Power/frequency (dB/Hz)Power/frequency (dB/Hz)Power/frequency (dB/Hz)

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제1강. 신호와 시스템의 개념 및 소개

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Course information



Time

• Tues, Fri 14:30-16:00



Location

• 제1공학관, 408호



Textbook (Required)

• A. Oppenheim and A. S. Willsky, “Signal and systems, second edition”, Prentice Hall

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Course information



Lecture note

• Course materials will be uploaded at Hanyang portal site.



Homework

• Late submission will get 20% reduction per day in score.



Grading

• Homework – 10%

• Midterm – 40%

• Final – 40%

• Attendance – 10%



Office hour

• Schedule an appointment via E-mail.

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Time(s)

What is “signal and systems”?



What is signal?

• A signal is a form of waveform or data sequence containing some

“information”.

• Example of the signal

• Speech, Music, Video (Multimedia), Light, Radio frequency (RF) signal, Text message, Noise, Temperature, X-ray, …

Waveform of speech signal

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

Speech signal

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Time(s)

[0], [1], [2], [3], [4], [5],..., [ ],....

x x x x x x x n

Discrete-time signal

Continuous-time signal

x t ( )

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

Image – two dimensional signal



Video signal – three dimensional signal

R,G,B 0~255

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

Example of signal acquisition

Microphone sensor

Natural sound (analog signal)

Transdu

cer Electrical waveform

ADC (Analog to

digital converter)

Signal processing

(in computer) Data storage

Transmission

Digital data

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

Image acquisition

Natural light (analog signal)

Lens Imaging

sensor CFA

Digital image processing Data storage

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

Digital signal

• Discrete in time (sampling)

• Discrete in amplitude (quantization)

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

Digital vs Analog signals

Analog signal Digital signal

Characteristic Continuous Discrete

Representation Real number , 실수 (0.2342122..)

Integer number, 정수 Resolution Infinite resolution Finite resolution

Example Physical quantities –

temperature, speed, pressure

Binary data, wav file, mp3, USB, Text message

High Low

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

What are systems?

• We convert the signal to a format that is suited for particular purpose.

System

Input signal

Output signal Output = f(Input)

f() describes a functional behavior of a system.

Example.

[ 1] [ 1]

[ ] 2

x n x n

x n    

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

Digital signal processing

• We process the digital data using “computer” equipped with

• digital signal processor

• purpose-specific hardware such as ASICS

• general purpose microprocessor

• field-programmable gate arrays (FPGA).

• Applications

• Audio signal processing, Digital image/video processing, Speech recognition, digital communication, radar, sonar, financial signal

processing, seismology, biomedical signal processing, bio infomatics, machine learning, big data analytics

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Frequency-domain analysis of signal and systems

 Fourier (frequency-domain) analysis

• Signal can be represented in different basis.

• Using Fourier transform, we can represent a signal using the sinusoidal basis.

• Very useful in analyzing a signal from a different viewpoint.

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

Example

• Time-domain waveform Desired

signal

Noise

Noise suppression

filter

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-2 0

2 Desired signal

20 40 60 80 100 120 140 160 180 200

-2 0 2

Noise

20 40 60 80 100 120 140 160 180 200

-2 0 2

Noisy signal

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

Frequency-domain analysis

0 0.2 0.4 0.6 0.8 1

-100 -80 -60 -40 -20 0

Frequency (kHz)

Power/frequency (dB/Hz) Welch Power Spectral Density Estimate

0 0.2 0.4 0.6 0.8 1

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Frequency (kHz)

0 0.2 0.4 0.6 0.8 1

-35 -30 -25 -20 -15

Frequency (kHz)

Desired signal

Noise

Noisy signal

Noise suppression filter

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Frequency-domain analysis

Continuous signal

Time-domain

(시간 영역)

Frequency-domain (주파수 영역)

Discrete signal

Continuous signal Discrete signal

Continuous –time Fourier transform (CTFT) Fourier series

Discrete-time Fourier transform (DTFT) Discrete-time Fourier series