Contents 1.Overview of DSP Chapter 1 ◆Overview of DSP Signals play an important role in our daily life ●●● .Classification of Signals .A signal is a function of independent variables Representation of Signals such as time,distance,position,temperature, and pressure Signals and Signal Processing Typical Signal Processing Operations A signal carries information .Examples of Typical Signals Why Digital Signal Processing The objective of signal processing is to extract the useful information carried by the signal 1.Overview of DSP 1.Overview of DSP 1.Overview of DSP Method information extraction:Depends on Signals can be represented in the domain of the This course is concerned with the discrete time the type of signal and the nature of the original independent variables or in a representation of signals and their discrete- information being carried by the signal transformed domain time processing DSP is concerned with the mathematical Likewise,the information extraction process representation of the signal and the algorithmic may be carried out in the original domain of operation carried out on it the signal or in a transformed domain
Chapter 1 Signals and Signal Processing 2 Contents Overview of DSP Classification of Signals Classification of Signals Representation of Signals Representation of Signals Typical Signal Processing Operations Typical Signal Processing Operations Examples of Typical Signals Examples of Typical Signals Why Digital Signal Processing 3 1. Overview of DSP Signals Signals play an important role in our daily life A signal is a function of independent variables independent variables such as time, distance, position, temperature, and pressure A signal carries information The objective of signal processing is to extract extract the useful information carried by the signal 4 1. Overview of DSP Method information extraction: Depends on the type of signal type of signal and the nature of the nature of the information being carried by the signal DSP is concerned with the mathematical mathematical representation of the signal and the algorithmic algorithmic operation carried out on it 5 1. Overview of DSP Signals can be represented in the domain of the domain of the original original independent variables or in a transformed domain Likewise, the information extraction process may be carried out in the original domain of the signal or in a transformed domain 6 1. Overview of DSP This course is concerned with the discrete time representation of signals and their discretetime processing
2.Classification of Signals 2.Classification of Signals 2.Classification of Signals Types of signals Continuous versus Discrete Examples Depends on the nature of the independent ●Real versus Complex .The speech signal is an example of a 1-D variables and the value of the function signal where the independent variable is time ·Scalar versus Vector defining the signal. An image signal,such as a photograph,is an One dimensional versus Multi-Dimensional example of a 2-D signal where the 2 Deterministic versus Random independent variables are the 2 spatial variables 2.Classification of Signals 2.Classification of Signals 2.Classification of Signals .A color image signal is composed of three 2- Red component Green component Blue component The full color image obtained by displaying D signals representing the three primary the previous 3 color components is shown colors:red,green and blue (RGB) below The 3 color components of a color image are shown in the next slide
7 2. Classification of Signals Types of signals Depends on the nature of the independent variables and the value of the function defining the signal. 8 2. Classification of Signals Continuous Continuous versus Discrete Discrete Real versus Complex Scalar versus Vector One dimensional One dimensional versus Multi-Dimensional Dimensional Deterministic Deterministic versus Random 9 2. Classification of Signals Examples The speech signal speech signal is an example of a 1-D signal where the independent variable is time An image signal image signal, such as a photograph, is an example of a 2-D signal where the 2 independent variables are the 2 spatial variables 10 2. Classification of Signals A color image signal is composed of three 2- D signals representing the three primary colors: red, green and blue (RGB) The 3 color components of a color image are shown in the next slide 11 2. Classification of Signals Red component Green component Blue component 12 2. Classification of Signals The full color image obtained by displaying the previous 3 color components is shown below
2.Classification of Signals 2.Classification of Signals 2.Classification of Signals For a 1-D signal,the independent variable is .A discrete-time signal with discrete-valued .A digital signal is thus a quantized sample data usually labeled as time amplitudes represented by a finite number of signal In this case,signals can be classified into digits is referred to as the digital signal .A continuous-time signal with discrete value continuous-time signals and discrete-time A discrete-time signal with continuous valued amplitudes is usually called a quantized boxcar signals(sequence of numbers) amplitudes is called a sampled-data signal signal(量化矩形信号) A continuous-time signal with a continuous .The figure in the next slide illustrates the 4 amplitude is usually called an analog signal types of signals 2.Classification of Signals 3.Representation of Signals 3.Representation of Signals (a)A confinuous-me signal fquandized sample data signal) For a continuous-time 1-D signal,the For example,vn)!represents a discrete time continuous independent variable is usually 1-D signal denoted by t Each member,vn),of a discrete-time signal is called a sample (c)A sampled-data signal For example,u(r)represents a continuous time d 1-D signal In many applications,a discrete-time signal is For a discrete-time 1-D signal,the discrete generated by sampling a parent continuous- independent variable is usually denoted by n time signal at uniform intervals of time
13 2. Classification of Signals For a 1-D signal, the independent variable is usually labeled as time In this case, signals can be classified into continuous continuous-time signals and discrete discrete-time signals (sequence of numbers sequence of numbers) A continuous-time signal with a continuous amplitude is usually called an analog signal analog signal 14 2. Classification of Signals A discrete-time signal with discrete-valued amplitudes represented by a finite number of digits is referred to as the digital signal digital signal A discrete-time signal with continuous valued amplitudes is called a sampled-data signal data signal 15 2. Classification of Signals A digital signal is thus a quantized sample data quantized sample data signal A continuous-time signal with discrete value amplitudes is usually called a quantized boxcar a quantized boxcar signal (䟿ॆ⸙ᖒؑਧ) The figure in the next slide illustrates the 4 types of signals 16 2. Classification of Signals (a) A continuous-time signal (b) A digital signal (quantized sample data signal) (c) A sampled-data signal (d) A quantized boxcar signal 17 3. Representation of Signals For a continuous continuous-time 1-D signal, the continuous independent variable is usually denoted by t For example, u(t) represents a continuous time 1-D signal For a discrete discrete-time 1-D signal, the discrete independent variable is usually denoted by n 18 3. Representation of Signals For example, {v(n)} represents a discrete time 1-D signal Each member, v(n), of a discrete-time signal is called a sample In many applications, a discrete-time signal is generated by sampling a parent continuoustime signal at uniform intervals of time uniform intervals of time
4.Typical Signal 3.Representation of Signals Processing Operations 4.1 Elementary Time-Domain Operations If the discrete instants of time at which a Most signal processing operations in the case .Three most basic time-domain signal discrete-time signal is defined are uniformly of analog signals are carried out in the time- operations are scaling,delay,and addition spaced,the independent discrete variable n can domain be normalized to assume integer values Three other elementary operations are In the case of discrete-time signals,both time- integration,differentiation and product domain or frequency-domain operations are usually employed More complex operations are implemented by combining two or more elementary operations 4.2 Filtering 4.2 Filtering 4.2 Filtering The range of frequencies that is allowed to Figures below illustrate the lowpass filtering of Filtering is one of the most widely used pass through the filter is called the passband, an input signal composed of 3 sinusoidal complex signal processing operations and the range of frequencies that is blocked by components of frequencies 50 Hz,110 Hz,and the filter is called the stopband 210Hz Filtering is used to pass certain frequency components in a signal through the system without any distortion and to block other .Several typical filters are lowpass,highpass, bandpass,bandstop filters frequency components .An important term associated with filtering is cutoff frequency(3dB cutoff frequency)
19 3. Representation of Signals If the discrete instants of time at which a discrete-time signal is defined are uniformly spaced, the independent discrete variable n can be normalized to assume integer values integer values 20 4. Typical Signal Processing Operations Most signal processing operations in the case of analog signals analog signals are carried out in the timedomain In the case of discrete discrete-time signals time signals, both timedomain or frequency-domain operations are usually employed 21 4.1 Elementary Time-Domain Operations Three most basic time-domain signal operations are scaling, delay, and addition Three other elementary operations are integration , differentiation and product product More complex operations are implemented by combining two or more elementary operations 22 4.2 Filtering Filtering is one of the most widely used complex signal processing operations Filtering is used to pass certain frequency components in a signal through the system without any distortion and to block other frequency components 23 4.2 Filtering The range of frequencies that is allowed to pass through the filter is called the passband, and the range of frequencies that is blocked by the filter is called the stopband Several typical filters are lowpass lowpass, highpass highpass, bandpass bandpass, bandstop filters filters An important term associated with filtering is cutoff frequency (3dB cutoff frequency) 24 4.2 Filtering Figures below illustrate the lowpass lowpass filtering of an input signal composed of 3 sinusoidal components of frequencies 50 Hz, 110 Hz, and 210 Hz
4.2 Filtering 4.2 Filtering 4.2 Filtering Figures below illustrate highpass and bandpass Other types of filters Example filtering of the same input signal .A filter blocking a single frequency component A common source of noise is power lines is called a notch filter radiating electric and magnetic fields A multiband filter has more than one passband The noise generated by power lines appears as and more than one stopband a 60-Hz sinusoidal signal corrupting the desired signal and can be removed by passing A comb filter blocks frequencies that are the corrupted signal through a notch filter with integral multiples of a low frequency a notch frequency at 60 Hz 7 4.3 Generation of Complex Signals 4.3 Generation of Complex Signals 4.3 Generation of Complex Signals All naturally generated signals are real-valued. The impulse response of a Hilbert transformer The output of the system shown in the block In some applications,it is desirable to develop is given by diagram is a complex signal,also called an a complex signal from a real signal having 知)=L analytic signal,has only positive frequency more desirable properties components. 0 The continuous-time Fourier transform (j) A complex signal can be generated from a real ofhr()）is given by ·0) signal by employing a Hilbert transformer Hilbert -,2>0 x(t) 0③ Hin(j)= Transforer 2<0 Generation of an analytic signal using a Hilbert transformer
25 4.2 Filtering Figures below illustrate highpass highpass and bandpass bandpass filtering of the same input signal 26 4.2 Filtering Other types of filters Other types of filters A filter blocking a single frequency component is called a notch filter notch filter A multiband filter multiband filter has more than one passband and more than one stopband A comb filter comb filter blocks frequencies that are integral multiples of a low frequency 27 4.2 Filtering Example Example A common source of noise is power lines radiating electric and magnetic fields The noise generated by power lines appears as a 60-Hz sinusoidal signal corrupting the desired signal and can be removed by passing the corrupted signal through a notch filter notch filter with a notch frequency at 60 Hz 28 4.3 Generation of Complex Signals All naturally generated signals are real-valued. In some applications, it is desirable to develop a complex signal complex signal from a real signal real signal having more desirable properties A complex signal can be generated from a real signal by employing a Hilbert transformer Hilbert transformer 29 4.3 Generation of Complex Signals The impulse response of a Hilbert transformer is given by The continuous-time Fourier transform of is given by 1 ( ) HT h t t ( ) H j HT ( ) HT h t , 0 ( ) , 0 HT j H j j 30 4.3 Generation of Complex Signals The output of the system shown in the block diagram is a complex signal, also called an analytic signal analytic signal, has only positive positive frequency components. x t( ) Hilbert Transformer + x t ˆ( ) x t( ) y t( ) Generation of an analytic signal using a Hilbert transformer j
4.Other Operations 5.Examples of Typical Signals 5.Examples of Typical Signals 4.4 Modulation and Demodulation Speech and music signals-Represent air Electrocardiography(ECG)Signals-represent pressure as a function of time at a point in the electrical activity of the heart 4.5 Multiplexing and Demultiplexing space 4.6 Quadrature Amplitude Modulation .Waveform of the speech signal"I like digital .A typical ECG signal is shown below 4.7 Signal Generation signal processing"is shown below 5.Examples of Typical Signals 5.Examples of Typical Signals 5.Examples of Typical Signals Electroencephalogram(EEG)Signals- Black-and-white picture-represents light Video signals-Consists of a sequence of Represent the electrical activity caused by the intensity as a function of two spatial images,called frames,and is a function of 3 random firings of billions of neurons in the coordinates variables:2 spatial coordinates and time brain ·x5利
31 4.4 Modulation and Demodulation 4.5 Multiplexing and 4.5 Multiplexing and Demultiplexing 4.6 Quadrature Amplitude Modulation 4.7 Signal Generation 4. Other Operations 32 5. Examples of Typical Signals Speech and music signals Speech and music signals - Represent air pressure pressure as a function of time at a point in space Waveform of the speech signal “I like digital I like digital signal processing” is shown below 33 5. Examples of Typical Signals Electrocardiography (ECG) Signals Electrocardiography (ECG) Signals - represent the electrical activity of the heart A typical ECG signal is shown below 34 5. Examples of Typical Signals Electroencephalogram (EEG) Signals Electroencephalogram (EEG) Signals - Represent the electrical activity caused by the random firings of billions of neurons in the brain 35 5. Examples of Typical Signals Black-and-white picture white picture - represents light intensity as a function of two spatial spatial coordinates coordinates 36 5. Examples of Typical Signals Video signals Video signals - Consists of a sequence of images, called frames, and is a function of 3 variables: 2 spatial coordinates spatial coordinates and time
6.Why Digital Signal Processing 6.Why Digital Signal Processing 6.Why Digital Signal Processing Digital processing of an analog signal are Advantages of DSP Improved quality level shown below Absence of drift in the filter characteristics -Quality of processing limited only by economic considerations 园巴 -Processing characteristics are fixed,e.g.by binary coefficients stored in memories Arbitrarily low degradations achieved with -Thus,they are independent of the external desired quality by increasing the number of 应图 environment and of parameters such as bits in data/coefficient representation temperature -An increase of I bit in the representation results in a 6 dB improvement in the SNR -Aging has no effect 6.Why Digital Signal Processing 6.Why Digital Signal Processing 6.Why Digital Signal Processing ●Reproducibility Ease of new function development Modularity -Easy to develop and implement adaptive Component tolerances do not affect system filters,programmable filters and -Uses standard digital circuits for performance with correct operation complementary filters implementation -No adjustments necessary during fabrication -Illustrates flexibility of digital techniques (加工、装配) 。Multiplexing -No realignment(调整)needed over lifetime Same equipment can be shared between of equipment several signals,with obvious financial advantages for each function
37 Digital processing of an analog signal are shown below 6. Why Digital Signal Processing Scheme for the digital processing of an analog signal Sampleand-Hold A/D Converter Digital Processor Analog input D/A Converter Analog Lowpass Filter Analog output 38 Advantages of DSP Absence of drift in the filter characteristics Absence of drift in the filter characteristics – Processing characteristics are fixed, e.g. by binary coefficients stored in memories – Thus, they are independent of the external environment and of parameters such as temperature – Aging has no effect 6. Why Digital Signal Processing 39 Improved quality level Improved quality level – Quality of processing limited only by economic considerations – Arbitrarily low degradations achieved with desired quality by increasing the number of bits in data/coefficient representation – An increase of 1 bit in the representation results in a 6 dB improvement in the SNR 6. Why Digital Signal Processing 40 Reproducibility – Component tolerances do not affect system performance with correct operation – No adjustments necessary during fabrication (ᐕǃ㻵䝽࣐) – No realignment (䈳ᮤ) needed over lifetime of equipment 6. Why Digital Signal Processing 41 Ease of new function development Ease of new function development – Easy to develop and implement adaptive filters, programmable filters and complementary filters – Illustrates flexibility of digital techniques Multiplexing – Same equipment can be shared between several signals, with obvious financial advantages for each function 6. Why Digital Signal Processing 42 Modularity – Uses standard digital circuits for implementation ... 6. Why Digital Signal Processing
6.Why Digital Signal Processing Limitations of DSP ·Lesser Reliability The End of Chapter 1 -Digital systems are active devices,and thus use more power and are less reliable Limited range of frequencies available for processing (whny?)
43 Limitations of DSP Lesser Reliability – Digital systems are active devices, and thus use more power and are less reliable Limited range of frequencies available for Limited range of frequencies available for processing (why?) 6. Why Digital Signal Processing 44 The End of Chapter The End of Chapter 1