Nguyễn Công Phương

SIGNAL PROCESSING
 Contents
I. Introduction
II. Discrete – Time Signals and Systems
III. The z – Transform
IV. Fourier Representation of Signals
V. Transform Analysis of LTI Systems
VI. Sampling of Continuous – Time Signals
VII.The Discrete Fourier Transform
VIII.Structures for Discrete – Time Systems
IX. Design of FIR Filters
X. Design of IIR Filters
XI. Random Signal Processing
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 References
[1] D. Manolakis and V. Ingle. Applied Digital
Signal Processing. Cambridge, 2011.
[2] J. G. Proakis and D. G. Manolakis. Digital
Signal Processing – Principles, Algorithms,
and Applications. Prentice – Hall, 1996.
[3] R. N. Bracewell. The Fourier Transform
and its Applications. McGraw-Hill, 2000.
[4] V. K. Madisetti, D. B. Williams. Digital
Signal Processing Handbook. CRC Press,
1999.
[5] A. V. Oppenheim, A. S. Willsky, and S. H.
Nawab. Signals and Systems. Prentice Hall,
1997.
[6] S. Stergiopoulos. Advanced Signal
Processing Handbook. CRC Press, 2001
[7] sites.google.com/site/ncpdhbkhn
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 Introduction

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To record, create, manipulate, transform, and transmit signals

https://en.wikipedia.org/wiki/Signal_processing#/media/File:Signal_processing_system.png
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 Introduction
• Signal Processing: [Bruce, 2001] the manipulation of a signal
for the purpose of:
– Extracting information from the signal,
– Extracting information about the relationships of two (or
more) signals,
– Producing an alternative representation of the signal.
• Why signals are processed? [Bruce, 2001]
– To remove unwanted signal components that are corrupting
the signal of interest,
– To extract information by rendering it in a more obvious or
more useful form,
– To predict future values of the signal in order to anticipate
the behavior of its source.
E.N. Bruce. Biomedical Signal Processing and Signal Modeling. Wiley, 2001
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 Introduction
1. Signals
2. Systems
3. Analog, Digital, and Mixed Signals
Processing
4. Applications of Digital Signal Processing

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 Signals (1)
• Signal: a physical quantity varying as a
function (of time, space, etc.) and carrying
information

R L Index

i + C
v
e –
+– M T W T F S

Closing value
Current as Image as a function
of the stock exchange index
a function of time of x–y coordinates
as a function of days
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 Signals (2)
i (A) Index

t (s)
M T W T F S

s(t) s[n]

Continuous – time signal Discrete – time signal

Value of s(t) is defined for Value of s(t) is defined

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 Signals (3)
s(t) s[n]

t (s) 1 2 5 6 n
0
3 4 7 8
s (t )
s(t)
s[n] = s(t ) t= nT = s(nT )

T : sampling period
1
f s = : sampling frequency
T
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 Signals (4)

Deterministic signal Random signal

The future value is The future value is

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 Introduction
1. Signals
2. Systems
3. Analog, Digital, and Mixed Signals
Processing
4. Applications of Digital Signal Processing

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 Systems
Continuous – Time
x (t ) System y (t )
Advantages of digital over analog signal processing:
• Digital system can be simply reprogrammed for other applications, or
ported to different hardware, or duplicated
Analog-to-Digital Digital-to-Analog
• DSP provides better control of accuracy requirement
Conversion (ADC) Conversion (DAC)
• Digital signals can be easily stored without deterioration
• More sophisticated signal processing algorithms can be implemented

x[n ] Discrete – Time y [n ]

Analog Pre-processing

ADC

DSP

DAC
Analog
Analog Post-processing
output
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 Applications of Digital Signal
Processing
• Speech processing
• Image processing
• Music applications
• Multimedia
• Communication
• Biomedical
• Military

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 Applications of DSP:
Speech Processing (1)
• Noise reduction

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 Applications of DSP:
Speech Processing (2)
• Speech recognition

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 Applications of DSP:
Speech Processing (3)
• Speech synthesis

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 Applications of DSP:
Image Processing (1)
• Content based image retrieval – browsing,
searching & retrieving images from database

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 Applications of DSP:
Image Processing (2)
• Image enhancement

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 Applications of DSP:
Image Processing (3)
• Image compression

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 Applications of DSP:
Music Applications

• Recording
• Playback
• Manipulation (mixing, special effects)

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 Applications of DSP:
Multimedia
• Generation, storage & transmission of sound,
still images, motion pictures

Digital TV

Video conference
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 Applications of DSP:
Communication
• Telephony
• Encoding & decoding of the information sent
over a physical channel

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 Applications of DSP:
Biomedical
• Electrocardiogram (ECG) signal: provides doctor with
information about the condition of the patient’s heart
• Electroencephalogram (EEG) signal: provides information
about the activity of the brain

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 Applications of DSP:
Military (1)
• Guidance & navigation

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 Applications of DSP
Military (2)
• Radar & sonar

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