# Typical Signal Processing Operations

AI and Robotics

Nov 24, 2013 (4 years and 5 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

Signals and Signal Processing
2

Outline

Characterization and Classification of Signals

Typical Signal Processing Operations

Examples of Typical Signals

Typical Signal Processing Applications

Why Digital Signal Processing

Signals and Signal Processing
3

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

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

Signals and Signal Processing
5

Elementary Time
-
Domain Operations

Scaling:

Integration:

Differentiation:

Delay operation:

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

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
  


 

Signals and Signal Processing
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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

 

Signals and Signal Processing
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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

( )
2
A
x t

Signals and Signal Processing
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Typical Signal Processing Operations

Multiplexing and De
-
multiplexing

For an efficient utilization of a wideband transmission
channel

Signal Generation

Square waves

Triangular waves

White noise

1 0 2 0
( ) ( )cos( ) ( )sin( )
y t Ax t t Ax t t
   

Signals and Signal Processing
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Examples of Typical Signals

Electrocardiography ( ECG ) Signal

Electroencephalogram ( EEG ) Signal

Seismic Signals

Diesel Engine Signal

Speech Signals

Musical Sound Signal

Time Series

Images

Signals and Signal Processing
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Examples of Typical Signals

Images

Original Image

Complement Image

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

Signals and Signal Processing
13

Why Digital Signal Processing

DSP everywhere

Signals and Signal Processing
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Why Digital Signal Processing

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 …

Stored almost indefinitely without loss of information

Signals and Signal Processing
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Why Digital Signal Processing

The increased system complexity

The limited range of frequencies available for
processing

Consume electrical power

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.