【正文】 小波分析在信號處理中的應(yīng)用 江 西理工大學(xué)畢業(yè)設(shè)計 I 小波分析在信號處理中的應(yīng)用 摘 要 小波分析是純數(shù)學(xué)、應(yīng)用數(shù)學(xué)和工程技術(shù)的完美結(jié)合。 小波變換在于音頻信號圖像信號的處理中具有重要的意義。 在傳統(tǒng)的傅立葉分析中，信號完全是在頻域展開的，不包含任何時頻的信息，這對于某些應(yīng)用來說是很恰當(dāng)?shù)?，因為信號的頻率的信息對其是非常重要的。但其丟棄的時域信息可能對某些應(yīng)用同樣非常重要 。 而小波分析則克服了短時傅立葉變換在單分辨率上的缺陷，具有多分辨率分析的特點(diǎn)，在時域和頻域都有表征信號局部信息的能力 。而在于信號之中圖像是一種重要的信息源，通過圖像處理可以幫助人們了解信息的內(nèi) 涵。本文簡述了小波包分析的原理，并基于MATLAB 實現(xiàn)了對二維圖像信號進(jìn)行消噪。對常用的幾種閾值去噪方法進(jìn)行了分析比較和仿真實現(xiàn)。最后結(jié)合理論分析和實驗結(jié)果，討論了去噪過程中影響去噪性能的各種因素。為在實際的圖像處理中，小波包閾值去噪法的選擇和改進(jìn)提供了數(shù)據(jù)參考和依據(jù) 關(guān)鍵詞：信號；圖像銳化；圖像去噪； 小波分析 CC 版權(quán)所有僅供參考！??！ XX：小波分析在信號處理中的應(yīng)用 II The application of wavelet analysis in signal processing ABSTRACT Wavelet analysis is pure mathematics, applied mathematics and engineering the perfect bination. Wavelet transform is the audio signal processing of the image signal has an important significance. In conventional Fourier analysis, the signal is pletely expanded in the frequency domain, the frequency does not contain any information, which for some applications is very appropriate because of its frequency of the signal information is very important. But its timedomain information may be discarded for certain applications is also very important. The wavelet analysis is to overe the shorttime Fourier transform in a single resolution of defects, with the multiresolution analysis of the characteristics of the time domain and frequency domain signals are characterized by the ability of local information. But rather among the image signal is an important source of information, through image processing can help people understand the information content. This paper describes the principle of wavelet packet analysis, and based on MATLAB realization of twodimensional image signal denoising. Several monly used thresholding methods were analyzed and pared and Simulation. Finally, theoretical analysis and experimental results are discussed denoising process a variety of factors affect the performance of denoising. As in the actual image processing, wavelet packet thresholding method selection and improvement of a data reference and basis. Keywords: signal。Image sharpening。 image denoising。 wavelet analysis 小波分析在信號處理中的應(yīng)用 江 西理工大學(xué)畢業(yè)設(shè)計 III 目錄 第一章 概述 .......................................................................................................................................................................... 1 小波分析的發(fā)展與應(yīng)用 ............................................................................................................................... 1 本文主要意義內(nèi)容 ............................................................................................................................................ 2 第二章 相關(guān)技術(shù)原理 ................................................................................................................................................. 3 小波分析的基本原理 ...................................................................................................................................... 3 幾種常用小波 ......................................................................................................................................................... 4 傅立葉變換與小波變換 ................................................................................................................................ 6 傅立葉變換與小波變換歷史 .......................................................................................................... 6 傅里葉變換 ..................................................................................................................................................... 7 小波變換 ............................................................................................................................................................ 8 小波包定義性質(zhì) ............................................................................................................................................... 11 小波包定義 ................................................................................................................................................ 11 小波包的性質(zhì) ........................................................................................................................................... 13 小波包算法 .................................................................................................................................................. 13 第三章 小波變換在信號處理中的應(yīng)用 .................................................................................................. 14 調(diào)試環(huán)境 MATLAB開發(fā)平臺 .................................................................................................................. 14 小波分析用于圖像壓縮 ............................................................................................................................ 14 小波包變換的圖像壓縮 ............................................................................................................................ 16 小波分析用于圖像去噪 ............................................................................................................................ 17 圖像噪聲分類 ......................................................................................................................................... 18 XX：小波分析在信號處理中的應(yīng)用 IV 圖像噪聲處理 ........................................................................................................................................... 19 小波分析用于圖像增強(qiáng) ............................................................................................................................ 21 圖像銳化 ................................................................................................................................................................. 21 第四章 圖片降噪中主要應(yīng)用的函數(shù)閾值選取 ............................................................................... 23 二維小波包分解函數(shù) .............