Digital fourier analysis: advanced techniques
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY [u.a.]
Springer
2015
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 178 S. teilw. farb. Ill., graph. Darst. |
| ISBN: | 9781493911264 |
Internformat
MARC
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| 001 | BV042117202 | ||
| 003 | DE-604 | ||
| 005 | 20150112 | ||
| 007 | t | ||
| 008 | 141014s2015 ad|| |||| 00||| eng d | ||
| 020 | |a 9781493911264 |c pbk. |9 978-1-4939-1126-4 | ||
| 035 | |a (OCoLC)915475740 | ||
| 035 | |a (DE-599)GBV791037029 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-11 | ||
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 100 | 1 | |a Kido, Ken'iti |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Digital fourier analysis |b advanced techniques |c Ken'iti Kido |
| 264 | 1 | |a New York, NY [u.a.] |b Springer |c 2015 | |
| 300 | |a XIII, 178 S. |b teilw. farb. Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4939-1127-1 |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027557510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027557510 | ||
Datensatz im Suchindex
| _version_ | 1804152590571667456 |
|---|---|
| adam_text | Titel: Digital fourier analysis
Autor: Kido, Ken iti
Jahr: 2015
Contents
1 Sine and Cosine Waves................................................................1
1.1 Synthesis of an Impulse by Cosine Waves..............................1
1.2 Synthesis of Rectangular Waveforms by Sine
and Cosine Waves................................................................2
1.3 Time Period........................................................................4
1.4 Harmonics and Waveforms....................................................5
1.5 Fourier Series......................................................................8
1.6 Shift of Harmonics on the Time Axis......................................9
1.7 Complex Exponential Functions and Sine
and Cosine Functions............................................................11
1.8 Phases of Cosine and Sine Functions......................................15
1.9 Synthesis of Sine Wave with Arbitrary Phase..........................17
1.10 Instantaneous Phase and Frequency........................................20
1.11 Exercise..............................................................................23
2 Fourier Series Expansion..............................................................25
2.1 Integrals of Sine and Cosine Functions....................................25
2.2 Calculations of Fourier Coefficients........................................28
2.3 Expressing Waveforms by Even Functions.........................32
2.4 Expressing Waveforms by Odd Functions................................36
2.5 Expressing Waveforms by Complex Exponential Functions ... 38
2.6 Fourier Transform................................................................41
2.7 Gibbs Phenomenon..............................................................46
2.8 Exercises..............................................................................49
3 Numerical (Digitized) Waveforms..................................................51
3.1 Fourier Series Expansion of Spectrum....................................51
3.2 Reproduction of the Continuous Waveform from
the Sequence of Sample Values..............................................56
3.3 Frequency Bandwidth and Sampling Frequency........................58
3.4 Smoothing of Sample Sequence by Low-Pass Filtering..............60
3.5 Sampling Theorem................................................................62
3.6 Smoothing of a Sample Sequence Using
the Sampling Theorem..........................................................63
3.7 Folding (Aliasing) of the Spectrum........................................65
3.8 Sampling Frequency Conversion I (Application
of the Fourier Transform)......................................................69
3.9 Sampling Frequency Conversion II (Application of LPF)..........72
3.10 Exercises..............................................................................74
4 Discrete Fourier Transform..........................................................77
4.1 Fourier Transform of Discrete Sequence of Numbers................77
4.2 Inverse Discrete Fourier Transform (IDFT)..............................80
4.3 The DFT and the Fourier Transform......................................84
4.4 Waveform and Its DFT..........................................................87
4.4.1 Sine and Cosine Waves..............................................87
4.4.2 Phase and Spectrum....................................................88
4.4.3 Harmonics................................................................89
4.4.4 Symmetric and Antisymmetric Waveforms....................91
4.4.5 Sine Waveforms with Noninteger Frequencies..............92
4.4.6 Too Wide Sample Spacing..........................................92
4.4.7 Rectangular Wave......................................................94
4.5 Discrete Cosine Transform (DCT)..........................................94
4.6 Extension of the Discrete Cosine Transform............................100
4.7 Exercises..............................................................................104
5 Fast Fourier Transform................................................................107
5.1 Decimation in Time Algorithm..............................................107
5.2 Decimation in Frequency Algorithm........................................111
5.3 2m-Point FFT by Decimation in Time Algorithm......................114
5.4 2m-Point FFT by Decimation in Frequency Algorithm..............121
5.5 Rearrangement of the Bit-Reversed Order................................125
5.6 Speed-Up Technique by Parallel Computation..........................128
5.7 Exercises..............................................................................130
6 DFT and Spectrum......................................................................131
6.1 Periodogram........................................................................131
6.2 Uncertainty Principle............................................................135
6.3 Spreading of the Spectrum....................................................138
6.4 Analysis of Short Waves........................................................139
6.5 DFT of Sine Waves..............................................................144
6.6 Removal of Discontinuity by the Adjustment
of the Sampling Frequency....................................................146
6.7 Removal of Discontinuity by the Weighting
of Sample Sequences............................................................148
6.8 Exercise..............................................................................151
7 Time Window..............................................................................153
7.1 Fourier Transform of a Product of Two Time Functions............153
7.2 Spectra of Tapered Functions................................................155
7.3 DFT of Short Waveforms......................................................159
7.4 Various Time Windows........................................................161
7.4.1 Rectangular Window..................................................161
7.4.2 Banning Window (Von Hann Window)........................163
7.4.3 Hamming Window......................................................167
7.4.4 Blackman-Harris Window............................................168
7.4.5 Half-Sine Window and Riesz Window..........................170
7.4.6 Flat-Top Window......................................................173
7.4.7 Bartlett Window........................................................176
7.4.8 Gaussian Window......................................................177
7.5 Comparison of Windows by the Results
of Frequency Analysis..........................................................179
7.6 Exercise..............................................................................181
Appendix..........................................................................................183
References........................................................................................193
Answers............................................................................................195
Index................................................................................................201
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| illustrated | Illustrated |
| indexdate | 2024-07-10T01:13:08Z |
| institution | BVB |
| isbn | 9781493911264 |
| language | English |
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| physical | XIII, 178 S. teilw. farb. Ill., graph. Darst. |
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| spelling | Kido, Ken'iti Verfasser aut Digital fourier analysis advanced techniques Ken'iti Kido New York, NY [u.a.] Springer 2015 XIII, 178 S. teilw. farb. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Erscheint auch als Online-Ausgabe 978-1-4939-1127-1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027557510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kido, Ken'iti Digital fourier analysis advanced techniques |
| title | Digital fourier analysis advanced techniques |
| title_auth | Digital fourier analysis advanced techniques |
| title_exact_search | Digital fourier analysis advanced techniques |
| title_full | Digital fourier analysis advanced techniques Ken'iti Kido |
| title_fullStr | Digital fourier analysis advanced techniques Ken'iti Kido |
| title_full_unstemmed | Digital fourier analysis advanced techniques Ken'iti Kido |
| title_short | Digital fourier analysis |
| title_sort | digital fourier analysis advanced techniques |
| title_sub | advanced techniques |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027557510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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