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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林致廷 | zh_TW |
| dc.contributor.advisor | Chih-Ting Lin | en |
| dc.contributor.author | 羅紹耘 | zh_TW |
| dc.contributor.author | Shao-Yun Luo | en |
| dc.date.accessioned | 2024-07-31T16:15:18Z | - |
| dc.date.available | 2024-08-01 | - |
| dc.date.copyright | 2024-07-31 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-07-19 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93423 | - |
| dc.description.abstract | 在訊號分析的領域中，高頻區的分析時常會遇到比較大的誤差，例如吉布斯現象。為了嘗試解決這些問題，本論文先提出了精準計算的概念，在有限項傅立葉級數中加入額外的修正項輔助分析訊號高頻區，並成功降低吉布斯現象，讓分析結果能夠更加正確。基於精準計算中區分訊號高低頻的想法，本論文透過自定義的方法將包含心電圖與腦電圖在內的一維訊號分為高頻區與低頻區，再分別透過離散餘弦轉換與勒壤德多項式展開的組合進行訊號分解，與其他方法進行壓縮效果的比較，發現當一維訊號的高頻區與低頻區之間的區分明顯且交雜不多時，本論文所提出的運算方法能夠在一維訊號壓縮中有卓越的表現，但在高低頻混雜的訊號就比較難以展現理想的結果。
接著，本論文亦將相關結果擴展到二維影像處理中，比較自定義方法與其他方法的壓縮效果，並嘗試將壓縮後的影像重建為新影像，同樣發現當圖片的高頻區與低頻區之間的區分明顯且交雜不多時，圖片的壓縮與重建效果非常理想。若圖片的高低頻混雜比較明顯，重建的圖片就會出現比較明顯的失真。 | zh_TW |
| dc.description.abstract | In the field of signal analyzing, the error often become significant in high frequency parts, such as Gibbs phenomenon. In order to solve the problem, the thesis advances the conception of precision calculation, adding extra correction items to support the analyzation of the high frequency parts of the signals, which reduces Gibbs phenomenon successfully. Based on the conception of separating the signal’s high frequency parts and low frequency parts in precision calculation, the thesis divides 1D signals, including ECG and EEG, into high frequency parts and low frequency parts by self-defined methods. Afterwards, we decompose the signal through the combination of discrete Fourier transform(DCT) and Legendre polynomial expansion respectively, then compare the compression efficiency of the proposed methods with other methods. We find out that the proposed methods work perfectly when the signal’s high frequency parts and low frequency parts are separated clearly without severe hybridization. However, the methods fail to show ideal outcome in severe hybridization ones. Moreover, we expand our proposed methods to 2D image compression, compare the compression efficiency of the proposed methods with other methods, then attempt to recover the new images from the compressed ones. Similar to 1D signals, when the signal’s high frequency parts and low frequency parts are separated clearly without severe hybridization, the recovery of the image shows ideal result, and distortions will be observed in severe hybridization images. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-31T16:15:18Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-31T16:15:18Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
誌謝 i 中文摘要 ii ABSTRACT iii CONTENTS iv LIST OF FIGURES ix LIST OF TABLES xv Chapter 1 Introduction 1 1.1 Signal Analyzing 1 1.2 ECG 1 1.3 EEG 4 Chapter 2 Signal Analysis and Compression Review 6 2.1 Classical Signal Analysis 6 2.1.1 Fourier Series 6 2.1.2 Legendre Polynomial Expansion 6 2.1.3 Discrete Cosine Transform(DCT) 7 2.1.4 Discrete Sine Transform(DST) 8 2.2 Newer Signal Analysis Methods 10 2.3 Classic Methods of ECG Compression 10 2.3.1 AZTEC[19] 10 2.3.2 TP[20] 11 2.3.3 CORTES[21] 11 2.3.4 SAPA-2[22] 12 2.4 Other ECG Compression Methods 13 2.5 EEG compression methods 13 2.6 Compressed Sensing 13 2.6.1 Matching Pursuit 13 2.6.2 Orthogonal Matching Pursuit 15 Chapter 3 Proposed Methods 16 3.1 Main Idea of Precision Calculation 16 3.1.1 Correction Basis 16 3.1.2 Trials of Precision Calculation 17 3.1.3 Precision Calculation’s Inspiration 19 3.2 Compared Compression Methods in 1D 20 3.2.1 Time Domain Expansion 20 3.2.2 Discrete Wavelet Transform 20 3.2.3 Linear Interpolation 21 3.2.4 Sinc Interpolation 21 3.2.5 Cubic B-spline 21 3.2.6 Cumulative Sum 22 3.2.7 Weighted Rank 22 3.3 Proposed Methods in 1D 23 3.3.1 Pre-processing 23 3.3.2 Piecewise Continuous Signal 24 3.3.3 Nearly Piecewise Continuous Signal 24 3.3.4 Less-variant Frequency Distribution Signal 25 3.3.5 Summary of the Methods 25 3.4 Compared Compression Methods in 2D 28 3.5 Proposed Method in 2D 28 3.5.1 Edge Detecting 29 3.5.2 Morphology 29 3.5.3 The Adapted-DCT 30 3.5.4 Image Recovery 32 3.5.5 Structural Similarity 32 Chapter 4 Experiment Results in 1D Cases 33 4.1 Financial Signals 33 4.1.1 Stock(TAIEX) 33 4.1.2 Stock(Dow Jones) 34 4.1.3 Stock(Nikkei) 35 4.1.4 Stock(DAX) 36 4.1.5 Stock(TSMC) 37 4.1.6 Exchange Rate(USD) 38 4.1.7 Exchange Rate(EUR) 39 4.1.8 Exchange Rate(JPY) 40 4.1.9 Futures(Gold) 41 4.1.10 Futures(Oil) 42 4.1.11 Futures(Gas) 43 4.2 Traffic Signals 44 4.2.1 MRT(Taichung) 45 4.2.2 MRT(Taipei) 45 4.2.3 MRT(Taoyuan) 46 4.2.4 MRT(Kaohsiung) 47 4.2.5 Kaohsiung Light Rail 48 4.2.6 Highway(Northbound) 49 4.2.7 Highway(Southbound) 50 4.2.8 Highway(total) 51 4.3 Meteorological Signals 52 4.3.1 Air Pressure 52 4.3.2 Temperature 53 4.3.3 Humidity 54 4.4 ECG Signals 55 4.4.1 100m 55 4.4.2 101m 56 4.4.3 102m 57 4.4.4 103m 58 4.4.5 104m 59 4.4.6 The average rank of other ECG signals 60 4.5 EEG Signals 61 4.6 Briefly discussion of 1D Signals 64 4.7 Row and Column of Images 64 4.7.1 Baboon(column) 66 4.7.2 Baboon(row) 67 4.7.3 Barbara(column) 67 4.7.4 Barbara(row) 68 4.7.5 Cameraman(column) 68 4.7.6 Cameraman(row) 69 4.7.7 Goldhill(column) 69 4.7.8 Goldhill(row) 70 4.7.9 Peppers(column) 70 4.7.10 Peppers(row) 71 Chapter 5 Experiment Results in 2D Cases 72 5.1 Five Images with Given Conditions 72 5.2 Baboon Results with Different Conditions 80 5.3 Recovered Five Images 86 5.4 The Results of Other Images 88 5.4.1 Image 1(Graduation 1) 89 5.4.2 Image 2(Graduation 2) 91 5.4.3 Image 3(Mobile Game Character, MGC) 93 5.4.4 Image 4(Animation Poster, AP) 96 5.4.5 The Discussion of Other Images 98 Chapter 6 Conclusion and Future Works 99 REFERENCE 101 | - |
| dc.language.iso | en | - |
| dc.subject | 離散餘弦轉換 | zh_TW |
| dc.subject | 訊號分析 | zh_TW |
| dc.subject | 影像處理 | zh_TW |
| dc.subject | 資料壓縮 | zh_TW |
| dc.subject | 心電圖 | zh_TW |
| dc.subject | 腦電圖 | zh_TW |
| dc.subject | 精準計算 | zh_TW |
| dc.subject | Data Compression | en |
| dc.subject | Signal Analyzing | en |
| dc.subject | Image Processing | en |
| dc.subject | Precision Calculation | en |
| dc.subject | Electroencephalogram(EEG) | en |
| dc.subject | Electrocardiography(ECG) | en |
| dc.subject | Discrete Fourier Transform(DCT) | en |
| dc.title | 以精準計算想法輔助一維訊號與圖片的擴展與壓縮 | zh_TW |
| dc.title | One-Dimensional Data and Image Expansion and Compression Using the Inspiration of Precision Calculation | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.coadvisor | 丁建均 | zh_TW |
| dc.contributor.coadvisor | Jian-Jiun Ding | en |
| dc.contributor.oralexamcommittee | 簡鳳村;張榮吉 | zh_TW |
| dc.contributor.oralexamcommittee | Feng-Tsun Chien;Rong-Chi Chang | en |
| dc.subject.keyword | 離散餘弦轉換,訊號分析,影像處理,資料壓縮,心電圖,腦電圖,精準計算, | zh_TW |
| dc.subject.keyword | Discrete Fourier Transform(DCT),Signal Analyzing,Image Processing,Data Compression,Electrocardiography(ECG),Electroencephalogram(EEG),Precision Calculation, | en |
| dc.relation.page | 109 | - |
| dc.identifier.doi | 10.6342/NTU202401836 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-07-19 | - |
| dc.contributor.author-college | 電機資訊學院 | - |
| dc.contributor.author-dept | 電子工程學研究所 | - |
| 顯示於系所單位： | 電子工程學研究所 | |
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| ntu-112-2.pdf | 8.2 MB | Adobe PDF | 檢視/開啟 |
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