运用m序列测量房间脉冲响应的技术研究
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摘要
m序列是一种伪随机序列,在通信、雷达、密码学等领域都有应用。近几十年来,运用m序列测量房间声学系统脉冲响应的技术研究也受到了人们的关注。m序列法测量技术有两大优点,其一是较强的抗噪声性能,其二是运算速度快、效率高。论文针对m序列法在应用过程中遇到的一些问题进行了深入研究,具体工作如下:
1.针对测量过程中非线性对测量的影响进行了研究。分析了非线性为Hammerstein模型时,运用m序列法测量线性脉冲响应的失真情况,针对非线性为偶数次时,常规的m序列法测量技术不能获得线性脉冲响应的信息的缺陷进行了改进;提出了运用0、1电平的m序列激励Hammerstein系统的思想,并在m序列电平为1、-1时的FMT变换基础上,加以改进得到偶数幂次非线性干扰时测量线性脉冲响应的快速算法。当非线性较弱时,以Volterra核模型的简化结构为室内声学系统模型,根据此模型,得到了单一非线性作用下m序列法测量脉冲响应的显式表达;分别分析了m序列的长度、幅度以及非线性的阶次等与m序列测量法抗非线性失真性能的关系。
2.为了改善m序列法的抗失真性能提高失真抑制度,在传统的截断法思想基础上,首次提出了一种确定截断点的方法。该方法利用了二次非线性误差与m序列三阶相关函数之间的关系,只需要计算出m序列三阶相关函数较小延时时的峰值位置,就可以确定截断点。对于不同本原多项式下的m序列,其三项式对位置是不相同的。为了尽可能减小非线性对测量的影响,应该有针对性地选用m序列。提出选择那些k1较小时对应的k 2较大的m序列作为测试信号,则幅度较大的非线性尖脉冲只会在远离线性脉冲响应位置出现,从而有效地减小非线性对测量的影响。
3.针对Gold序列的长度是2n-1,不能直接运用FFT变换计算两序列间的互相关,阐述了一种快速相关算法,并对其实现流程进行了改良。
4.针对m序列的最大联通集内序列数量少,不能满足多通道同步测量的需求,提出了运用平衡Gold序列作为测试信号的测量方法。理论分析及仿真实验证明了方法的可行性。
A maximal length sequence (m-sequence) is a pseudorandom binary sequence which has been widely exploited in areas of communication, radar and cryptography. During the last decades special attention also has been devoted to the study of technologies of using m-sequences to measure home acoustic impulse responses. There are two advantages in m-sequence technique, the one is its high noise immunity, and the other one is its quick computation speed and high efficiency. This dissertation has lucubrated many problems been met during the usage of this method. The key contributions of this dissertation are:
1. The effects due to nonlinearity on m-sequence measurement are studied. We analyze the distortion in m-sequence measurement caused by nonlinearity with a Hammerstein structure. Because information of linear impulse response cannot be obtained by classical m-sequence method for an even order nonlinear Hammerstein system, an improved method has been presented. We propose an idea of using m-sequence with binary values 0 and 1 to stimulate a Hammerstein model system and acquired a fast improvement algorithm based on FMT of m-sequence with elements of 1 and -1 levels for measuring the linear impulse response. Home acoustic system with weak nonlinearity can be modeled by a simplified Volterra kernel model.
According to this model, expressions of distorted linear impulse response corrupted by different order nonlinearity have been concluded. Factors which influence distortion immunity in m-sequence technique, for example, the period and amplitude of m-sequences and orders of nonlinearity, are investigated in detail, and many important results are also obtained.
2. In order to improve distortion immunity, a method based on conventional truncation idea is proposed firstly, by which a truncation point can be determined accurately. Based on the relationship between second-order nonlinearity errors and third-order cross-correlation function of m-sequences, the truncation point can be simply obtained by choosing the peak value position with the smallest time lag of m-sequence’s third-order cross-correlation function. The trinomial pairs of m-sequence with different original polynomial are different. To reduce the effect of nonlinearities selection of particular m-sequence is an important consideration. An idea is proposed that those m-sequences of which k 2 is big enough while k1 is smaller should be chosen so that those bigger 2-order nonlinearity impulses are far from linear impulse response and their effect on measurement can be decreased.
3. As the length of Gold sequence is 2n-1, which is not directly suitable for FFT-based algorithm, a fast cross-correlation algorithm is expounded and improved.
4. As few numbers in a preferred m-sequence maximal set cannot meet the need of simultaneous impulse response measurement, a kind of measurement exploiting balanced Gold sequences as test stimulus is proposed. Theoretic analysis and computer simulation results demonstrate the feasibility of the proposed method.
1.针对测量过程中非线性对测量的影响进行了研究。分析了非线性为Hammerstein模型时,运用m序列法测量线性脉冲响应的失真情况,针对非线性为偶数次时,常规的m序列法测量技术不能获得线性脉冲响应的信息的缺陷进行了改进;提出了运用0、1电平的m序列激励Hammerstein系统的思想,并在m序列电平为1、-1时的FMT变换基础上,加以改进得到偶数幂次非线性干扰时测量线性脉冲响应的快速算法。当非线性较弱时,以Volterra核模型的简化结构为室内声学系统模型,根据此模型,得到了单一非线性作用下m序列法测量脉冲响应的显式表达;分别分析了m序列的长度、幅度以及非线性的阶次等与m序列测量法抗非线性失真性能的关系。
2.为了改善m序列法的抗失真性能提高失真抑制度,在传统的截断法思想基础上,首次提出了一种确定截断点的方法。该方法利用了二次非线性误差与m序列三阶相关函数之间的关系,只需要计算出m序列三阶相关函数较小延时时的峰值位置,就可以确定截断点。对于不同本原多项式下的m序列,其三项式对位置是不相同的。为了尽可能减小非线性对测量的影响,应该有针对性地选用m序列。提出选择那些k1较小时对应的k 2较大的m序列作为测试信号,则幅度较大的非线性尖脉冲只会在远离线性脉冲响应位置出现,从而有效地减小非线性对测量的影响。
3.针对Gold序列的长度是2n-1,不能直接运用FFT变换计算两序列间的互相关,阐述了一种快速相关算法,并对其实现流程进行了改良。
4.针对m序列的最大联通集内序列数量少,不能满足多通道同步测量的需求,提出了运用平衡Gold序列作为测试信号的测量方法。理论分析及仿真实验证明了方法的可行性。
A maximal length sequence (m-sequence) is a pseudorandom binary sequence which has been widely exploited in areas of communication, radar and cryptography. During the last decades special attention also has been devoted to the study of technologies of using m-sequences to measure home acoustic impulse responses. There are two advantages in m-sequence technique, the one is its high noise immunity, and the other one is its quick computation speed and high efficiency. This dissertation has lucubrated many problems been met during the usage of this method. The key contributions of this dissertation are:
1. The effects due to nonlinearity on m-sequence measurement are studied. We analyze the distortion in m-sequence measurement caused by nonlinearity with a Hammerstein structure. Because information of linear impulse response cannot be obtained by classical m-sequence method for an even order nonlinear Hammerstein system, an improved method has been presented. We propose an idea of using m-sequence with binary values 0 and 1 to stimulate a Hammerstein model system and acquired a fast improvement algorithm based on FMT of m-sequence with elements of 1 and -1 levels for measuring the linear impulse response. Home acoustic system with weak nonlinearity can be modeled by a simplified Volterra kernel model.
According to this model, expressions of distorted linear impulse response corrupted by different order nonlinearity have been concluded. Factors which influence distortion immunity in m-sequence technique, for example, the period and amplitude of m-sequences and orders of nonlinearity, are investigated in detail, and many important results are also obtained.
2. In order to improve distortion immunity, a method based on conventional truncation idea is proposed firstly, by which a truncation point can be determined accurately. Based on the relationship between second-order nonlinearity errors and third-order cross-correlation function of m-sequences, the truncation point can be simply obtained by choosing the peak value position with the smallest time lag of m-sequence’s third-order cross-correlation function. The trinomial pairs of m-sequence with different original polynomial are different. To reduce the effect of nonlinearities selection of particular m-sequence is an important consideration. An idea is proposed that those m-sequences of which k 2 is big enough while k1 is smaller should be chosen so that those bigger 2-order nonlinearity impulses are far from linear impulse response and their effect on measurement can be decreased.
3. As the length of Gold sequence is 2n-1, which is not directly suitable for FFT-based algorithm, a fast cross-correlation algorithm is expounded and improved.
4. As few numbers in a preferred m-sequence maximal set cannot meet the need of simultaneous impulse response measurement, a kind of measurement exploiting balanced Gold sequences as test stimulus is proposed. Theoretic analysis and computer simulation results demonstrate the feasibility of the proposed method.
引文
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