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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 貝蘇章 | |
dc.contributor.author | Kuo-Wei Chang | en |
dc.contributor.author | 張國韋 | zh_TW |
dc.date.accessioned | 2021-05-12T09:34:34Z | - |
dc.date.available | 2018-07-26 | |
dc.date.available | 2021-05-12T09:34:34Z | - |
dc.date.copyright | 2018-07-26 | |
dc.date.issued | 2018 | |
dc.date.submitted | 2018-06-21 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/1229 | - |
dc.description.abstract | 本論文利用拉瑪努江和(Ramanujan’s sum)的特性,舉出兩種信號處理上的應用。其一為建構零自相關的整數序列(Integer zero autocorrleation sequence),這在通訊系統上有廣泛的應用。他的原理是利用傅立葉轉換,把建構零自相關序列的數論問題,轉換成建構一個固定振幅信號(constant amplitude) 的問題,這裡巧妙用上拉瑪努江和整數的特性。另一個應用是一維與二維的信號週期偵測。利用拉瑪努江和週期以及整數的特性,週期信號可以被分解成一個個因數的週期,往後便可以針對不同的週期進行不同的處理,如同以前的濾波器組(filter bank)。最後我們針對拉瑪努江和只能找出因數週期的缺點,採用全相位快速傅立葉(all phase FFT) 演算法來改進。全相位快速傅立葉演算法為利用相位的差,求出非整數的頻率,改進了以往頻率只能在整數上的缺點,可以幫助我們進行週期偵測。我們也順帶提到全相位快速傅立葉演算法的一些其他應用,包含唧聲信號(chirp signal) 的頻率追蹤、快速二維頻率偵測等等。 | zh_TW |
dc.description.abstract | This thesis presents two applications of Ramanujan’s sum in the domain of signal processing. The first one is integer zero autocorrelation sequence construction, which is useful in modern communication system. The concept is to transform this number theoretic problem into a constant amplitude signal construction problem, by Fourier transform and the integer property of Ramanujan’s sum. The second application is 1D and 2D period estimation. The periodic signal is separated into sub-period signals, just like filter bank. Each sub-period is a factor of the length. Finally we use all phase FFT to enhance the period estimation. All phase FFT use phase information to estimate frequency. The advantage is the frequency is non integer. Finally we propose some other applications of all phase FFT, such as chirp signal pitch tracking and fast 2D frequency estimation. | en |
dc.description.provenance | Made available in DSpace on 2021-05-12T09:34:34Z (GMT). No. of bitstreams: 1 ntu-107-D00942009-1.pdf: 1241486 bytes, checksum: f2f534f61952f76a56507596bccb6364 (MD5) Previous issue date: 2018 | en |
dc.description.tableofcontents | 誌謝iii
Acknowledgements v 摘要vii Abstract ix 1 Introduction 1 1.1 Definition and Properties of Ramanujan’s Sum . . . . . . . 1 1.2 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 First Application: Integer and Gaussian Integer Zero Autocorrelation Sequences 5 2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Time domain method I: Making extra constraints . . 8 2.2.2 Time domain method II:Linear equation method . . . 9 2.2.3 Frequency domain method I:The Geometric sequence method . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.4 Frequency domain method I:Legendre sequence method 15 2.3 Generate IZAC using Ramanujan’s Sum . . . . . . . . . . . . 21 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3 Second Application:Period Estimation 27 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 1D Period Estimation . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.1 1D period filterbank . . . . . . . . . . . . . . . . . . . . 29 3.2.2 1D Impulse Train and Möbius Inversion . . . . . . . . 31 3.3 2D Period Estimation . . . . . . . . . . . . . . . . . . . . . . . 36 3.3.1 2D Ramanujan’s Sum and period filterbank . . . . . . 40 3.3.2 2D LCM for Period Detection . . . . . . . . . . . . . . 48 3.3.3 2D Period Detection Examples . . . . . . . . . . . . . 53 3.3.4 Discussion on Möbius Inversion in 2D . . . . . . . . . 63 4 All phase FFT 71 4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Definition and Properties . . . . . . . . . . . . . . . . . . . . . 72 4.3 Applications of apFFT . . . . . . . . . . . . . . . . . . . . . . . 76 4.3.1 Determine the proper frequency for period estimation 76 4.3.2 1D/2D frequency estimation . . . . . . . . . . . . . . . 79 4.3.3 Chirp rate tracking . . . . . . . . . . . . . . . . . . . . 81 4.3.4 Sparse FFT and Signal reconstruction . . . . . . . . . 83 5 Conclusion 87 Bibliography 89 | |
dc.language.iso | en | |
dc.title | 拉瑪努江和於信號處理及週期偵測之應用 | zh_TW |
dc.title | Ramanujan’s Sum and Its Application to Signal
Processing and Period Estimation | en |
dc.type | Thesis | |
dc.date.schoolyear | 106-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 李枝宏,丁建均,吳家麟,黃文良,廖弘源 | |
dc.subject.keyword | 拉瑪努江,信號處理,週期偵測,傅立葉轉換, | zh_TW |
dc.subject.keyword | Signal Processing,Period Estimation,Fourier Transform, | en |
dc.relation.page | 94 | |
dc.identifier.doi | 10.6342/NTU201800930 | |
dc.rights.note | 同意授權(全球公開) | |
dc.date.accepted | 2018-06-21 | |
dc.contributor.author-college | 電機資訊學院 | zh_TW |
dc.contributor.author-dept | 電信工程學研究所 | zh_TW |
顯示於系所單位: | 電信工程學研究所 |
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