CHAPTER 1
Signals and Signal Processing
Wang Weilian
wlwang@ynu.edu.cn
School of Information Science and Technology
Yunnan University
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
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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
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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
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Typical Signal Processing Operations
• Elementary Time-Domain Operations
– Scaling:
y( t )   x ( t )
y (t )  
– Integration:

– Differentiation:
– Delay operation:
– Addition:
x( )d
w(t )  dx(t ) / dt
y (t )  x(t  t0 )
y(t )  x1(t )  x2 (t )  x3 (t )
– Product of two signals:
云南大学滇池学院课程：数字信号处理
t
y (t )  x1(t ) x2 (t )
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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

y (t )   h(t   ) x( )d

– Categories
• Lowpass filter
• notch filter
• Highpass filter
• Multiband filter
• Bandpass filter
• comb filter
• Bandstop filter
云南大学滇池学院课程：数字信号处理
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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
1
hHT (t ) 
t
– Method:
• A real analog signal x(t) is passed through a Hilbert transformer


x(t )   hHT (t   ) x( )d

• The continuous-time Fourier transform of
•
 j,
H HT ( j)  
 j,

The complex signal is
0
0
hHT (t )
is

y(t )  x(t )  j x(t )
云南大学滇池学院课程：数字信号处理
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Typical Signal Processing Operations
• Modulation
y( t )  Ax ( t )cos( 0 t )
x ( t )    y( t )

A cos(  0 t )
• Demodulation
y( t )   
r(t )

低通滤波器
A
 x( t )
2
A cos( 0 t )
云南大学滇池学院课程：数字信号处理
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Typical Signal Processing Operations
• Multiplexing and De-multiplexing
– For an efficient utilization of a wideband transmission
channel
• Quadrature Amplitude Modulation
y(t )  Ax1(t )cos(0t )  Ax2 (t )sin(0t )
• Signal Generation
– Square waves
– Triangular waves
– White noise
云南大学滇池学院课程：数字信号处理
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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
云南大学滇池学院课程：数字信号处理
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Examples of Typical Signals
• Images
Original Image
云南大学滇池学院课程：数字信号处理
Complement Image
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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
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Why Digital Signal Processing
•
DSP everywhere
云南大学滇池学院课程：数字信号处理
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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
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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
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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.
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