Typical Signal Processing Operations

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Nov 24, 2013 (3 years and 8 months ago)

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CHAPTER 1

Signals and Signal Processing

Wang Weilian

wlwang@ynu.edu.cn

School of Information Science and Technology

Yunnan University



云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Outline


Characterization and Classification of Signals


Typical Signal Processing Operations


Examples of Typical Signals


Typical Signal Processing Applications


Why Digital Signal Processing

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Characterization and Classification of
Signals


Signals


In mathematics: a function of independent variables


In physics: anything that carries information


Examples: speech, music, picture, and video signals


Signal processing:


To extract useful information carried by the signal


In domain or in the transformed domain

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
4

Characterization and Classification of
Signals


Signal classification


1
-
D / M
-
D signal


Scalar


vector


Real
-
valued



complex
-

valued


Continuous
-
time / discrete
-
time signals


Analog signal


digital signal


A sampled
-
data signal



a quantized boxcar signal


Deterministic / random signals

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Elementary Time
-
Domain Operations


Scaling:



Integration:



Differentiation:


Delay operation:



Addition:



Product of two signals:

( ) ( )
y t x t


Typical Signal Processing Operations

( ) ( )
t
y t x d
 



0
( ) ( )
y t x t t
 
1 2 3
( ) ( ) ( ) ( )
y t x t x t x t
  
( ) ( )/
w t dx t dt

1 2
( ) ( ) ( )
y t x t x t

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Typical Signal Processing Operations


Filtering


convolutional integral


To improve the quality of the signal


To pass / block certain frequency components in a signal
through the filter without any distortion




Categories


Lowpass filter


Highpass filter


Bandpass filter


Bandstop filter



notch filter


Multiband filter


comb filter


( ) ( ) ( )
y t h t x d
  


 

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
7

Typical Signal Processing Operations




Generation of Complex Signals


A complex signal can be generated from a real signal by
employing a Hilbert transformer


Method:


A real analog signal x(t) is passed through a Hilbert transformer




The continuous
-
time Fourier transform of is




The complex signal is



1
( )
HT
h t
t


( ) ( ) ( )
HT
x t h t x d
  



 

( )
HT
h t
, 0
( )
, 0
HT
j
H j
j


 

 

( ) ( ) ( )
y t x t j x t

 
云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
8

Typical Signal Processing Operations

0
0
cos( )
( ) ( )cos( )
( ) ( )
A t
y t Ax t t
x t y t


 

( )
0
( )
cos( )
r t
y t
A t




Modulation


Demodulation

低通滤波器

( )
2
A
x t

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
9

Typical Signal Processing Operations


Multiplexing and De
-
multiplexing


For an efficient utilization of a wideband transmission
channel


Quadrature Amplitude Modulation



Signal Generation


Square waves


Triangular waves


White noise

1 0 2 0
( ) ( )cos( ) ( )sin( )
y t Ax t t Ax t t
   
云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
10

Examples of Typical Signals


Electrocardiography ( ECG ) Signal


Electroencephalogram ( EEG ) Signal


Seismic Signals


Diesel Engine Signal


Speech Signals


Musical Sound Signal


Time Series


Images

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Examples of Typical Signals


Images

Original Image

Complement Image

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Typical Signal Processing Applications


Sound Recording Applications


Compressors and limiters


Expanders and noise gates


Equalizers and filters


Noise reduction system


Delay and reverberation systems


Special effects


Telephone Dialing Applications


Dual
-
tone multi
-
frequency ( DTMF )


FM Stereo Applications


Electronic Music Synthesis


Echo Cancellation in Telephone Networks

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
13

Why Digital Signal Processing


DSP everywhere

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
14

Why Digital Signal Processing


Advantages:


Less sensitive to tolerances of component value


Enable to full integration


Any desirable accuracy


Timesharing


Easy adjustment of processor characteristics during
processing


The impossible with analog implementation


linear
phase, multi
-
rate processing …


Cascade without any loading problems


Stored almost indefinitely without loss of information

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Why Digital Signal Processing


Disadvantages:


The increased system complexity


The limited range of frequencies available for
processing


Consume electrical power

云南大学滇池学院课程:数字信号处理

Signals and Signal Processing
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Summary


This chapter provides an overview of signals and signal
processing methods.


The mathematical characterization of the signal is
discussed along with a classification of signals.


A review of some commonly used signal processing
operations is provided and illustrated through examples.


Advantages and disadvantages of digital processing of
signals are discussed.


We hope that you can feel interesting and indulge in DSP.