本文關(guān)鍵詞： 信號(hào)去噪 小波模極大值 小波系數(shù) 重構(gòu)信號(hào) Blackman窗函數(shù)　出處：《河南理工大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：信號(hào)去噪算法的研究一直是信號(hào)處理領(lǐng)域的難點(diǎn)和熱點(diǎn),長期以來人們常用傅里葉變換分析處理信號(hào),而且取得了較好的效果。然而傅里葉變換是一種全域的整體變換,只能顯示一個(gè)域內(nèi)的信號(hào)特性,對(duì)于分析非平穩(wěn)信號(hào)有很大的局限性。小波變換是繼傅里葉變換迅猛發(fā)展起來的一種分析非平穩(wěn)信號(hào)的強(qiáng)有力工具,具有在時(shí)頻域內(nèi)同時(shí)表征信號(hào)局部化特性和多分辨分析的能力,不但在信號(hào)處理領(lǐng)域有極好的發(fā)展前景,而且與科學(xué)界其他領(lǐng)域相互融合、相互滲透形成一種新生力量。本文主要研究了利用小波模極大值重構(gòu)小波系數(shù)實(shí)現(xiàn)信號(hào)重構(gòu)的算法,在分析了模極大值直接重構(gòu)算法和交替投影算法之后,總結(jié)了兩種經(jīng)典算法存在的優(yōu)缺點(diǎn),發(fā)現(xiàn)模極大值直接重構(gòu)算法雖然簡單快捷,但重構(gòu)后的信號(hào)信息不完整,有較大失真;而交替投影算法雖然能達(dá)到很高的重構(gòu)精度,但計(jì)算量太大,運(yùn)算速度太慢,實(shí)用性不強(qiáng)。如何找到一種由信號(hào)的模極大值重構(gòu)信號(hào)的合理有效、方便快捷的算法,就是本文要解決的問題。考慮到Blackman窗函數(shù)有主瓣寬且幅值大,旁瓣寬度小以及衰減速度快的特性,本文以Blackman窗函數(shù)作為插值函數(shù),并在此基礎(chǔ)上,構(gòu)造了一種基于Blackman窗函數(shù)插值的小波模極大值去噪算法,該算法利用插值技術(shù)填補(bǔ)了各尺度上那些不是模極大值點(diǎn)的值,從而得到重構(gòu)信號(hào)。最后采用blocks和bumps信號(hào)從重構(gòu)精度、信噪比增益和運(yùn)算時(shí)間上對(duì)本文構(gòu)造的算法與兩種經(jīng)典算法進(jìn)行了仿真比較,結(jié)果表明Blackman窗函數(shù)插值的去噪算法有較好的去噪效果,信號(hào)信息完整,計(jì)算量小,且失真小,收斂速度快,實(shí)用性較強(qiáng)。
[Abstract]:The research of signal denoising algorithm has been a difficult and hot spot in the field of signal processing. For a long time, people often use Fourier transform to analyze and process signals. But Fourier transform is a global transform, which can only show the signal characteristics in one domain. Wavelet transform is a powerful tool for analyzing non-stationary signals after Fourier transform developed rapidly. It has the ability of simultaneously characterizing signal localization and multi-resolution analysis in time-frequency domain. It not only has an excellent prospect in the field of signal processing, but also merges with other scientific fields. Mutual penetration forms a new force. This paper mainly studies the algorithm of signal reconstruction using wavelet modulus maximum reconstruction coefficients, after analyzing the modulus maximum direct reconstruction algorithm and alternating projection algorithm. The advantages and disadvantages of the two classical algorithms are summarized. It is found that the modulus maximum direct reconstruction algorithm is simple and fast, but the reconstructed signal information is incomplete and has large distortion. Although the alternating projection algorithm can achieve a high reconstruction accuracy, but the calculation is too large, the operation speed is too slow, the practicability is not strong. How to find a signal reconstruction signal from the modulus maximum reasonable and effective. The convenient and fast algorithm is the problem to be solved in this paper, considering that the Blackman window function has the characteristics of large amplitude and width of the main lobe, small width of the sidelobe and fast attenuation speed. In this paper, the Blackman window function is used as the interpolation function, and on this basis, a wavelet modulus maximum denoising algorithm based on the Blackman window function interpolation is constructed. The algorithm makes use of interpolation technique to fill up the values which are not modulus maximum points on each scale, and obtains the reconstructed signal. Finally, the blocks and bumps signals are used to reconstruct the precision. Compared with two classical algorithms in SNR gain and computation time, the results show that the denoising algorithm based on Blackman window function interpolation has better denoising effect. The signal information is complete, the computation is small, the distortion is small, the convergence speed is fast, and the practicability is strong.
【學(xué)位授予單位】：河南理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.4

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