous independent variable (e.g time)and continuous dependent
variable (e.g voltage).
 Quantized signal
continuous independent variable and discrete dependent variable.
 Discrete signal
Discrete independent variable and continuous dependent variable.
 Digital signal
Discrete independent variable and discrete dependent variable.
Slide 5
Classification of signals
Classification of Signals
Slide 6
What is a system?

A system is defined as a physical device that performs an operation on a signal.

System is characterized by the type of operation that performs on the signal. Such
operations are referred to as signal processing.
 Representation of systems
x(n)
Signal processor
» x(n): input, stimulus
» y(n): output, response
System analysis
–To understand the properties of a given system
• System design
–To find system that meets given specifications
• System synthesis
–To find a system structure
• System implementation
–To realize a system using software or hardware
Slide 7
y(n)
What is signal processing ?

The purpose of signal processing is to make it easier to extract useful information
and to make correct decisions.
For this purpose, we have
– Signal enhancement
– Signal restoration
– Signal reconstruction
– Signal synthesis
– Signal estimation and prediction

After signal processing, we can extract more important information, and recognize,
aware, and make decisions.
Slide 8
What is signal processing
 Signal Enhancement
– Signal amplification in radio, TV, human ears
– Image enhancement in image processing
 Signal Restoration
Restore a signal corrupted by noise or useless background
–Tuning in radio and TV
–Noise cleaning
–Pick up the voice of a certain person in a party
 Signal Reconstruction
Reconstruct a signal from different measurement
–Computerized tomogram (CT)
–Synthetic aperture radar (SAR) imaging
–Reconstruct 3D images from different 2D views
Slide 9
What is signal processing
 Signal Synthesis
Find a system that can generate the desired signal
–Speech synthesis
–3D sound synthesis
–Make a virtual world in computer
 Signal Estimation
Estimate the future values from observed data
–Stock prediction
–Electrical Demand prediction
–Image compression
–Adaptive signal processing
Slide 10
Basic signals
Some basic signals
• There are four basic signals
–The unit sample signal (impulse signal)
–The unit step signal (step signal)
–The ramp signal
–The exponential signal
–The sinusoidal signal
• All other signals can be represented by the
basic signals given above.
–Fourier series
–Fourier transformation
Slide 11
Digital Signal processing
Slide 12
DSP in a global chain
Slide 13