Fractional signals and systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2020]
|
| Series: | Fractional Calculus in Applied Sciences and Engineering
volume 7 |
| Subjects: | |
| Online Access: | Unbekannt Inhaltsverzeichnis |
| Physical Description: | XVI, 281 Seiten 50 Illustrationen 24 cm x 17 cm |
| ISBN: | 9783110621297 3110621290 |
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| 020 | |a 9783110621297 |c : EUR 103.95 (DE) (freier Preis), EUR 103.95 (AT) (freier Preis) |9 978-3-11-062129-7 | ||
| 020 | |a 3110621290 |9 3-11-062129-0 | ||
| 024 | 3 | |a 9783110621297 | |
| 035 | |a (OCoLC)1109195463 | ||
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| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-83 | ||
| 084 | |a ZN 6025 |0 (DE-625)157494: |2 rvk | ||
| 100 | 1 | |a Ortigueira, Manuel Duarte |d 1949- |e Verfasser |0 (DE-588)120670764X |4 aut | |
| 245 | 1 | 0 | |a Fractional signals and systems |c Manuel D. Ortigueira and Valério Duarte |
| 263 | |a 201910 | ||
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2020] | |
| 300 | |a XVI, 281 Seiten |b 50 Illustrationen |c 24 cm x 17 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fractional Calculus in Applied Sciences and Engineering |v volume 7 | |
| 650 | 0 | 7 | |a Signalverarbeitung |0 (DE-588)4054947-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gebrochene Analysis |0 (DE-588)4722475-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gebrochene Analysis |0 (DE-588)4722475-7 |D s |
| 689 | 0 | 1 | |a Signalverarbeitung |0 (DE-588)4054947-1 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Valério, Duarte |e Verfasser |0 (DE-588)1206708050 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 9783110621327 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 9783110624588 |
| 830 | 0 | |a Fractional Calculus in Applied Sciences and Engineering |v volume 7 |w (DE-604)BV045897010 |9 volume 7 | |
| 856 | 4 | 2 | |m X:MVB |u http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110621297&searchTitles=true |v 2019-07-17 |x Verlag |3 Unbekannt |
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| _version_ | 1804181590900736000 |
|---|---|
| adam_text | CONTENTS
ACKNOWLEDGEMENT
*
VII
PREFACE
*
IX
PART
I:
CONTINUOUS-TIME
1
INTRODUCTION
TO
SIGNALS
AND
SYSTEMS
*
3
1.1
SIGNALS
*
3
1.1.1
SIGNALS
AND
THEIR
CHARACTERISTICS
*
3
1.1.2
IMPORTANT
SIGNALS
IN
CONTINUOUS-TIME
*
5
1.1.3
IMPORTANT
SIGNALS
IN
DISCRETE-TIME
*
7
1.1.4
DISCRETE
SIGNALS
VS.
CONTINUOUS
SIGNALS
*
8
1.1.5
OPERATIONS
WITH
SIGNALS:
ENERGY
AND
POWER
*
9
1.1.6
OPERATIONS
WITH
SIGNALS:
CONVOLUTIONS
------
11
1.2
SYSTEMS
*
12
1.3
CHARACTERISATION
OF
LINEAR
SYSTEMS
*
17
2
CONTINUOUS-TIME
LINEAR
SYSTEMS
AND
THE
LAPLACE
TRANSFORM
*
21
2.1
THE
IMPULSE
RESPONSE
AND
THE
PROPERTIES
OF
LINEAR
SYSTEMS
*
21
2.2
EXPONENTIALS
AND
LTIS
-----
21
2.2.1
THE
LAPLACE
TRANSFORM
------
22
2.2.2
EXISTENCE
AND
MAIN
PROPERTIES
OF
THE
LAPLACE
TRANSFORM
*
24
2.3
THE
DIFFERINTEGRATOR
-----
27
2.4
IMPULSE
AND
STEP
RESPONSES
OF
CAUSAL
LS
*
30
2.4.1
THE
GENERAL
INITIAL
VALUE
THEOREM
*
30
2.4.2
THE
GENERAL
FINAL
VALUE
THEOREM
*
31
2.4.3
TRANSFER
FUNCTION
SERIES
REPRESENTATION
*
31
2.5
TRANSFER
FUNCTION
SERIES
REPRESENTATION
FOR
COMMENSURATE
LS
*
35
3
FRACTIONAL
COMMENSURATE
LINEAR
SYSTEMS:
TIME
RESPONSES
*
39
3.1
IMPULSE
AND
STEP
RESPONSES:
THE
MITTAG-LEFFLER
FUNCTION
*
39
3.1.1
IN
TERMS
OF
THE
MITTAG-LEFFLER
FUNCTION
-----
41
3.1.2
BY
INTEGER/FRACTIONAL
DECOMPOSITION
*
41
3.2
STABILITY
-----
45
3.2.1
KNOWING
THE
PSEUDO-POLES
*
45
3.2.2
ROUTH-HURWITZ
CRITERION
FOR
AN
INTEGER
TF
-----46
3.2.3
SPECIAL
CASES
OF
THE
ROUTH-HURWITZ
CRITERION
FOR
AN
INTEGER
TF
*
49
3.2.4
ROUTH-HURWITZ
CRITERION
FOR
A
FRACTIONAL
COMMENSURATE
TF
*
50
XII
*
CONTENTS
3.2.5
SPECIAL
CASES
OF
THE
ROUTH-HURWITZ
CRITERION
FOR
A
FRACTIONAL
COMMENSURATE
TF
*
53
3.3
3.4
3.4.1
CAUSAL
PERIODIC
IMPULSE
RESPONSE
-----
56
INITIAL
CONDITIONS
*
57
SPECIAL
CASES
*
59
4
4.1
4.2
4.2.1
4.2.2
4.2.3
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.4
THE
FRACTIONAL
COMMENSURATE
LINEAR
SYSTEMS.
FREQUENCY
RESPONSES
*
61
STEADY-STATE
BEHAVIOUR:
THE
FREQUENCY
RESPONSE
*
61
BODE
DIAGRAMS
OF
TYPICAL
EXPLICIT
SYSTEMS
*
64
THE
DIFFERINTEGRATOR
*
64
ONE
PSEUDO-POLE
OR
ONE
PSEUDO-ZERO
*
64
COMPLEX
CONJUGATE
PAIR
OF
PSEUDO-POLES
OR
PSEUDO-ZEROES
*
67
IMPLICIT
SYSTEMS
*
69
IMPLICIT
FRACTIONAL
ORDER
ZERO
OR
POLE
*
70
FRACTIONAL
RID
*
70
FRACTIONAL
LEAD
COMPENSATOR
-----
72
FRACTIONAL
LAG
COMPENSATOR
*
74
APPROXIMATIONS
TO
TRANSFER
FUNCTIONS
BASED
UPON
A
FREQUENCY
RESPONSE
*
75
4.4.1
4.4.2
4.4.3
4.5
4.6
4.6.1
4.6.2
4.6.3
4.6.4
OUSTALOUP
*
S
CRONE
APPROXIMATION
*
75
THE
CARLSON
*
S
APPROXIMATION
*
76
THE
MATSUDA
*
S
APPROXIMATION
*
76
SYSTEM
MODELLING
AND
IDENTIFICATION
FROM
A
FREQUENCY
RESPONSE
*
77
FILTERS
-----
79
GENERALITIES.
IDEAL
FILTERS
*
79
PROTOTYPES
OF
INTEGER
ORDER
FILTERS
*
82
TRANSFORMATIONS
OF
FREQUENCIES
*
85
FRACTIONAL
FILTERS
*
85
5
5.1
5.2
5.3
5.4
STATE-SPACE
REPRESENTATION
*
87
GENERAL
CONSIDERATIONS
*
87
STANDARD
FORM
OF
THE
EQUATIONS
*
88
STATE
TRANSITION
OPERATOR
*
90
CANONICAL
REPRESENTATIONS
OF
SISO
SYSTEMS
*
92
6
6.1
6.2
6.3
6.3.1
6.3.2
FEEDBACK
REPRESENTATION
*
95
WHY
FEEDBACK?
*
95
ON
CONTROLLERS
*
96
THE
NYQUIST
STABILITY
CRITERION
*
98
DRAWING
THE
NYQUIST
DIAGRAM
*
100
GAIN
AND
PHASE
MARGINS
*
102
CONTENTS
*
XIII
7
ON
FRACTIONAL
DERIVATIVES
*
105
7.1
INTRODUCTION
-----
105
7.2
SOME
HISTORICAL
CONSIDERATIONS
*
105
7.2.1
RETURNING
TO
THE
DIFFERINTEGRATOR
*
106
7.3
FRACTIONAL
INCREMENTAL
RATIA
APPROACH
*
108
7.3.1
THE
DERIVATIVE
OPERATORS
AND
THEIR
INVERSES
*
108
7.3.2
FRACTIONAL
INCREMENTAL
RATIA
*
109
7.3.3
SOME
EXAMPLES
*
112
7.3.4
CLASSIC
RIEMANN-LIOUVILLE
AND
CAPUTO
DERIVATIVES
*
113
7.4
ON
COMPLEX
ORDER
DERIVATIVES
*
113
PART
II:
DISCRETE-TIME
8
DISCRETE-TIME
LINEAR
SYSTEMS.
DIFFERENCE
EQUATIONS
*
119
8.1
ON
TIME
SCALES
*
119
8.2
SYSTEMS
ON
UNIFORM
TIME
SCALES:
DIFFERENCE
EQUATIONS
*
120
8.3
EXPONENTIALS
AS
EIGENFUNCTIONS
*
120
8.3.1
DETERMINATION
OF
THE
IMPULSE
RESPONSE
FROM
THE
DIFFERENCE
EQUATION
*
122
8.3.2
FROM
THE
IMPULSE
RESPONSE
TO THE
DIFFERENCE
EQUATION
*
123
8.4
THE
FREQUENCY
RESPONSE
*
124
8.5
CLASSIFICATION
OF
SYSTEMS
*
126
8.6
SINGULAR
SYSTEMS
-----
128
9
Z
TRANSFORM.
TRANSIENT
RESPONSES
*
131
9.1
Z
TRANSFORM
*
131
9.1.1
INTRODUCTION
*
131
9.1.2
DEFINITION
*
131
9.2
MAIN
PROPERTIES
OF
THE
ZT
----
133
9.3
SIGNALS
WHOSE
TRANSFORMS
ARE
SIMPLE
FRACTIONS
*
136
9.4
INVERSION
OF
THE
ZT
-----
137
9.4.1
INVERSION
INTEGRAL
*
137
9.4.2
INVERSION
BY
DECOMPOSITION
INTO
A
POLYNOMIAL
AND
PARTIAL
FRACTIONS
*
138
9.4.3
INVERSION
BY
SERIES
EXPANSION
*
140
9.4.4
STEP
RESPONSE
*
141
9.4.5
RESPONSE
TO
A
CAUSAL
SINUSOID
*
142
9.5
STABILITY
AND
JURY
CRITERION
*
145
9.6
INITIAL
CONDITIONS
-----
148
9.7
INITIAL
AND
FINAL
VALUE
THEOREMS
*
150
9.8
CONTINUOUS
TO
DISCRETE
CONVERSION
(S2Z)
*
151
9.8.1
SOME
CONSIDERATIONS
*
151
XIV
CONTENTS
9.8.2
APPROXIMATION
OF
DERIVATIVES
*
152
9.8.3
TUSTIN
RULE
OR
BILINEAR
TRANSFORMATION
*
154
9.8.4
DIRECT
CONVERSION
OF
POLES
AND
ZEROS
INTO
POLES
AND
ZEROS
*
156
9.8.5
INVARIANT
RESPONSE
S
TO
Z
CONVERSION
*
157
9.8.6
CONVERSION
FROM
PARTIAL
FRACTION
DECOMPOSITION
*
159
10
DISCRETE-TIME
DERIVATIVES
AND
TRANSFORMS
*
163
10.1
INTRODUCTION:
DIFFERENCE
VS.
DIFFERENTIAL
*
163
10.2
DERIVATIVES
AND
INVERSES
*
163
10.2.1
NABLA
AND
DELTA
DERIVATIVES
*
163
10.2.2
EXISTENCE
OF
FRACTIONAL
DERIVATIVES
*
166
10.2.3
PROPERTIES
*
166
10.2.4
THE
NABLA
AND
DELTA
EXPONENTIALS
*
168
10.3
SUITABLE
TRANSFORMS
*
172
10.3.1
THE
NABLA
TRANSFORM
*
172
10.3.2
MAIN
PROPERTIES
OF
THE
NLT
-----
173
10.3.3
EXAMPLES
*
174
10.3.4
EXISTENCE
OF
NLT
-----
176
10.3.5
UNICITY
OF
THE TRANSFORM
*
176
10.3.6
INITIAL
VALUE
THEOREM
*
177
10.3.7
FINAL
VALUE THEOREM
*
177
10.3.8
THE
DELTA
TRANSFORM
AND
THE
CORRELATION
*
178
10.3.9
BACKWARD
COMPATIBILITY
*
179
10.4
DISCRETE-TIME
FRACTIONAL
LINEAR
SYSTEMS
*
180
10.4.1
POLYNOMIAL
CASE
*
181
10.4.2
PROPER
FRACTION
CASE
*
181
10.4.3
THE
ANTI-CAUSAL
CASE
*
185
10.4.4
INVERSION
WITHOUT
PARTIAL
FRACTIONS
*
185
10.4.5
SOME
STABILITY
ISSUES
*
188
10.4.6
A
CORRESPONDENCE
PRINCIPLE
*
188
10.4.7
ON
INITIAL
CONDITIONS
*
191
10.5
THE
FOURIER
TRANSFORM
AND
THE
FREQUENCY
RESPONSE
*
192
PART
III:
ADVANCED
TOPICS
11
FRACTIONAL
STOCHASTIC
PROCESSES
AND
TWO-SIDED
DERIVATIVES
*
197
11.1
STOCHASTIC
INPUT
*
197
11.2
TWO-SIDED
DERIVATIVES
*
199
11.2.1
DERIVATIVE
OF
WHITE
NOISE
*
199
11.2.2
GL
TYPE
TWO-SIDED
DERIVATIVE
*
199
11.2.3
THE
GENERAL
TWO-SIDED
FRACTIONAL
DERIVATIVE
*
200
11.2.4
THE
INTEGER
ORDER
CASES
*
203
CONTENTS
XV
11.2.5
11.2.6
11.3
11.3.1
11.3.2
OTHER
PROPERTIES
AND
REGULARISATIONS
*
203
FELLER
DERIVATIVE
-----
205
THE
FRACTIONAL
BROWNIAN
MOTION
*
206
DEFINITION
-----
206
PROPERTIES
-----
208
12
12.1
12.2
12.3
12.4
12.5
FRACTIONAL
DELAY
DISCRETE-TIME
LINEAR
SYSTEMS
*
213
INTRODUCTION
-----
213
FRACTIONAL
DELAYS
*
213
IMPULSE
RESPONSES
*
214
SCALE
CONVERSION
*
215
LINEAR
PREDICTION
*
216
13
13.1
13.2
13.3
13.4
13.5
13.6
FRACTIONAL
DERIVATIVES
WITH
VARIABLE
ORDERS
*
221
INTRODUCTION
-----
221
PAST
PROPOSALS
*
221
AN
APPROACH
TO
VO
DERIVATIVES
BASED
ON
THE
GL
DERIVATIVE
-----
224
VARIABLE
ORDER
LINEAR
SYSTEMS
*
227
THE
VO
MITTAG-LEFFLER
FUNCTION
-----
228
VARIABLE
ORDER
TWO-SIDED
DERIVATIVES
*
230
APPENDIXES
A
A.L
A.2
ON
DISTRIBUTIONS
*
237
INTRODUCTION
-----
237
THE
AXIOMS
-----
238
B
THE
GAMMA
FUNCTION
AND
BINOMIAL
COEFFICIENTS
*
240
C
C.L
C.2
THE
CONTINUOUS-TIME
FOURIER
TRANSFORM
*
243
DEFINITION
-----
243
DIFFERENTIATION
AND
INTEGRATION
IN
THE
CONTEXT
OF
FT
*
244
D
D.L
D.2
THE
DISCRETE-TIME
FOURIER
TRANSFORM
*
247
DEFINITION
-----
247
EXISTENCE
-----
249
E
E.L
E.2
E.3
PARTIAL
FRACTION
DECOMPOSITION
WITHOUT
DERIVATIONS
*
252
SIMPLIFICATION
WHEN
THERE
ARE
NO
CONJUGATE
PAIRS
OF
POLES
*
252
SIMPLIFICATION
FOR
CONJUGATE
PAIRS
OF
POLES
ON
THE
IMAGINARY
AXIS
*
254
SIMPLIFICATION
FOR
CONJUGATE
PAIRS
OF
POLES
NOT
ON
THE
IMAGINARY
AXIS
*
256
XVI
*
CONTENTS
F
THE
MITTAG-LEFFLER
FUNCTION
*
258
F.L
DEFINITION
------
258
F.2
COMPUTATION
OF
THE
MLF
------
264
BIBLIOGRAPHY
*
267
FURTHER
READING
*
273
INDEX
*
279
|
| adam_txt |
CONTENTS
ACKNOWLEDGEMENT
*
VII
PREFACE
*
IX
PART
I:
CONTINUOUS-TIME
1
INTRODUCTION
TO
SIGNALS
AND
SYSTEMS
*
3
1.1
SIGNALS
*
3
1.1.1
SIGNALS
AND
THEIR
CHARACTERISTICS
*
3
1.1.2
IMPORTANT
SIGNALS
IN
CONTINUOUS-TIME
*
5
1.1.3
IMPORTANT
SIGNALS
IN
DISCRETE-TIME
*
7
1.1.4
DISCRETE
SIGNALS
VS.
CONTINUOUS
SIGNALS
*
8
1.1.5
OPERATIONS
WITH
SIGNALS:
ENERGY
AND
POWER
*
9
1.1.6
OPERATIONS
WITH
SIGNALS:
CONVOLUTIONS
------
11
1.2
SYSTEMS
*
12
1.3
CHARACTERISATION
OF
LINEAR
SYSTEMS
*
17
2
CONTINUOUS-TIME
LINEAR
SYSTEMS
AND
THE
LAPLACE
TRANSFORM
*
21
2.1
THE
IMPULSE
RESPONSE
AND
THE
PROPERTIES
OF
LINEAR
SYSTEMS
*
21
2.2
EXPONENTIALS
AND
LTIS
-----
21
2.2.1
THE
LAPLACE
TRANSFORM
------
22
2.2.2
EXISTENCE
AND
MAIN
PROPERTIES
OF
THE
LAPLACE
TRANSFORM
*
24
2.3
THE
DIFFERINTEGRATOR
-----
27
2.4
IMPULSE
AND
STEP
RESPONSES
OF
CAUSAL
LS
*
30
2.4.1
THE
GENERAL
INITIAL
VALUE
THEOREM
*
30
2.4.2
THE
GENERAL
FINAL
VALUE
THEOREM
*
31
2.4.3
TRANSFER
FUNCTION
SERIES
REPRESENTATION
*
31
2.5
TRANSFER
FUNCTION
SERIES
REPRESENTATION
FOR
COMMENSURATE
LS
*
35
3
FRACTIONAL
COMMENSURATE
LINEAR
SYSTEMS:
TIME
RESPONSES
*
39
3.1
IMPULSE
AND
STEP
RESPONSES:
THE
MITTAG-LEFFLER
FUNCTION
*
39
3.1.1
IN
TERMS
OF
THE
MITTAG-LEFFLER
FUNCTION
-----
41
3.1.2
BY
INTEGER/FRACTIONAL
DECOMPOSITION
*
41
3.2
STABILITY
-----
45
3.2.1
KNOWING
THE
PSEUDO-POLES
*
45
3.2.2
ROUTH-HURWITZ
CRITERION
FOR
AN
INTEGER
TF
-----46
3.2.3
SPECIAL
CASES
OF
THE
ROUTH-HURWITZ
CRITERION
FOR
AN
INTEGER
TF
*
49
3.2.4
ROUTH-HURWITZ
CRITERION
FOR
A
FRACTIONAL
COMMENSURATE
TF
*
50
XII
*
CONTENTS
3.2.5
SPECIAL
CASES
OF
THE
ROUTH-HURWITZ
CRITERION
FOR
A
FRACTIONAL
COMMENSURATE
TF
*
53
3.3
3.4
3.4.1
CAUSAL
PERIODIC
IMPULSE
RESPONSE
-----
56
INITIAL
CONDITIONS
*
57
SPECIAL
CASES
*
59
4
4.1
4.2
4.2.1
4.2.2
4.2.3
4.3
4.3.1
4.3.2
4.3.3
4.3.4
4.4
THE
FRACTIONAL
COMMENSURATE
LINEAR
SYSTEMS.
FREQUENCY
RESPONSES
*
61
STEADY-STATE
BEHAVIOUR:
THE
FREQUENCY
RESPONSE
*
61
BODE
DIAGRAMS
OF
TYPICAL
EXPLICIT
SYSTEMS
*
64
THE
DIFFERINTEGRATOR
*
64
ONE
PSEUDO-POLE
OR
ONE
PSEUDO-ZERO
*
64
COMPLEX
CONJUGATE
PAIR
OF
PSEUDO-POLES
OR
PSEUDO-ZEROES
*
67
IMPLICIT
SYSTEMS
*
69
IMPLICIT
FRACTIONAL
ORDER
ZERO
OR
POLE
*
70
FRACTIONAL
RID
*
70
FRACTIONAL
LEAD
COMPENSATOR
-----
72
FRACTIONAL
LAG
COMPENSATOR
*
74
APPROXIMATIONS
TO
TRANSFER
FUNCTIONS
BASED
UPON
A
FREQUENCY
RESPONSE
*
75
4.4.1
4.4.2
4.4.3
4.5
4.6
4.6.1
4.6.2
4.6.3
4.6.4
OUSTALOUP
*
S
CRONE
APPROXIMATION
*
75
THE
CARLSON
*
S
APPROXIMATION
*
76
THE
MATSUDA
*
S
APPROXIMATION
*
76
SYSTEM
MODELLING
AND
IDENTIFICATION
FROM
A
FREQUENCY
RESPONSE
*
77
FILTERS
-----
79
GENERALITIES.
IDEAL
FILTERS
*
79
PROTOTYPES
OF
INTEGER
ORDER
FILTERS
*
82
TRANSFORMATIONS
OF
FREQUENCIES
*
85
FRACTIONAL
FILTERS
*
85
5
5.1
5.2
5.3
5.4
STATE-SPACE
REPRESENTATION
*
87
GENERAL
CONSIDERATIONS
*
87
STANDARD
FORM
OF
THE
EQUATIONS
*
88
STATE
TRANSITION
OPERATOR
*
90
CANONICAL
REPRESENTATIONS
OF
SISO
SYSTEMS
*
92
6
6.1
6.2
6.3
6.3.1
6.3.2
FEEDBACK
REPRESENTATION
*
95
WHY
FEEDBACK?
*
95
ON
CONTROLLERS
*
96
THE
NYQUIST
STABILITY
CRITERION
*
98
DRAWING
THE
NYQUIST
DIAGRAM
*
100
GAIN
AND
PHASE
MARGINS
*
102
CONTENTS
*
XIII
7
ON
FRACTIONAL
DERIVATIVES
*
105
7.1
INTRODUCTION
-----
105
7.2
SOME
HISTORICAL
CONSIDERATIONS
*
105
7.2.1
RETURNING
TO
THE
DIFFERINTEGRATOR
*
106
7.3
FRACTIONAL
INCREMENTAL
RATIA
APPROACH
*
108
7.3.1
THE
DERIVATIVE
OPERATORS
AND
THEIR
INVERSES
*
108
7.3.2
FRACTIONAL
INCREMENTAL
RATIA
*
109
7.3.3
SOME
EXAMPLES
*
112
7.3.4
CLASSIC
RIEMANN-LIOUVILLE
AND
CAPUTO
DERIVATIVES
*
113
7.4
ON
COMPLEX
ORDER
DERIVATIVES
*
113
PART
II:
DISCRETE-TIME
8
DISCRETE-TIME
LINEAR
SYSTEMS.
DIFFERENCE
EQUATIONS
*
119
8.1
ON
TIME
SCALES
*
119
8.2
SYSTEMS
ON
UNIFORM
TIME
SCALES:
DIFFERENCE
EQUATIONS
*
120
8.3
EXPONENTIALS
AS
EIGENFUNCTIONS
*
120
8.3.1
DETERMINATION
OF
THE
IMPULSE
RESPONSE
FROM
THE
DIFFERENCE
EQUATION
*
122
8.3.2
FROM
THE
IMPULSE
RESPONSE
TO THE
DIFFERENCE
EQUATION
*
123
8.4
THE
FREQUENCY
RESPONSE
*
124
8.5
CLASSIFICATION
OF
SYSTEMS
*
126
8.6
SINGULAR
SYSTEMS
-----
128
9
Z
TRANSFORM.
TRANSIENT
RESPONSES
*
131
9.1
Z
TRANSFORM
*
131
9.1.1
INTRODUCTION
*
131
9.1.2
DEFINITION
*
131
9.2
MAIN
PROPERTIES
OF
THE
ZT
----
133
9.3
SIGNALS
WHOSE
TRANSFORMS
ARE
SIMPLE
FRACTIONS
*
136
9.4
INVERSION
OF
THE
ZT
-----
137
9.4.1
INVERSION
INTEGRAL
*
137
9.4.2
INVERSION
BY
DECOMPOSITION
INTO
A
POLYNOMIAL
AND
PARTIAL
FRACTIONS
*
138
9.4.3
INVERSION
BY
SERIES
EXPANSION
*
140
9.4.4
STEP
RESPONSE
*
141
9.4.5
RESPONSE
TO
A
CAUSAL
SINUSOID
*
142
9.5
STABILITY
AND
JURY
CRITERION
*
145
9.6
INITIAL
CONDITIONS
-----
148
9.7
INITIAL
AND
FINAL
VALUE
THEOREMS
*
150
9.8
CONTINUOUS
TO
DISCRETE
CONVERSION
(S2Z)
*
151
9.8.1
SOME
CONSIDERATIONS
*
151
XIV
CONTENTS
9.8.2
APPROXIMATION
OF
DERIVATIVES
*
152
9.8.3
TUSTIN
RULE
OR
BILINEAR
TRANSFORMATION
*
154
9.8.4
DIRECT
CONVERSION
OF
POLES
AND
ZEROS
INTO
POLES
AND
ZEROS
*
156
9.8.5
INVARIANT
RESPONSE
S
TO
Z
CONVERSION
*
157
9.8.6
CONVERSION
FROM
PARTIAL
FRACTION
DECOMPOSITION
*
159
10
DISCRETE-TIME
DERIVATIVES
AND
TRANSFORMS
*
163
10.1
INTRODUCTION:
DIFFERENCE
VS.
DIFFERENTIAL
*
163
10.2
DERIVATIVES
AND
INVERSES
*
163
10.2.1
NABLA
AND
DELTA
DERIVATIVES
*
163
10.2.2
EXISTENCE
OF
FRACTIONAL
DERIVATIVES
*
166
10.2.3
PROPERTIES
*
166
10.2.4
THE
NABLA
AND
DELTA
EXPONENTIALS
*
168
10.3
SUITABLE
TRANSFORMS
*
172
10.3.1
THE
NABLA
TRANSFORM
*
172
10.3.2
MAIN
PROPERTIES
OF
THE
NLT
-----
173
10.3.3
EXAMPLES
*
174
10.3.4
EXISTENCE
OF
NLT
-----
176
10.3.5
UNICITY
OF
THE TRANSFORM
*
176
10.3.6
INITIAL
VALUE
THEOREM
*
177
10.3.7
FINAL
VALUE THEOREM
*
177
10.3.8
THE
DELTA
TRANSFORM
AND
THE
CORRELATION
*
178
10.3.9
BACKWARD
COMPATIBILITY
*
179
10.4
DISCRETE-TIME
FRACTIONAL
LINEAR
SYSTEMS
*
180
10.4.1
POLYNOMIAL
CASE
*
181
10.4.2
PROPER
FRACTION
CASE
*
181
10.4.3
THE
ANTI-CAUSAL
CASE
*
185
10.4.4
INVERSION
WITHOUT
PARTIAL
FRACTIONS
*
185
10.4.5
SOME
STABILITY
ISSUES
*
188
10.4.6
A
CORRESPONDENCE
PRINCIPLE
*
188
10.4.7
ON
INITIAL
CONDITIONS
*
191
10.5
THE
FOURIER
TRANSFORM
AND
THE
FREQUENCY
RESPONSE
*
192
PART
III:
ADVANCED
TOPICS
11
FRACTIONAL
STOCHASTIC
PROCESSES
AND
TWO-SIDED
DERIVATIVES
*
197
11.1
STOCHASTIC
INPUT
*
197
11.2
TWO-SIDED
DERIVATIVES
*
199
11.2.1
DERIVATIVE
OF
WHITE
NOISE
*
199
11.2.2
GL
TYPE
TWO-SIDED
DERIVATIVE
*
199
11.2.3
THE
GENERAL
TWO-SIDED
FRACTIONAL
DERIVATIVE
*
200
11.2.4
THE
INTEGER
ORDER
CASES
*
203
CONTENTS
XV
11.2.5
11.2.6
11.3
11.3.1
11.3.2
OTHER
PROPERTIES
AND
REGULARISATIONS
*
203
FELLER
DERIVATIVE
-----
205
THE
FRACTIONAL
BROWNIAN
MOTION
*
206
DEFINITION
-----
206
PROPERTIES
-----
208
12
12.1
12.2
12.3
12.4
12.5
FRACTIONAL
DELAY
DISCRETE-TIME
LINEAR
SYSTEMS
*
213
INTRODUCTION
-----
213
FRACTIONAL
DELAYS
*
213
IMPULSE
RESPONSES
*
214
SCALE
CONVERSION
*
215
LINEAR
PREDICTION
*
216
13
13.1
13.2
13.3
13.4
13.5
13.6
FRACTIONAL
DERIVATIVES
WITH
VARIABLE
ORDERS
*
221
INTRODUCTION
-----
221
PAST
PROPOSALS
*
221
AN
APPROACH
TO
VO
DERIVATIVES
BASED
ON
THE
GL
DERIVATIVE
-----
224
VARIABLE
ORDER
LINEAR
SYSTEMS
*
227
THE
VO
MITTAG-LEFFLER
FUNCTION
-----
228
VARIABLE
ORDER
TWO-SIDED
DERIVATIVES
*
230
APPENDIXES
A
A.L
A.2
ON
DISTRIBUTIONS
*
237
INTRODUCTION
-----
237
THE
AXIOMS
-----
238
B
THE
GAMMA
FUNCTION
AND
BINOMIAL
COEFFICIENTS
*
240
C
C.L
C.2
THE
CONTINUOUS-TIME
FOURIER
TRANSFORM
*
243
DEFINITION
-----
243
DIFFERENTIATION
AND
INTEGRATION
IN
THE
CONTEXT
OF
FT
*
244
D
D.L
D.2
THE
DISCRETE-TIME
FOURIER
TRANSFORM
*
247
DEFINITION
-----
247
EXISTENCE
-----
249
E
E.L
E.2
E.3
PARTIAL
FRACTION
DECOMPOSITION
WITHOUT
DERIVATIONS
*
252
SIMPLIFICATION
WHEN
THERE
ARE
NO
CONJUGATE
PAIRS
OF
POLES
*
252
SIMPLIFICATION
FOR
CONJUGATE
PAIRS
OF
POLES
ON
THE
IMAGINARY
AXIS
*
254
SIMPLIFICATION
FOR
CONJUGATE
PAIRS
OF
POLES
NOT
ON
THE
IMAGINARY
AXIS
*
256
XVI
*
CONTENTS
F
THE
MITTAG-LEFFLER
FUNCTION
*
258
F.L
DEFINITION
------
258
F.2
COMPUTATION
OF
THE
MLF
------
264
BIBLIOGRAPHY
*
267
FURTHER
READING
*
273
INDEX
*
279 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ortigueira, Manuel Duarte 1949- Valério, Duarte |
| author_GND | (DE-588)120670764X (DE-588)1206708050 |
| author_facet | Ortigueira, Manuel Duarte 1949- Valério, Duarte |
| author_role | aut aut |
| author_sort | Ortigueira, Manuel Duarte 1949- |
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| bvnumber | BV046796513 |
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| ctrlnum | (OCoLC)1109195463 (DE-599)DNB1190464063 |
| discipline | Elektrotechnik / Elektronik / Nachrichtentechnik |
| discipline_str_mv | Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV046796513 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:54:40Z |
| indexdate | 2024-07-10T08:54:05Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110621297 3110621290 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032205361 |
| oclc_num | 1109195463 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XVI, 281 Seiten 50 Illustrationen 24 cm x 17 cm |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | De Gruyter |
| record_format | marc |
| series | Fractional Calculus in Applied Sciences and Engineering |
| series2 | Fractional Calculus in Applied Sciences and Engineering |
| spelling | Ortigueira, Manuel Duarte 1949- Verfasser (DE-588)120670764X aut Fractional signals and systems Manuel D. Ortigueira and Valério Duarte 201910 Berlin ; Boston De Gruyter [2020] XVI, 281 Seiten 50 Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier Fractional Calculus in Applied Sciences and Engineering volume 7 Signalverarbeitung (DE-588)4054947-1 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 gnd rswk-swf Gebrochene Analysis (DE-588)4722475-7 s Signalverarbeitung (DE-588)4054947-1 s DE-604 Valério, Duarte Verfasser (DE-588)1206708050 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe 9783110621327 Erscheint auch als Online-Ausgabe 9783110624588 Fractional Calculus in Applied Sciences and Engineering volume 7 (DE-604)BV045897010 volume 7 X:MVB http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110621297&searchTitles=true 2019-07-17 Verlag Unbekannt DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032205361&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ortigueira, Manuel Duarte 1949- Valério, Duarte Fractional signals and systems Fractional Calculus in Applied Sciences and Engineering Signalverarbeitung (DE-588)4054947-1 gnd Gebrochene Analysis (DE-588)4722475-7 gnd |
| subject_GND | (DE-588)4054947-1 (DE-588)4722475-7 |
| title | Fractional signals and systems |
| title_auth | Fractional signals and systems |
| title_exact_search | Fractional signals and systems |
| title_exact_search_txtP | Fractional signals and systems |
| title_full | Fractional signals and systems Manuel D. Ortigueira and Valério Duarte |
| title_fullStr | Fractional signals and systems Manuel D. Ortigueira and Valério Duarte |
| title_full_unstemmed | Fractional signals and systems Manuel D. Ortigueira and Valério Duarte |
| title_short | Fractional signals and systems |
| title_sort | fractional signals and systems |
| topic | Signalverarbeitung (DE-588)4054947-1 gnd Gebrochene Analysis (DE-588)4722475-7 gnd |
| topic_facet | Signalverarbeitung Gebrochene Analysis |
| url | http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110621297&searchTitles=true http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032205361&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV045897010 |
| work_keys_str_mv | AT ortigueiramanuelduarte fractionalsignalsandsystems AT valerioduarte fractionalsignalsandsystems AT walterdegruytergmbhcokg fractionalsignalsandsystems |