（！！）Digital Signal Processing for Measurement Systems_2006

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CONTENTS
Contributors ...................................................................................................................
Preface .............................................................................................................................
CHAPTER 1 – THE DIGITAL SIGNAL PROCESSING..................................................1
CHAPTER 2 – DISCRETE-TIME SIGNALS AND SYSTEMS.......................................5
Introduction........................................................................................................................5
The sequences. ....................................................................................................................6
DEFINITION..................................................................................................................6
PARTICULAR SEQUENCES.............................................................................................7
PERIODIC SEQUENCES. .................................................................................................9
OPERATIONS BETWEEN SEQUENCES. ..........................................................................11
The discrete-time systems.................................................................................................12
DEFINITION................................................................................................................12
THE LINEAR SYSTEMS. ...............................................................................................13
THE SHIFT-INVARIANT LINEAR SYSTEMS....................................................................13
THE CONVOLUTION COMPUTATION............................................................................16
STABILITY AND CAUSALITY. ......................................................................................22
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Frequency-domain representation of the discrete-time signals and systems.....................24
THE FREQUENCY RESPONSE OF THE LINEAR, SHIFT-INVARIANT SYSTEMS. .................24
THE FOURIER TRANSFORM OF A SEQUENCE. ..............................................................29
SYMMETRY PROPERTIES OF THE FOURIER TRANSFORM..............................................31
CHAPTER 3 – SIGNAL TRANSFORMATION FROM THE CONTINUOUS TIME
Introduction......................................................................................................................33
The sampling theorem.......................................................................................................35
THE GENERAL FORMULATION. ...................................................................................35
Shannon interpolation formula. ............................................................................41
THE CASE OF THE PERIODIC SIGNALS. ........................................................................43
Fourier-series approach. .......................................................................................43
Convolution approach ..........................................................................................47
The interpolation formula.....................................................................................51
The leakage errors ................................................................................................52
CHAPTER 4 – METHODS FOR THE REDUCTION OF THE LEAKAGE ERRORS..57
Introduction......................................................................................................................57
The weighing windows. ....................................................................................................58
THE RECTANGULAR WINDOW.....................................................................................58
THE COSINE WINDOWS...............................................................................................60
Cosine windows with maximum asymptotic decay..............................................63
Cosine windows with minimum amplitude for the second lobe...........................67
Flat-top cosine windows.......................................................................................70
THE SELECTION OF THE OBSERVATION INTERVAL......................................................72
The interpolation methods ................................................................................................74
TIME-DOMAIN INTERPOLATION METHOD ...................................................................74
FREQUENCY-DOMAIN INTERPOLATION METHOD ........................................................76
Hardware synchronization ................................................................................................80
INSTRUMENTS…………………………………………………………………………83
Introduction......................................................................................................................83
The analog-to-digital conversion ......................................................................................84
DEFINITIONS ..............................................................................................................84
TO THE DISCRETE TIME DOMAIN……………………………………………….... 33
CHAPTER 5 – ARCHITECTURE AND PERFORMANCE OF DSP-BASED
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THE IDEAL ADC CHARACTERISTIC ............................................................................85
The dithering technique........................................................................................88
THE REAL ADC CHARACTERISTIC .............................................................................91
The offset error.....................................................................................................91
The gain error .......................................................................................................92
The non-linearity error .........................................................................................94
ADC BEHAVIOUR IN THE PRESENCE OF A VARIABLE INPUT SIGNAL ...........................96
The Sample & Hold devices.................................................................................97
ADC BEHAVIOUR IN THE PRESENCE OF NOISE..........................................................10
ADC ARCHITECTURES .............................................................................................10
The integrating converters..................................................................................104
The successive approximation converters ..........................................................104
The flash converters ...........................................................................................10
The ΔΣ converters ..............................................................................................105
The processing unit .........................................................................................................10
THE PROCESSOR.......................................................................................................107
THE MEMORY...........................................................................................................10
Bandwidth estimation .....................................................................................................110
SINGLE-CHANNEL STRUCTURES ...............................................................................110
MULTI-CHANNEL STRUCTURES ................................................................................111
The non-multiplexed structure............................................................................111
The multiplexed structure...................................................................................112
CHAPTER 6 – ANTI-ALIASING METHODS AND SAMPLING STRATEGIES…..115
Introduction....................................................................................................................115
The anti-aliasing filter.....................................................................................................115
The equivalent-time sampling technique ........................................................................122
Multi converter structures ...............................................................................................124
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The Heterodyne conversion ........................................................................................... 119
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Introduction....................................................................................................................127
Dynamical discrete systems. ...........................................................................................127
n-domain representation of dynamical discrete systems: difference equations...............129
Stability of linear shift invariant discrete systems. .........................................................135
The z-transform...............................................................................................................141
EXAMPLES OF Z-TRANSFORMS. ................................................................................152
The inverse z-transform. .................................................................................................155
EXAMPLES OF INVERSE Z-TRANSFORMS...................................................................156
z-domain representation of causal discrete linear shift invariant systems.......................162
Linear shift invariant discrete filters. ..............................................................................166
Relationships between sequences and sampled functions in the z and s domains...........169
CHAPTER 8 – FINITE IMPULSE RESPONSE (FIR) FILTERS……………………..179
n-domain representation of FIR filters............................................................................179
z-domain representation of FIR filters. ...........................................................................180
Linear phase FIR filters ..................................................................................................186
FIR filter synthesis by Fourier series expansion. ............................................................192
FIR filter synthesis by the frequency sampling method..................................................200
Effects of filter coefficients quantization........................................................................206
FIR filter architectures. ...................................................................................................209
CHAPTER 7 – DYNAMICAL DISCRETE SYSTEMS…………………………….…127
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z-domain representation of IIR filters. ............................................................................221
n-domain representation of IIR filters.............................................................................222
Purely recursive IIR filters..............................................................................................224
IIR filters design from analog specifications. .................................................................230
BUTTERWORTH FILTERS...........................................................................................231
CHEBYSHEV FILTERS ...............................................................................................232
ELLIPTIC FILTERS.....................................................................................................233
ANALOG TO DISCRETE DOMAIN MAPPING ................................................................234
Input response invariance ...................................................................................235
Frequency domain design...................................................................................240
Frequency transformation from low-pass filters to band-pass and
band-stop filters ..............................................................................................250
IIR design by numerical optimization.............................................................................253
Effects of filter coefficients quantization........................................................................255
IIR filter architectures. ....................................................................................................259