chapter 1 signals and signal processing wang weilian [email protected] school of information science...

CHAPTER 1 Signals and Signal Processing

CHAPTER 1 Signals and Signal Processing

Wang Weilian

[email protected]

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 2

OutlineOutline

• Characterization and Classification of Signals

• Typical Signal Processing Operations

• Examples of Typical Signals

• Typical Signal Processing Applications

• Why Digital Signal Processing


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




• 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


• Elementary Time-Domain Operations

– Scaling:

– Integration:

– Differentiation:

– Delay operation:

– Addition:

– Product of two signals:

( ) ( )y t x t

Typical Signal Processing OperationsTypical 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



• 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



• 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( )HTh t

t

( ) ( ) ( )HTx t h t x d

( )HTh t

, 0( )

, 0HT

jH j

j

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



0

0

cos( )

( ) ( )cos( )

( ) ( )

A t

y t Ax t t

x t y t

( )

0

( )

cos( )

r ty t

A t

• Modulation

• Demodulation

低通滤波器 ( )2

Ax t



• 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


Examples of Typical SignalsExamples of Typical Signals

• Electrocardiography ( ECG ) Signal

• Electroencephalogram ( EEG ) Signal

• Seismic Signals

• Diesel Engine Signal

• Speech Signals

• Musical Sound Signal

• Time Series

• Images


Examples of Typical SignalsExamples of Typical Signals

• Images

Original Image Complement Image


Typical Signal Processing ApplicationsTypical 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


Why Digital Signal ProcessingWhy Digital Signal Processing

• DSP everywhere



• 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



• Disadvantages:

– The increased system complexity

– The limited range of frequencies available for processing

– Consume electrical power


SummarySummary

• 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.

chapter 1 signals and signal processing wang weilian [email protected] school of information science...

Documents