【正文】 i 基于數(shù)字濾波的譜數(shù)據(jù)的平滑算法的研究與實現(xiàn) 摘要 ： 當前正處于數(shù)字信息化時代，數(shù)字信號處理技術(shù)受到人們的廣泛關(guān)注，其理論及算法隨計算機技術(shù)和微電子技術(shù)的發(fā)展得到了飛速的發(fā)展，被廣泛應(yīng)用 語音圖像處理、數(shù)字通訊、譜分析、模式識別、自動控制等領(lǐng)域。數(shù)字濾波器是數(shù)字信號中最重要的組成部分之一，幾乎出現(xiàn)在所有的數(shù)字信號處理系統(tǒng)中。數(shù)字濾波器是指完成信號濾波處理的功能，用有限精度算法實現(xiàn)的離散時間線性非時變系統(tǒng)，其輸入是一組（由模擬信號取樣和量化）數(shù)字量，其輸出是經(jīng)過變換的另一組數(shù)字量。數(shù)據(jù)平滑是統(tǒng)計語言建模的關(guān)鍵技術(shù)， 它不僅可以改進語言模型的性能，還可以提高語音識別、文字識別等應(yīng)用領(lǐng)域的系統(tǒng)識別率，不同的數(shù)據(jù)平滑方法之間的對應(yīng)在各種不同規(guī)模的訓練集上操作。各種平滑算法中，以Good— Turing估計、線性插值平滑、 Katz’ s回退式平滑最為典型和常用。 由于射線和探測器中固有的統(tǒng)計漲落、電子學系統(tǒng)的噪聲影響，譜數(shù)據(jù)有很大的統(tǒng)計漲落。譜數(shù)據(jù)的漲落使譜數(shù)據(jù)處理產(chǎn)生誤差。在 γ 能譜的分析中，如果被分析的核素活度很低，或被分析的是發(fā)射多支 γ 射線核素所輻射的弱分支，或測量時間太短，那么，由于計數(shù)的統(tǒng)計漲落，可能使譜中相鄰道計數(shù)的分 散度較大，致使譜峰模糊。為了減少能譜測量數(shù)據(jù)的統(tǒng)計漲落，又保留譜峰的全部重要的特征，以便譜的分析，必須對實測 γ 能譜原始數(shù)據(jù)進行光滑。 關(guān)鍵詞 ： 數(shù)字濾波器； 數(shù)據(jù)平滑；語料庫；線性插值平滑； 統(tǒng)計漲落 ii Research and implementation of spectral data smoothing algorithm based on the digital filtering Abstract:Current is in the digital information age, digital signal processing technology is widespread attention, its theory and algorithm along with the development of the puter technology and microelectronic technology obtained the rapid development and be widely applied in voice and image processing, digital munications, spectrum analysis, pattern recognition, automatic control and other fields. Digital filter is one of the most important part of digital signal, almost appeared in all digital signal processing systems. Filtering processing of digital filter is refers to the plete function, with limited accuracy algorithm of discrete time linear timeinvariant system, its input is a set of (by the analog signal sampling and quantization) digital quantity, its output is another digital quantity after transforming. Data smoothing is the key technology of statistical language modeling, It not only can improve the performance of language modeling, it Can also improve speech recognition and Application areas such as language identification system recognition rate. Different data smoothing method should be at the contrast between the different scale of operation on the training set. A variety of smoothing algorithms, To GoodTuring estimate, linear interpolation smoothing, Katz’s backofftype is most typical and monly used smoothing. In this paper, various methods of data smoothing empirical parison, and discussed the impact of these data smoothing method performance of relevant factors. Due to inherent statistical fluctuation and the electronics system of noise influence in the rays and the probe, Spectral data has a lot of fluctuations. Spectral data fluctuation spectrum data processing error is produced. In gamma energy spectrum analysis, if the analysis of nuclide activity is very low, or is the analysis of the emission of radiation by gamma rays nuclide more weak branches, or the measuring time is too short, so, because of the statistical fluctuation count, may make the adjacent word count in the spectral dispersion larger and lead to the peak fuzzy. In order to reduce the spectrum measurement data of statistical fluctuation, and keep all the important feature of spectral peak to facilitate analysis of the spectral , must be smooth to the measured gamma spectrometry original data. KeyWords： Digital filter。 Data smoothing。 Corpus。 Linear interpolation is smooth。 Statistical fluctuation iii 目 錄 摘要 ....................................................................... i ABSTRACT. .................................................................. i 目錄 ..................................................................... iii 1 緒論 .................................................................... 1 譜數(shù)據(jù)的平滑處理概念 及方法 ..........................................1 濾波器的選用 ........................................................ 1 常用的數(shù)字濾波算法 與選擇原則 ........................................ 3 2 能譜平滑算法的研究 ...................................................... 5 幾種能譜平 滑算法 .................................................... 5 其他算法的基本思想 ..................................................5 算數(shù)滑動平均法基本思想 ..........................................5 重心法基本思想 ..................................................5 傅里葉變換法基本思想 ............................................6 指數(shù)平滑法基本思想 ..............................................6 最小二乘 移動平滑 法 ..................................................7 SavitzkyGolay 濾波 .............................................7 最小二乘移動平滑法基本思想 與方法 ................................8 移動最小二乘法與最小二乘法比較 .................................12 小波變換 方法 .......................................................13 小波 算法 原理 ...................................................13 小波 算法 去噪的基 本方法 .........................................14 連續(xù)小波變換與局部時域分析 .....................................16 3 能譜平滑算法的實現(xiàn) .....................................................18 系統(tǒng)的實現(xiàn) .........................................................18 四種 平滑法 的仿真 ...............................................18 兩種仿真的結(jié)果分析以及比較 .....................................22 譜 平滑的幾個具體問題 ...........................................23 本章小結(jié) ...........................................................26 4 未來展望與全文總結(jié) ..................................................... 28 未來展望 ........................................................... 28 全文總結(jié) ........................................................... 28 iv 參考文獻 .................................................................. 30 致謝 ...................................................................... 31 參考附錄 .................................................................. 32 1 1 緒論 譜數(shù)據(jù)的平滑處理的概念 及方法 在放射性測量中，由于存在統(tǒng)計漲落 ，使得測量數(shù)據(jù)的規(guī)律不顯著，尤其在能譜分析工作中，當被分析的放射性核素的活度很低時，在有限的測量時間內(nèi)，每道計數(shù)較少，峰面積 統(tǒng)計漲落較大，給測量結(jié)果帶來較大的誤差。 其 主要表現(xiàn)為在尋峰過程中丟失弱峰或出現(xiàn)假峰、峰凈面積計算的誤差加大等等。 為了減少漲落的影響，有必要借助某些數(shù)學的手段對實驗測得的能譜數(shù)據(jù)進行初步的處理，從離散的能譜中消除統(tǒng)計漲落，使之光滑，即能譜的數(shù)據(jù)平滑。譜數(shù)據(jù)的平滑就是以一定的數(shù)學