Introduction to Shannon sampling and interpolation theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1991
|
| Schriftenreihe: | Springer texts in electrical engineering
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben |
| Beschreibung: | XIII, 324 S. zahlr. graph. Darst. |
| ISBN: | 0387973915 3540973915 |
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| 245 | 1 | 0 | |a Introduction to Shannon sampling and interpolation theory |c Robert J. Marks |
| 264 | 1 | |a New York u.a. |b Springer |c 1991 | |
| 300 | |a XIII, 324 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Springer texts in electrical engineering | |
| 500 | |a Literaturangaben | ||
| 650 | 4 | |a Sampling (Statistics) | |
| 650 | 4 | |a Signal processing |x Statistical methods | |
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Datensatz im Suchindex
| _version_ | 1804118450052792320 |
|---|---|
| adam_text | Titel: Introduction to Shannon sampling and interpolation theory
Autor: Marks, Robert J
Jahr: 1991
Contents
Preface
vii
1
Introduction
1
1.1
The
Cardinal
Series.................
1
1.2
History........................
2
2
Fundamentals
of
Fourier
Analysis
and
Stochastic
Processes
7
2.1
Signal
Classes
.....................
7
2.2
The
Fourier
Transform...............
9
2.2.1
The
Fourier
Series
.............11
2.2.1.1
Convergence
...........11
2.2.1.2
Orthogonal
Basis
Functions
...
12
2.2.2
Some
Elementary
Functions........13
2.2.3
Some
Transforms
of
Elementary
Functions
18
2.2.4
Other
Properties..............21
2.3
Stochastic
Processes
................22
2.3.1
First
and
Second
Order
Statistics.....22
2.3.2
Stationary
Processes............23
2.3.2.1
Power
Spectral
Density.....23
2.3.2.2
Some
Stationary
Noise
Models
.
24
2.3.2.3
Linear
Systems
with
Stationary
Stochastic
Inputs.........25
2.4
Exercises.......................26
3
The
Cardinal
Series
33
3.1
Interpretation....................33
3.2
Proofs........................35
3.2.1
Using
Comb
Functions...........35
x
Contents
3.2.2
Fourier
Series
Proof.............37
3.2.3
Papoulis’
Proof...............38
3.3
Properties......................38
3.3.1
Convergence.................39
3.3.1.1
For
Finite
Energy
Signals
....
39
3.3.1.2
For
Bandlimited
Functions
with
Finite
Area
Spectra
.......40
3.3.2
Trapezoidal
Integration...........41
3.3.2.1
Of
Bandlimited
Functions
....
41
3.3.2.2
Of
Linear
Integral
Transforms
.
.
42
3.3.2.3
Parseval’s
Theorem
for
the
Cardinal
Series..........49
3.3.3
The
Time-Bandwidth
Product
......50
3.4
Application
to
Spectra
Containing
Distributions
.
50
3.5
Application
to
Bandlimited
Stochastic
Processes
.
52
3.6
Exercises.......................54
4
Generalizations
of
the
Sampling
Theorem
57
4.1
Generalized
Interpolation
Functions........57
4.1.1
Oversampling................58
4.1.1.1
Sample
Dependency.......58
4.1.1.2
Relaxed
Interpolation
Formulae
.
63
4.1.2
Criteria
for
Generalized
Interpolation
Functions..................64
4.1.2.1
Interpolation
Functions.....66
4.1.2.2
Reconstruction
from
a
Filtered
Signal’s
Samples.........67
4.2
Papoulis’
Generalization..............68
4.2.1
Derivation..................71
4.2.2
Interpolation
Function
Computation
...
75
4.2.3
Example
Applications
............76
4.2.3.1
Recurrent
Nonuniform
Sampling
76
4.2.3.2
Interlaced
Signal-Derivative
Sampling.............77
4.2.3.3
Higher
Order
Derivative
Sampling
80
4.2.3.4
Effects
of
Oversampling.....81
4.3
Derivative
Interpolation
..............82
4.3.1
Properties
of
the
Derivative
Kernel
....
83
Contents
xi
4.4
A
Relation
Between
the
Taylor
and
Cardinal
Series
88
4.5
Sampling
Trigonometric
Polynomials.......88
4.6
Sampling
Theory
for
Bandpass
Functions.....92
4.6.1
Heterodyned
Sampling...........93
4.6.2
Direct
Bandpass
Sampling.........96
4.7
A
Summary
of
Sampling
Theorems
for
Directly
Sampled
Signals...................97
4.8
Lagrangian
Interpolation..............100
4.9
Kramer’s
Generalization..............102
4.10
Exercises.......................104
5
Sources
of
Error
111
5.1
Effects
of
Additive
Data
Noise...........Ill
5.1.1
On
Cardinal
Series
Interpolation
.....Ill
5.1.1.1
Interpolation
Noise
Level
.
.
.
.112
5.1.1.2
Effects
of
Oversampling
and
Filtering..............113
5.1.2
Interpolation
Noise
Variance
for
Directly
Sampled
Signals...............117
5.1.2.1
Interpolation
with
Lost
Samples
.
118
5.1.2.2
Bandpass
Functions.......127
5.1.3
On
Papoulis’
Generalization........129
5.1.3.1
Examples.............131
5.1.3.2
Notes...............132
5.1.4
On
Derivative
Interpolation........136
5.1.4.1
A
Lower
Bound
on
the
NINV
.
.138
5.1.4.2
Examples.............139
5.2
Jitter.........................145
5.2.1
Filtered
Cardinal
Series
Interpolation
.
.
.
145
5.2.2
Unbiased
Interpolation
from
Jittered
Samples...................146
5.2.3
In
Stochastic
Bandlimited
Signal
Interpolation
................148
5.2.3.1
NINV
of
Unbiased
Restoration
.
150
5.2.3.2
Examples.............151
5.3
Truncation
Error..................153
5.3.1
An
Error
Bound
..............153
xii
Contents
5.3.2
Noisy
Stochastic
Signals..........156
5.4
Exercises.......................163
6
The
Sampling
Theorem
in
Higher
Dimensions
167
6.1
Multidimensional
Fourier
Analysis.........167
6.1.1
Properties..................169
6.1.1.1
Separability............169
6.1.1.2
Rotation,
Scale
and
Transposition...........171
6.1.1.3
Polar
Representation.......176
6.1.2
Fourier
Series................
178
6.1.2.1
Multidimensional
Periodicity
.
.
178
6.1.2.2
The
Fourier
Series
Expansion
.
.181
6.2
The
Multidimensional
Sampling
Theorem.....184
6.2.1
The
Nyquist
Density............187
6.2.2
Generalized
Interpolation
Functions
....
192
6.2.2.1
Tightening
the
Integration
Region...............192
6.2.2.2
Allowing
Slower
Roll
Off.....195
6.3
Restoring
Lost
Samples...............195
6.3.1
Restoration
Formulae............195
6.3.2
Noise
Sensitivity
..............198
6.3.2.1
Filtering..............200
6.3.2.2
Deleting
Samples
from
Optical
Images...............200
6.4
Periodic
Sample
Decimation
and
Restoration
.
.
.
203
6.4.1
Preliminaries
................204
6.4.2
First
Order
Decimated
Sample
Restoration.................208
6.4.3
Sampling
Below
the
Nyquist
Density
.
.
.
211
6.4.4
Higher
Order
Decimation..........215
6.5
Raster
Sampling
..................216
6.6
Exercises.......................219
7
Continuous
Sampling
225
7.1
Interpolation
From
Periodic
Continuous
Samples
.
228
7.1.1
The
Restoration
Algorithm
........230
Contents
xiii
7.1.2
Noise
Sensitivity..............239
7.1.2.1
White
Noise............239
7.1.2.2
Colored
Noise...........242
7.1.3
Observations
................244
7.1.3.1
Comparison
with
the
NINV
of
the
Cardinal
Series........244
7.1.3.2
In
the
Limit
as
an
Extrapolation
Algorithm.............244
7.1.4
Application
to
Interval
Interpolation
.
.
.
245
7.2
Prolate
Spheroidal
Wave
Functions........254
7.2.1
Properties..................254
7.2.2
Application
to
Extrapolation........257
7.2.3
Application
to
Interval
Interpolation
.
.
.
259
7.3
The
Papoulis-Gerchberg
Algorithm........260
7.3.1
The
Basic
Algorithm........
260
7.3.2
Proof
of
the
PGA
using
PSWF’s
.....266
7.3.3
Geometrical
Interpretation
in
a
Hilbert
Space
....................268
7.3.4
Remarks...................270
7.4
Exercises.......................271
Appendix
279
Index
320
|
| any_adam_object | 1 |
| author | Marks, Robert J. |
| author_facet | Marks, Robert J. |
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| dewey-search | 517.2 |
| dewey-sort | 3517.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Elektrotechnik Mathematik |
| format | Book |
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| id | DE-604.BV004253862 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:10:29Z |
| institution | BVB |
| isbn | 0387973915 3540973915 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002646160 |
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| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR DE-29T DE-83 DE-188 |
| physical | XIII, 324 S. zahlr. graph. Darst. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in electrical engineering |
| spelling | Marks, Robert J. Verfasser aut Introduction to Shannon sampling and interpolation theory Robert J. Marks New York u.a. Springer 1991 XIII, 324 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer texts in electrical engineering Literaturangaben Sampling (Statistics) Signal processing Statistical methods Signalanalyse (DE-588)4181260-8 gnd rswk-swf Stichprobe (DE-588)4057502-0 gnd rswk-swf Abtasttheorem (DE-588)4258507-7 gnd rswk-swf Interpolation (DE-588)4162121-9 gnd rswk-swf Abtasttheorem (DE-588)4258507-7 s DE-604 Stichprobe (DE-588)4057502-0 s Signalanalyse (DE-588)4181260-8 s Interpolation (DE-588)4162121-9 s DE-188 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002646160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Marks, Robert J. Introduction to Shannon sampling and interpolation theory Sampling (Statistics) Signal processing Statistical methods Signalanalyse (DE-588)4181260-8 gnd Stichprobe (DE-588)4057502-0 gnd Abtasttheorem (DE-588)4258507-7 gnd Interpolation (DE-588)4162121-9 gnd |
| subject_GND | (DE-588)4181260-8 (DE-588)4057502-0 (DE-588)4258507-7 (DE-588)4162121-9 |
| title | Introduction to Shannon sampling and interpolation theory |
| title_auth | Introduction to Shannon sampling and interpolation theory |
| title_exact_search | Introduction to Shannon sampling and interpolation theory |
| title_full | Introduction to Shannon sampling and interpolation theory Robert J. Marks |
| title_fullStr | Introduction to Shannon sampling and interpolation theory Robert J. Marks |
| title_full_unstemmed | Introduction to Shannon sampling and interpolation theory Robert J. Marks |
| title_short | Introduction to Shannon sampling and interpolation theory |
| title_sort | introduction to shannon sampling and interpolation theory |
| topic | Sampling (Statistics) Signal processing Statistical methods Signalanalyse (DE-588)4181260-8 gnd Stichprobe (DE-588)4057502-0 gnd Abtasttheorem (DE-588)4258507-7 gnd Interpolation (DE-588)4162121-9 gnd |
| topic_facet | Sampling (Statistics) Signal processing Statistical methods Signalanalyse Stichprobe Abtasttheorem Interpolation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002646160&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT marksrobertj introductiontoshannonsamplingandinterpolationtheory |