全相位数字间断信号处理
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摘要
本论文主要探讨了全相位方法对间断信号的处理,其中包括:对连续信号的全相位截断;对本身存在间断点的信号的全相位处理;还有对于有限变换域滤波器中边界引起的间断的全相位处理及对频率特性有间断点的FIR滤波器全相位设计和应用。
首先,提出考虑了所有截断情况的全相位截断,这种截断方式造成信号的截断误差很小。文中对经过全相位截断后的信号进行频谱分析,称为全相位频谱分析,实验证明,全相位频谱分析具有良好的频谱分析性能,可以明显减小泄漏,并且可以分析出来幅值很小的信号的谱线,本文还对全相位频谱分析泄漏小的原因进行了深入剖析。另外,提出全相位DFT频率、幅值、相位精确校正法,校正精度很高。文中还对间断函数进行了全相位最小二乘方的逼近,逼近误差小于传统方法。
其次,推导出全相位FIR滤波器的两种频率采样设计方法,全相位滤波器设计方法尤其适用于具有间断频率特性的滤波器的逼近,不仅能保证采样点上的期望响应,还改善了采样点之间的性能。本论文对全相位FIR滤波器进行了仔细研究,设计出四种全相位线性相位FIR滤波器,进一步完善了全相位理论。另外,两种全相位滤波器设计方法相结合通过移位补偿解决了传统频率采样法不能精确控制截止频率的难题,文中给出实例验证。并且尝试了用全相位FRM方法设计过渡带陡峭的滤波器,可以很大程度的节约计算量。
第三,本文提出全相位半带滤波器新的设计方法,可以根据频率采样点数选择使用全相位两种频率采样法之一设计无过渡点的,频率响应无过冲的,通阻带纹波小的,过渡带陡峭的半带滤波器,此半带滤波器可直接进行谱分解得到QMF组的信号重构误差仅为5×10~(-13),传统方法为5×10~(-4)。
最后,用全相位分析方法对随机信号的功率谱估计及全相位有色噪声进行了研究。分别用Welch功率谱估计方法和全相位功率谱估计方法对有色噪声进行分析,发现全相位功率谱估计可以有效的检测出混在有色噪声中的小信号,在信息隐藏中有很大应用价值。
This dissertation deals with processing discontinuous signal by the method of All Phase including All Phase truncating of continuous signal, All Phase processing to the signal with discontinues point, All Phase processing to the truncation caused by the boundary of finite frequency filter, and All Phase designing of the filter with discontinuous frequency characteristic. First, the paper introduces All Phase truncation considering all kinds of truncation situations, which can make the truncation error less. The signal is analyzed through All Phase spectrum analysis. It can be verified by experimental results that All Phase spectrum analysis has good characters which can reduce leakage and distinguish the spectrum of a small signal beside a big signal, and the reason of which is interpreted deeply. And All phase DFT frequency amplitude phase correction is put forward which has higher precision. All Phase least square approximation to the discontinuous signal is also introduced with less error than the traditional method.
Secondly, two kinds of All Phase frequency sampling method are deduced, which are especially suitable for designing filters with discontinuous frequency characteristic. This method not only can assure the expect response of sampling points, but also improve the character between sampling points. The dissertation researches All Phase FIR filter deeply and four kinds of All Phase linear filters are designed which make the theory of All Phase more integrity. Additionally, the problem of controlling cut-off frequency can be resolved through the combination of the two kinds of All Phase sampling method and through the shift and compensation. Some examples are given in the paper. Some researches were also accomplished on the designing of sharp-pass band filters by the All phase FRM method, which requairs few arithmetic operations.
Thirdly, this paper proposes a new design method of All Phase half band filte with no transition point, small overshooting, small pass and stop band ripple, sharp transition band. It can be implemented spectrum factorization to get QMF, which can get perfect reconstruction signal with error is only 5×10~(-13), while traditional error is 5×10~(-4).
Finally, the All Phase power spetrum estimation and All Phase color noise are researched. The color noise is analyzed by using Welch method and All Phase power spectrum method seperatly, of which the test result shows that our method can detect
首先,提出考虑了所有截断情况的全相位截断,这种截断方式造成信号的截断误差很小。文中对经过全相位截断后的信号进行频谱分析,称为全相位频谱分析,实验证明,全相位频谱分析具有良好的频谱分析性能,可以明显减小泄漏,并且可以分析出来幅值很小的信号的谱线,本文还对全相位频谱分析泄漏小的原因进行了深入剖析。另外,提出全相位DFT频率、幅值、相位精确校正法,校正精度很高。文中还对间断函数进行了全相位最小二乘方的逼近,逼近误差小于传统方法。
其次,推导出全相位FIR滤波器的两种频率采样设计方法,全相位滤波器设计方法尤其适用于具有间断频率特性的滤波器的逼近,不仅能保证采样点上的期望响应,还改善了采样点之间的性能。本论文对全相位FIR滤波器进行了仔细研究,设计出四种全相位线性相位FIR滤波器,进一步完善了全相位理论。另外,两种全相位滤波器设计方法相结合通过移位补偿解决了传统频率采样法不能精确控制截止频率的难题,文中给出实例验证。并且尝试了用全相位FRM方法设计过渡带陡峭的滤波器,可以很大程度的节约计算量。
第三,本文提出全相位半带滤波器新的设计方法,可以根据频率采样点数选择使用全相位两种频率采样法之一设计无过渡点的,频率响应无过冲的,通阻带纹波小的,过渡带陡峭的半带滤波器,此半带滤波器可直接进行谱分解得到QMF组的信号重构误差仅为5×10~(-13),传统方法为5×10~(-4)。
最后,用全相位分析方法对随机信号的功率谱估计及全相位有色噪声进行了研究。分别用Welch功率谱估计方法和全相位功率谱估计方法对有色噪声进行分析,发现全相位功率谱估计可以有效的检测出混在有色噪声中的小信号,在信息隐藏中有很大应用价值。
This dissertation deals with processing discontinuous signal by the method of All Phase including All Phase truncating of continuous signal, All Phase processing to the signal with discontinues point, All Phase processing to the truncation caused by the boundary of finite frequency filter, and All Phase designing of the filter with discontinuous frequency characteristic. First, the paper introduces All Phase truncation considering all kinds of truncation situations, which can make the truncation error less. The signal is analyzed through All Phase spectrum analysis. It can be verified by experimental results that All Phase spectrum analysis has good characters which can reduce leakage and distinguish the spectrum of a small signal beside a big signal, and the reason of which is interpreted deeply. And All phase DFT frequency amplitude phase correction is put forward which has higher precision. All Phase least square approximation to the discontinuous signal is also introduced with less error than the traditional method.
Secondly, two kinds of All Phase frequency sampling method are deduced, which are especially suitable for designing filters with discontinuous frequency characteristic. This method not only can assure the expect response of sampling points, but also improve the character between sampling points. The dissertation researches All Phase FIR filter deeply and four kinds of All Phase linear filters are designed which make the theory of All Phase more integrity. Additionally, the problem of controlling cut-off frequency can be resolved through the combination of the two kinds of All Phase sampling method and through the shift and compensation. Some examples are given in the paper. Some researches were also accomplished on the designing of sharp-pass band filters by the All phase FRM method, which requairs few arithmetic operations.
Thirdly, this paper proposes a new design method of All Phase half band filte with no transition point, small overshooting, small pass and stop band ripple, sharp transition band. It can be implemented spectrum factorization to get QMF, which can get perfect reconstruction signal with error is only 5×10~(-13), while traditional error is 5×10~(-4).
Finally, the All Phase power spetrum estimation and All Phase color noise are researched. The color noise is analyzed by using Welch method and All Phase power spectrum method seperatly, of which the test result shows that our method can detect
引文
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