CN101527698B - Non-stationary interference suppression method based on Hilbert-Huang transformation and adaptive notch - Google Patents

Non-stationary interference suppression method based on Hilbert-Huang transformation and adaptive notch Download PDF

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CN101527698B
CN101527698B CN 200910081419 CN200910081419A CN101527698B CN 101527698 B CN101527698 B CN 101527698B CN 200910081419 CN200910081419 CN 200910081419 CN 200910081419 A CN200910081419 A CN 200910081419A CN 101527698 B CN101527698 B CN 101527698B
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安建平
邵高平
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北京理工大学
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Abstract

The invention provides a non-stationary interference suppression method based on Hilbert-huang transformation and adaptive notch and relates to the interference suppression technical application field of a direct-sequence spread-spectrum communication system. Firstly, sampling results of accepted data are normalized; the Hilbert-Huang transformation is carried out on the normalized data to obtaina Hilbert spectrum; a threshold level for inhibiting noises and a direct-sequence spread spectrum is determined according to the Hilbert spectrum to obtain the non-stationary interference Hilbert spectrum; non-stationary interference instantaneous frequency is worked out according to the non-stationary interference Hilbert spectrum; parameters of an adaptive IIR lattice notch filter are determined by the non-stationary interference instantaneous frequency; the convolution operation between the sampling results and the impulse responses of the adaptive notch filter is carried out to obtain data after the inhibition of the non-stationary interference. The method fully utilizes the good adaptability and the energy accumulation of the Hilbert-Huang transformation and inhibits the non-stationary interference more effectively.

Description

基于希尔伯特黄变换和自适应陷波的非平稳干扰抑制方法 Nonstationary Interference yellow Hilbert transform and the method of suppressing adaptive notch

技术领域 FIELD

[0001] 本发明涉及直扩通信系统抗干扰技术应用领域,具体来说,涉及为进一步提高直扩通信系统的抗干扰能力而采取的一种基于希尔伯特黄变换(HHT)和自适应陷波的非平稳干扰抑制方法。 [0001] The present invention relates to a DSSS communication system application areas anti-jamming technology, particularly, relates to a method to further improve the anti-interference ability of the DSSS system taken Hilbert-Huang Transform (the HHT) and adaptive notch nonstationary interference suppression method.

背景技术 Background technique

[0002] 直扩通信系统是用具有良好相关特性的伪随机序列对数据信息进行频谱扩展,在接收端用精确同步的本地伪随机序列对接收信号进行解扩,由此实现通信任务的通信系统。 [0002] DSSS communication system is a pseudo-random sequence having good correlation properties of spread spectrum information data, the receiver pseudo-random sequence in precise synchronization of the local reception signal despread, thereby enabling communication system tasks . 因其具有信号功率谱密度低、保密性好、抗干扰能力强、抗多径衰落、易于组网等优点, 己经成为一种能够解决通信频谱利用率、通信系统顽存性和通信任务保密性等诸多技术难题的通信核心技术,成为当代通信干扰抑制技术和通信对抗技术的主要发展方向与体制, 在军事通信、测速、导航定位等军事领域以及民用通信领域都得到了广泛的应用。 Because of its low signal power spectral density, good security, anti-jamming, anti-multipath fading, easy networking, etc., has become capable of solving the confidential communication spectrum utilization, communication system and communication tasks survivability and many other technical problems of communications core technology, modern communication interference suppression become the main direction of development and institutional and communications technology against technology in military communications, speed, navigation and other military and civilian areas of the field of communication have been widely used.

[0003] 虽然扩频系统利用扩频增益将干扰信号能量在比数据带宽大得多的频带上进行扩展,且通过数据滤波器可以将大部分干扰信号能量抑制,具有较强的抗干扰能力,但随着直扩通信系统所处电磁环境越来越复杂,除了平稳窄带干扰外,还出现非平稳宽带干扰。 [0003] While the gain of a spread spectrum system using a spread spectrum interference signal energies spread over a bandwidth much greater than the data band, and most interfering signal energy may be suppressed by the filter data, has strong anti-interference ability, However, with the DSSS system more complex electromagnetic environment in which, in addition to stable narrowband interference, but also non-stationary wide-band interference occurs. 以往都是针对窄带平稳干扰进行抑制方法研究,因干扰特性的不同,这些方法对非平稳干扰抑制难以奏效。 Previous studies are carried out smoothly suppression method for narrow-band interference, interference due to the different characteristics of these methods for non-stationary interference suppression to be ineffective. 目前,常用的非平稳干扰抑制方法为采用时频分析方法(如Wigner-Ville 分布),通过分析非平稳干扰的相关特征,将干扰与有用信号区分开来,从而抑制非平稳干扰。 Currently, common non-stationary interference suppression method for an analytical method (e.g., Wigner-Ville distribution) When using frequency, characterized by a correlation analysis of non-stationary interference, interference distinguish the desired signal, thereby suppressing non-stationary interference. 但像Wigner-Ville分布存在交叉项,影响了非平稳干扰的准确检测和有效抑制,且在二维空间处理,算法比较复杂费时。 However, like the presence of Wigner-Ville distribution cross terms, the influence of interference accurately detect non-stationary and effectively inhibited, and the processing in the two-dimensional space, the algorithm is complex and time-consuming.

[0004] 希尔伯特黄变换(HHT)通过信号本身自适应的分解和希尔伯特变换,具有良好的能量聚集性,特别适合非平稳非线性信号的分析和处理,能够提供非平稳信号更有效更准确估计,从而能更有效地抑制非平稳干扰。 [0004] Hilbert-Huang Transform (the HHT) by adaptive signal into itself and Hilbert transform, with good energy aggregation, especially suitable for the analysis of non-stationary and non-linear signal processing, it is possible to provide a more non-stationary signals effective more accurate estimate, which can be more effectively suppress non-stationary interference.

[0005] 对于陷波器,当信号的频率与陷波器的陷波频率一致时就可有效抑制该信号。 [0005] For the trap, when the trap frequency of the same notch frequency signal can be effectively suppressed signal. 所以当陷波滤波器的陷波频率与干扰瞬时频率同步就可有抑制干扰。 Therefore, when the notch filter notch frequency interference and instantaneous frequency synchronization can inhibit interference. 当陷波器的陷波频率变化跟随非平稳干扰的频率变化就可实现非平稳干扰的有效抑制,所以可采用自适应陷波滤波器抑制非平稳干扰。 When the frequency variation notch frequency variation notch filter to follow the non-stationary interference can be achieved effectively suppressing non-stationary interference, it can be an adaptive notch filter to suppress non-stationary interference.

[0006] 将基于HHT的非平稳干扰检测与自适应陷波干扰抑制方法结合,就能有效地抑制非平稳干扰。 [0006] The interference detector nonstationary adaptive notch HHT interference suppression method based on the combination, can effectively suppress non-stationary interference.

发明内容 SUMMARY

[0007] 本发明的目的是为了克服已有技术的不足,为提高直扩通信系统的抗干扰能力, 提供一种基于希尔伯特黄变换和自适应陷波的非平稳干扰抑制方法。 [0007] The object of the present invention is to overcome the deficiencies of the prior art, to improve the anti-interference ability DSSS system, a method based on a non-stationary interference Hilbert-Huang Transform and adaptive notch suppression method.

[0008] 本发明的目的是通过下述技术方案实现的。 [0008] The object of the present invention is achieved by the following technical solutions.

[0009] 一种基于希尔伯特黄变换和自适应陷波的非平稳干扰抑制方法,具体步骤如下: [0009] A method for suppressing non-stationary interference based on Hilbert-Huang Transform and adaptive notch, the following steps:

[0010] 步骤一、为了便于数据的处理,对基带接收数据的采样结果进行归一化。 [0010] Step a, in order to facilitate data processing, the results of the sampling baseband reception data normalized. 实现步骤为: Implementation steps are:

[0011] 首先,求取采样结果r(n)的绝对值最大值Xmax ; [0011] First, the sampling result is obtained the maximum absolute value Xmax r (n); and

[0012] 之后,将采样结果r (η)除以r(n)中绝对值的最大值Xmax : After [0012] the sampling result r (η) divided by r (n) of the maximum absolute value Xmax:

[0013] x(n) = r(n)lxm^ [0013] x (n) = r (n) lxm ^

[0014] 可η)即为采样结果r (n)归一化后的数据。 [0014] to [eta]) is the normalized data sampling result r (n).

[0015] 步骤二、对归一化后的数据,按照希尔伯特黄变换中的经验模式分解(EMD)算法进行分解和希尔伯特变换,得到希尔伯特谱。 [0015] Step two, the data after the normalization according to the Hilbert-Huang Transform empirical mode decomposition (EMD) algorithm decomposition and Hilbert transformation, Hilbert spectrum. 实现步骤为: Implementation steps are:

[0016] Α、根据希尔伯特黄变换的经验模式分解,将经步骤一得到的归一化后的数据马《) 分解为M个内蕴模式函数(IMF)Ci(n)分量之和,即 [0016] [alpha], according to the empirical mode decomposition Hilbert-Huang Transform, the data obtained by the step a horse after normalization ") is decomposed into M intrinsic mode function (IMF) Ci (n) the sum of components , which is

M M

[0017] x(n) = ^Ci(n) + rM(n) [0017] x (n) = ^ Ci (n) + rM (n)

i=l i = l

[0018] 其中,ι·Μ(η)为分解后剩余分量,M为分解得到的内蕴模式函数的个数,M的值根据对ι·Μ(η)的大小要求来确定。 [0018] wherein the number ι · Μ (η) after decomposing the residual component, M is decomposed intrinsic mode function, the value of M is determined according to the size requirements ι · Μ (η) of.

[0019] B、对每一个内蕴模式函数分量进行希尔伯特变换,得到相应的解析信号,将所得 [0019] B, for each of the components intrinsic mode function Hilbert transform, the corresponding analytic signal, the resulting

M M

到的M个解析信号带入只《) = 中,表示为 To the M analytic signal only into ") = medium, expressed as

[0020] [0020]

Figure CN101527698BD00051

[0021 ] [0021]

Figure CN101527698BD00052

[0022] [0022]

Figure CN101527698BD00053

[0023] 其中,Htci (η)]为Ci(Ii)的希尔伯特变换,a, (η)为Ci(Ii)解析信号的瞬时幅度, fi(n) ^ci(Ii)的瞬时频率,θ“η) ^ci(Ii)的瞬时相位。Ts为采样间隔,i为内蕴模式函数分量的序号,即i = 1〜M ;b为采样点序号,b = 1〜η ;n为第η个采样点。 [0023] wherein, Htci (η)] is Ci (Ii) of the Hilbert transform, a, (η) is the instantaneous amplitude Ci (Ii) of the analytical signal, fi (n) ^ ci (Ii) of the instantaneous frequency , θ "η) ^ ci (Ii) is the instantaneous phase .Ts i.e. i = 1~M sampling interval, i is the serial number of intrinsic mode function component,; b = 1~η b is the number of sampling points,; n is η of sampling points.

[0024] C、将珥《)表示成时间η、瞬时频率0、幅值〜(1!)的三维谱图,即希尔伯特谱Η( ω, η): ! [0024] C, the Er ") is represented as [eta] time, the instantaneous frequency of 0, the amplitude ~ (1) dimensional spectrum, i.e., spectrum Hilbert Η (ω, η):

M M

[0025] [0025]

Figure CN101527698BD00054

[0026] 其中,1^为开关因子,当ω = Oi时,bi = l,否则bi = 0。 [0026] wherein 1 ^ is the switching factor, as when ω = Oi, bi = l, or bi = 0. M代表内蕴模式函数分量的个数,i为内蕴模式函数分量的序号,即i = 1〜M。 M represents the number of intrinsic mode function component, i is the serial number of intrinsic mode function component, i.e., i = 1~M.

[0027] 步骤三、根据得到的希尔伯特谱确定抑制噪声和直扩信号谱的门限电平,将高于门限电平的谱保留,将低于门限电平的谱清零,得到非平稳干扰的希尔伯特谱。 [0027] Step three, according to the obtained spectra determined Hilbert inhibition gate signal DS and noise spectrum threshold level, the threshold level is higher than the reserved spectrum, below the threshold level of the spectrum is cleared to give non-stationary interference Hilbert spectrum. 实现步骤为: Implementation steps are:

[0028]( 一)通过连续平均抑制(CME)算法,确定抑制噪声和直扩信号谱的门限电平,即 [0028] (a) by continuous average inhibition (CME) algorithm, and is determined to suppress gates noise spectrum DSSS signal threshold level, i.e.

[0029] ①将所有希尔伯特谱线作为初始谱线,并把它们放入集合I,得到所有希尔伯特谱线值的累加和,即Am。 [0029] ① all Hilbert spectrum as the initial spectrum, and put them into a collection I, to give all Hilbert spectral values ​​and accumulated, i.e., Am. 将Am除以希尔伯特谱线总数,求出希尔伯特谱线的均值Ε[ |Η(ω, η) I]: Am divided by the total number of lines Hilbert, Hilbert obtain mean spectrum Ε [| Η (ω, η) I]:

Figure CN101527698BD00061

[0031] Ε[|Η(ω,η) |] =Am/(NXM) [0031] Ε [| Η (ω, η) |] = Am / (NXM)

[0032] 其中,M为内蕴模式函数分量的个数,N为采样点数。 [0032] wherein, M being the number of intrinsic mode function component, N is the number of sampling points.

[0033] ②根据希尔伯特谱线的均值E [ IH (ω,n) I ],采用下式估计希尔伯特谱线的标准差σ [|Η(ω,η)]: [0033] ② The Hilbert spectrum mean E [IH (ω, n) I], using the standard deviation estimated by Hilbert spectrum σ [| Η (ω, η)]:

Figure CN101527698BD00062

[0035] 根据得到的标准差ο [|Η(ω,η) |],确定出门限η [0035] The difference obtained by standard ο [| Η (ω, η) |], [eta] is determined to go out limit

[0036] η = Ε[|Η(ω,η) |]+3 σ [|Η(ω,η) |] [0036] η = Ε [| Η (ω, η) |] +3 σ [| Η (ω, η) |]

[0037] ③将集合I中的希尔伯特谱线的模与门限η进行比较,大于该门限的希尔伯特谱线被认为是被干扰的希尔伯特谱线,从集合I中去除。 [0037] ③ The Hilbert spectrum I set in a mold with a threshold η is compared, is greater than the threshold are considered Hilbert lines interfered Hilbert lines, from the set I removed. 集合I被更新。 I is a collection of updates.

[0038] ④更新集合I后,更新Am和E [ IH (ω,n) I ],之后重复②和③,直到没有希尔伯特谱线的模大于门限η为止。 [0038] ④ updated collection I, and updating Am E [IH (ω, n) I], and after repeating ② ③, until the mold is not Hilbert spectrum far greater than the threshold η. 最终得到没有希尔伯特谱线的模大于门限η的集合Γ。 No Hilbert finally obtained spectrum mold set greater than a threshold η Γ.

[0039] ⑤以集合I'中的希尔伯特谱线,估计最终的门限"=外|「尽I巧Ί ^L &Κ。 [0039] ⑤ with the collection I 'in Hilbert spectrum, estimated that the final threshold "= outside |" I do clever Ί ^ L & Κ.

[0040] (二)将高于最终门限η电平的希尔伯特谱保留,将低于门限n电平的希尔伯特谱清零,从而得到非平稳干扰的希尔伯特谱。 [0040] (ii) will be higher than the final level of the threshold η Hilbert spectrum reserved, will be below the threshold level of the n Hilbert spectrum is cleared, whereby the non-stationary interference Hilbert spectrum.

[0041] 步骤四、依照非平稳干扰的希尔伯特谱,求取出非平稳干扰的瞬时频率,由该瞬时频率决定自适应无限冲激响应(IIR)格型陷波器的参数,由此得到自适应陷波器冲激响应。 [0041] Step 4 in accordance with the Hilbert nonstationary interference spectrum, the instantaneous frequency seeking remove interfering non-stationary, the instantaneous frequency is determined by parameters adaptive infinite impulse response (IIR) lattice notch filter, thereby obtained adaptive notch filter impulse response.

[0042] 步骤五、将步骤一中的采样结果与自适应陷波器冲激响应进行卷积运算,得到抑制非平稳干扰后的数据,将该数据和同步的PN码序列进行相关运算,完成接收数据的解扩。 [0042] Step five, the result of the sampling step one adaptive notch filter impulse response convolution operation is performed to obtain data of suppressing non-stationary interference, the PN code sequence synchronized data and performs a correlation operation is completed Solutions of the reception data expander.

[0043] 有益效果 [0043] beneficial effects

[0044] 本发明方法利用希尔伯特黄变换估计非平稳干扰的瞬时频率,比用采用Wigner-Ville分布估计更准确,效率更高。 [0044] The method of the present invention utilizes the Hilbert-Huang Transform instantaneous frequency estimated non-stationary interference estimate is more accurate than using the Wigner-Ville distribution with higher efficiency. 对相关器输出信干噪比改善因子而言,采用基于本发明方法的格型UR滤波器,能够获得比采用Wigner-Ville分布方法的五系数HR滤波器多7dB的改善,具有更好的抑制非平稳干扰的性能。 Of the correlator output SINR improvement factor, the use of UR lattice filter based method of the present invention can be improved more than five HR filter coefficients using Wigner-Ville distribution method of the plurality of 7dB, with better suppression non-stationary interference.

附图说明 BRIEF DESCRIPTION

[0045] 图1为本发明基于希尔伯特黄变换和自适应陷波的非平稳干扰抑制方法的流程图; [0045] Figure 1 is a flowchart of the Hilbert-Huang Transform and adaptive notch nonstationary interference suppression method based on;

[0046] 图2为本发明实施例中所用的采样结果r(n)的频谱; [0046] FIG. 2 spectral sampling result r (n) used in the examples of embodiment of the invention;

[0047] 图3为采用本发明实施例中估计非平稳干扰瞬时频率与用Wigner-Ville分布方法估计的比较示意图; [0047] Figure 3 estimated instantaneous frequency interference and non-stationary with Wigner-Ville distribution method of estimating a schematic comparison of the present invention;

[0048] 图4为本发明实施例中所采用的自适应无限冲激响应(IIR)格型陷波器的结构图; [0048] FIG 4 a configuration diagram of an infinite impulse response (IIR) lattice adaptive notch filter embodiment employed in the embodiment of the present invention;

[0049] 图5为本发明实施例中基于希尔伯特黄变换和自适应无限冲激响应(IIR)格型陷波器的非平稳干扰抑制方法框图; [0049] FIG. 5 a block diagram of a method embodiment Hilbert transform and adaptive Infinite Impulse yellow Nonstationary Interference response (IIR) lattice notch filter to suppress the present invention;

[0050] 图6为本发明实施例中采样结果r (η)经过算法处理抑制非平稳干扰后所得数据吖…的频谱。 Spectral data obtained after the sampling result embodiment r (η) after the arithmetic processing to suppress non-stationary interference Embodiment [0050] FIG. 6 of the present invention, acridine ....

具体实施方式 Detailed ways

[0051] 为使本发明的目的、技术方案和优点更加清楚明白,下面通过结合具体实施例和附图,对本发明作进一步详细说明。 [0051] To make the objectives, technical solutions, and advantages of the present invention will become apparent from the following specific embodiments and in conjunction with the accompanying drawings, the present invention is described in further detail.

[0052] 本发明对基于希尔伯特黄变换和自适应无限冲激响应(IIR)格型陷波器的非平稳干扰抑制过程在桌面计算机平台上实现。 [0052] The present invention achieves the inhibition of Hilbert transform and adaptive Infinite Impulse yellow Nonstationary Interference response (IIR) lattice notch filter process on the desktop computer internet. 在具体实施时,非平稳干扰抑制按如图1所示的流程进行,最终给出抑制干扰后的数据。 In a specific embodiment, for non-stationary interference suppression according to the process shown in Figure 1, the final data is given interference suppression. 基带接收数据的采样频率为fs = 2000Hz,个数N = 1500,信息码长度为lOObits,扩频码序列周期为L = 15。 Baseband reception data sampling frequency is fs = 2000Hz, number of N = 1500, code length information lOObits, spreading code sequence period is L = 15. 干信比JSR = 10dB,信噪比SNR = 5dB,所得数据的频谱如图2所示,中间幅度较高就是非平稳干扰的频谱。 Dry signal ratio JSR = 10dB, signal to noise ratio SNR = 5dB, spectral data obtained is shown in Figure 2, the higher is the amplitude spectrum of the intermediate non-stationary interference. 采样结果r (η)如表1所示: Sampling result r (η) as shown in Table 1:

[0053] 表1采样结果r (η) [0053] The results in Table 1 samples r (η)

[0054] r(n)= [0054] r (n) =

[6.6009 6.4157 4.6043 2.8640 3.7252 1.5890 -2.9121 -5.7211 -8.5248 -6.2168 -6.4400 -7.3346 -3.5176 -4.6545 1.2088 1.1827 4.8304 2.7025 9.7289 6.3441 8.3165 5.7965 7.7253 3.4604 1.6281 -3.6675 -5.1425 -9.8763 -8.6077 -12.0674 -7.5318 -5.7143 -4.3168 1.8203 -1.1740 6.6820 6.5412 4.8397 8.9164 5.9087 4.6300 6.5819 3.6268 -3.4207 -2.3384 -7.2667 -8.7919 -10.6744 -9.1430 -5.2549 -4.3033 -1.7824 -0.4419 4.4467 7.1761 10.0178 7.1495 8.8643 9.3208 6.1655 0.6243 -1.7543 -3.7080 -5.1465 -10.2583 -9.1297 -7.0078 -4.8218 -4.8722 -2.0538 -1.8952 5.3987 4.3015 8.1956 7.1643 6.6400 5.5613 2.0502 -1.9698 -0.9228 -8.0027 -6.4848 -11.5578 -7.7461 -5.1579 -2.5042 1.3633 2.9861 8.1960 7.9960 5.5935 6.5649 6.0398 0.0819 -1.0573 -5.0753 -4.8577 -8.4346 -11.8858 -3.9772 -5.7614 -4.0611 4.4534 5.0245 4.7529 7.2238 9.0395 8.2649 5.1373 [6.6009 6.4157 4.6043 2.8640 3.7252 1.5890 -2.9121 -5.7211 -8.5248 -6.2168 -6.4400 -7.3346 -3.5176 -4.6545 1.2088 1.1827 4.8304 2.7025 9.7289 6.3441 8.3165 5.7965 7.7253 3.4604 1.6281 -3.6675 -5.1425 -9.8763 -8.6077 -7.5318 -5.7143 -4.3168 -12.0674 1.8203 -1.1740 6.6820 6.5412 4.8397 8.9164 5.9087 4.6300 6.5819 3.6268 -3.4207 -2.3384 -7.2667 -8.7919 -9.1430 -5.2549 -4.3033 -1.7824 -0.4419 -10.6744 4.4467 7.1761 10.0178 7.1495 8.8643 9.3208 6.1655 0.6243 -1.7543 -3.7080 -5.1465 -9.1297 -10.2583 - 7.0078 -4.8218 -4.8722 -2.0538 -1.8952 5.3987 4.3015 8.1956 7.1643 6.6400 5.5613 2.0502 -1.9698 -0.9228 -8.0027 -6.4848 -7.7461 -5.1579 -2.5042 -11.5578 1.3633 2.9861 8.1960 7.9960 5.5935 6.5649 6.0398 0.0819 -1.0573 -5.0753 -4.8577 -8.4346 -11.8858 -3.9772 -5.7614 -4.0611 4.4534 5.0245 4.7529 7.2238 9.0395 8.2649 5.1373

6.4575 -0.7380 -3.1079 -9.3065 -8.6466 -9.4891 -6.1520 -4.9375 -1.7703 2.6316 3.9739 9.2903 10.4682 10.5251 11.2707 3.3415 -0.7237 -3.7562 -3.3919 -6.4092 -10.1090 -6.7797 -5.9170 -2.8065 -0.9B32 4.5098 8.7730 10.2356 12.8403 6.4575 -0.7380 -3.1079 -9.3065 -8.6466 -9.4891 -6.1520 -4.9375 -1.7703 2.6316 3.9739 9.2903 10.4682 10.5251 11.2707 3.3415 -0.7237 -3.7562 -3.3919 -6.4092 -10.1090 -6.7797 -5.9170 -2.8065 -0.9B32 4.5098 8.7730 10.2356 12.8403

9.5770 1.6068 4.5510 -5.1991 -6.6846 -8.2162 -9.6765 -8.5111 -8.2203 0.0767 0.5425 4.1779 9.8166 10.1141 7.3952 4.2950 5.2113 -1.8675 -3.3073 -8.9271 -6.5659 -6.7637 -4.7095 -8.8926 3.5180 5.9699 11.1229 7.1151 10.0625 4.1278 5.0031 3.0212 -2.7540 -5.0330 -7.3944 -6.0212 -9.5542 -2.9895 -0.6222 5.7836 10.7380 10.4172 10.4273 6.3742 0.2914 -1.5333 -6.0433 -4.3380 -10.7215 9.5770 1.6068 4.5510 -5.1991 -6.6846 -8.2162 -9.6765 -8.5111 -8.2203 0.0767 0.5425 4.1779 9.8166 10.1141 7.3952 4.2950 5.2113 -1.8675 -3.3073 -8.9271 -6.5659 -6.7637 -4.7095 -8.8926 3.5180 5.9699 11.1229 7.1151 10.0625 4.1278 5.0031 3.0212 -2.7540 -5.0330 - 7.3944 -6.0212 -9.5542 -2.9895 -0.6222 5.7836 10.7380 10.4172 10.4273 6.3742 0.2914 -1.5333 -6.0433 -4.3380 -10.7215

-5.9719 -1.4251 -4.6546 1.7758 7.1056 9.1880 6.2547 5.5959 4.0286 1.5658 -5.9719 -1.4251 -4.6546 1.7758 7.1056 9.1880 6.2547 5.5959 4.0286 1.5658

[0055]-5.2645 -5.4942 -7.8717 -6.3188 -4.6386 1.7282 2.0907 8.8793 7.0380 11.8542 [0055] -5.2645 -5.4942 -7.8717 -6.3188 -4.6386 1.7282 2.0907 8.8793 7.0380 11.8542

6.3846 3.2944 -0.7553 -2.6393 -6.5275 -9.9035 -8.1462 -6.4446 1.3699 3.6649 6.3846 3.2944 -0.7553 -2.6393 -6.5275 -9.9035 -8.1462 -6.4446 1.3699 3.6649

8.1790 11.2138 8.9098 5.8219 3 4841 -1.7887 -3 3481 -8 9178 -7.9481 -9.9880 34841 11.2138 8.9098 5.8219 8.1790 -1.7887 -7.9481 -9.9880 -33481-89178

-2.5317 2.4138 1.1043 6.3454 8.0134 5.2855 5.6490 -2.9447 -3.9557 -7.4354 -2.5317 2.4138 1.1043 6.3454 8.0134 5.2855 5.6490 -2.9447 -3.9557 -7.4354

-10.0128 -8.5548 -7.6379 -2.3598 2.2579 9.1545 6.8847 7.0208 7.1997 -10.0128 -8.5548 -7.6379 -2.3598 2.2579 9.1545 6.8847 7.0208 7.1997

2.0386 -3.7627 -8.9163 -5.7024 -8.3477 -6.2449 1.6488 4.9357 8.5782 11.7298 2.0386 -3.7627 -8.9163 -5.7024 -8.3477 -6.2449 1.6488 4.9357 8.5782 11.7298

5.9339 4.6543 -0.8858 2.2030 -9.7983 -10.4144 -6.2934 -3.4240 2.1432 5.1969 5.9339 4.6543 -0.8858 2.2030 -3.4240 2.1432 -6.2934 5.1969 -9.7983 -10.4144

7.1147 8.7379 7.4178 3.4328 1.4693 -2.3332 -8.2826 -5.6414 -7.1288 -0.6256 7.1147 8.7379 7.4178 3.4328 1.4693 -2.3332 -8.2826 -5.6414 -7.1288 -0.6256

0.9756 7.2370 9.6904 6.5243 5.0929 1.0647 -3.8405 -5.8616 -12.0485 0.9756 7.2370 9.6904 6.5243 5.0929 1.0647 -3.8405 -5.8616 -12.0485

-4.7500 -2.3041 2.4294 5.3687 6.3457 8.9607 5.1692 4.2898 -1.3436 -5.8057 -4.7500 -2.3041 2.4294 5.3687 6.3457 8.9607 5.1692 4.2898 -1.3436 -5.8057

-7.2621 -7.4369 -8.5079 1.2516 3.6825 6.7507 10.3251 7.7195 0.7555 -5.4989 -7.2621 -7.4369 -8.5079 1.2516 3.6825 6.7507 7.7195 0.7555 10.3251 -5.4989

-6.4191 -9.3589 -8.0066 -2.1720 0.1930 3.5088 10.5289 5.3844 5.8331 -6.4191 -9.3589 -8.0066 -2.1720 0.1930 3.5088 5.3844 5.8331 10.5289

-2.5168 -1.6378 -8.3253 -7.2901 -4.4708 -2.6581 6.9683 4.1063 11.5825 8.5334 -2.5168 -1.6378 -8.3253 -7.2901 -4.4708 -2.6581 6.9683 4.1063 11.5825 8.5334

4.0315 -2.7905 -6.9092 -7.9034 -7.5785 -7.6748 -1.3949 4.3577 6.1734 8.4131 4.0315 -2.7905 -6.9092 -7.9034 -7.5785 -7.6748 -1.3949 4.3577 6.1734 8.4131

6.9708 -0.3514 -2.0063 -9.5227 -9.6831 -5.6262 0.3182 2.3239 7.6233 8.0760 6.9708 -0.3514 -2.0063 -9.5227 -9.6831 -5.6262 0.3182 2.3239 7.6233 8.0760

6.9545 4.6972 -3.3728 -6.9300 -9.2574 -74896 -2.6600 2.0981 9.0604 8.7850 6.9545 4.6972 -3.3728 -6.9300 -9.2574 -2.6600 2.0981 9.0604 8.7850 -74 896

6.9629 1.2520 -3.9129 -8.0803 -7.0192 -8.5187 -1.8546 4.9001 6.5947 8.5020 6.9629 1.2520 -3.9129 -8.0803 -7.0192 -8.5187 -1.8546 4.9001 6.5947 8.5020

6.6045 2.4524 -3.5972 -7.0790 -8.9916 -5.5452 -0.5218 5.3088 4.6952 9.1877 6.6045 2.4524 -3.5972 -7.0790 -8.9916 -5.5452 -0.5218 5.3088 4.6952 9.1877

4.7557 1.4555 -6.8688 -10.4818 -10.3330 -4.2539 -0.2833 7.3249 7.9638 6.3072 4.7557 1.4555 -6.8688 -10.4818 -10.3330 -4.2539 -0.2833 7.3249 7.9638 6.3072

3.1718 -1.7004 -3.8602 -7.1633 -7.0914 -0.0312 6.4985 7.0974 7.2969 3.8636 3.1718 -1.7004 -3.8602 -7.1633 -7.0914 -0.0312 6.4985 7.0974 7.2969 3.8636

1.0048 -6.6882 -6.5733 -9.3537 -10.0101 2.8863 3.9409 8.2108 9.3031 5.0825 1.0048 -6.6882 -6.5733 -9.3537 -10.0101 2.8863 3.9409 8.2108 9.3031 5.0825

-4.6011 -7.1993 -11.5756 -7.5542 1.0655 6.5479 7.9143 6.6765 2.9669 -4.2672 -11.5756 -4.6011 -7.1993 -7.5542 1.0655 6.5479 7.9143 6.6765 2.9669 -4.2672

-5.2383 -8.0020 -5.8258 1.0467 3.0204 10.3949 9.9025 4.1305 -0.8964 -5.2383 -8.0020 -5.8258 -0.8964 4.1305 9.9025 1.0467 3.0204 10.3949

-4.0080 -9.7394 -3.8233 1.1346 1.2823 8.0977 4.2110 1.7157 2.2144 -4.0080 -9.7394 -3.8233 1.1346 1.2823 8.0977 4.2110 1.7157 2.2144

-8.9776 -7.9130 -6 3 474 0.7942 2 2380 4.5348 6.4828 1.3790 -1.4391 0.7942 -8.9776 -7.9130 -63 474 22 380 4.5348 6.4828 1.3790 -1.4391

-5.5592 -10.6058 -5.5292 2.5193 7.8486 5.6808 8.1400 -0.2581 -5.5454 -9.3906 -10.6058 -5.5592 -5.5292 2.5193 7.8486 5.6808 8.1400 -0.2581 -5.5454 -9.3906

-10.4034 -2.7961 7.5973 7.8439 7.8506 3.4674 -0.9236 -4.9140 -10.4520 -6.9093 -10.4034 7.5973 7.8439 7.8506 3.4674 -2.7961 -0.9236 -4.9140 -6.9093 -10.4520

-0.5279 6.4205 8.7371 2.8396 1.7873 -6.8891 -9.0885 -6.2817 -4.2765 4.5519 -0.5279 6.4205 8.7371 2.8396 1.7873 -6.8891 -9.0885 -6.2817 -4.2765 4.5519

4.8524 10.30% 3.5551 -8.3180 -9.7853 -5.9745 -4.5397 1.5914 5.2384 9.2640 4.8524 -8.3180 -9.7853 -5.9745 3.5551 10.30% 1.5914 5.2384 9.2640 -4.5397

5.1817 -1.6547 -7.3448 -10.0564 -2.9141 -0.8364 8.5488 8.8169 4.2857 -2.1598 -10.0564 -2.9141 -0.8364 -1.6547 -7.3448 5.1817 8.5488 8.8169 4.2857 -2.1598

-6.7699 -11.8449 -7.9049 1.0097 2.8150 4.6003 3.7094 -1.0252 -3.1296 -9.4310 -11.8449 -6.7699 -7.9049 1.0097 2.8150 4.6003 3.7094 -1.0252 -3.1296 -9.4310

-5.2544 -1.2150 3.0524 7.4932 6.0985 -1.0395 -5.9841 -6.6706 -4.4646 -5.2544 -1.2150 3.0524 7.4932 6.0985 -1.0395 -5.9841 -6.6706 -4.4646

-0.6649 8.8108 9.2616 4.7570 -1.3845 -6.6133 -6.9596 -6.9258 1.3972 10.0900 -0.6649 8.8108 -1.3845 -6.6133 -6.9596 -6.9258 9.2616 4.7570 1.3972 10.0900

7.1986 3.1197 -3.1708 -3.5544 -5.7965 -6.0369 0.3356 8.3734 8.3105 4.9496 7.1986 3.1197 -3.1708 -3.5544 -5.7965 -6.0369 0.3356 8.3734 8.3105 4.9496

-4.4925 -5.8210 -7.9077 -3.8454 5.3546 11.5328 7.1869 2.0145 -7.4961 -8.3377 -4.4925 -5.8210 -7.9077 -3.8454 -7.4961 -8.3377 2.0145 7.1869 5.3546 11.5328

-4.9389 0.7035 5.0355 8.7419 3.0576 -6.5208 -5.8380 -9.0395 -2.5450 6.9739 -4.9389 0.7035 5.0355 8.7419 3.0576 -6.5208 -5.8380 -9.0395 -2.5450 6.9739

9.1303 6.6423 3.3602 -4.0170 -3.2392 -3.5952 2.3119 9.1836 8.0126 2.1627 9.1303 6.6423 3.3602 -4.0170 -3.2392 -3.5952 2.3119 9.1836 8.0126 2.1627

-3.0334 -10.4857 -5 1733 1.7875 5.1572 5.8349 5 9452 -4.9841 -8.4454 -6.7499 -3.0334 -10.4857 -51,733 1.7875 5.1572 5.8349 -4.9841 -8.4454 -6.7499 59452

-2.3486 2.6952 7.4788 4.7916 1.5616 -8.9376 -5.8773 -6.3500 1.0116 7.6836 -2.3486 2.6952 7.4788 4.7916 1.5616 -8.9376 -5.8773 -6.3500 1.0116 7.6836

7.3921 -0.2978 -5.2948 -9.3564 -7.0815 -0.3122 9.4130 6.8940 0.3662 -3.9699 7.3921 -0.2978 -5.2948 -9.3564 -7.0815 -0.3122 9.4130 6.8940 0.3662 -3.9699

-11.7623 -3.9804 -0.1300 6.6202 9.3914 -0.9245 -5.2505 -8.1013 -3.7462 3.2331 -11.7623 -3.9804 -0.1300 -0.9245 -5.2505 -8.1013 -3.7462 6.6202 9.3914 3.2331

7.2525 10.7827 0.8945 -5.4982 -8.4081 -3.1671 2.5417 8.7430 10.0121 2.1941 7.2525 10.7827 0.8945 -5.4982 -8.4081 -3.1671 2.5417 8.7430 10.0121 2.1941

-5.9130 -8.9807 -5.5631 1.8192 6.3348 7.1250 0.5075 -7.5702 -8.7659 -2.1648 -5.9130 -8.9807 -5.5631 1.8192 6.3348 7.1250 0.5075 -7.5702 -8.7659 -2.1648

3.5286 6.6901 5.9326 -2.1797 -5.9437 -5.1172 -3.4036 6.5319 10.9282 5.5363 3.5286 6.6901 5.9326 -2.1797 -5.9437 -5.1172 -3.4036 6.5319 10.9282 5.5363

0.8209 -7.1083 -7.8309 2.4661 8.3111 10.1216 -1.1651 -7.4043 -9.8504 -4.2062 0.8209 -7.1083 -7.8309 2.4661 8.3111 10.1216 -1.1651 -7.4043 -9.8504 -4.2062

0.9756 12.4741 5.2639 -3.8850 -9.4607 -5.7729 0.6656 4.7358 10.5522 1.5883 [0056]-6.7604 -8.7692 -3.4466 0.6349 6.2860 4.7427 0.5565 -6.8530 -10.0146 -1.9473 0.9756 12.4741 5.2639 10.5522 -3.8850 -9.4607 -5.7729 0.6656 4.7358 1.5883 [0056] 0.6349 -6.7604 -8.7692 -3.4466 -1.9473 6.2860 4.7427 0.5565 -6.8530 -10.0146

6.9941 10.6770 2.7370 -5.2922 -8.9367 -3.6250 4.2313 11.0028 8.4412 -1.7043 6.9941 10.6770 2.7370 -5.2922 -8.9367 -3.6250 -1.7043 8.4412 4.2313 11.0028

-9.0612 -7.8359 1.5205 8.7840 5.5569 1.3308 -6.5384 -7.1819 -3.4083 5.6529 -9.0612 -7.8359 1.5205 8.7840 5.5569 1.3308 -6.5384 -7.1819 -3.4083 5.6529

10.5822 0.0522 -4.2590 -10.1350 -5.2854 2.7692 9.1226 5.5266 -5.4354 -9.6939 -10.1350 10.5822 0.0522 -4.2590 -5.2854 -5.4354 -9.6939 2.7692 9.1226 5.5266

-5.8733 3.4592 9.2241 4.2325 -3.1077 -6.1330 -6.3566 2.1655 10.5872 6.8722 -5.8733 -3.1077 -6.1330 -6.3566 3.4592 9.2241 4.2325 2.1655 10.5872 6.8722

-2.1399 -6.0318 -8.6209 -2.0131 7.4085 6.2506 0.3558 -8.5256 -8.2889 -1.8253 -2.1399 -6.0318 -8.6209 -2.0131 -8.5256 -8.2889 -1.8253 7.4085 6.2506 0.3558

4.6667 8.9501 -1.7030 -5.0722 -6.6795 -0.5846 6.4287 5.7078 -ϋ.2842 -6.2491 4.6667 8.9501 -1.7030 -5.0722 -6.6795 -0.5846 6.4287 5.7078 -ϋ.2842 -6.2491

-7.6067 -1.3123 5.6383 5.8970 2.7263 -9.0828 -6.8981 0.0168 5.1851 11.2426 -7.6067 -1.3123 -9.0828 -6.8981 5.6383 5.8970 2.7263 0.0168 5.1851 11.2426

-2.1136 -10.8206 -4.9045 -0.8434 9.5390 7.2578 -3.5920 -8.4098 -4.7288 -1.3991 -10.8206 -4.9045 -0.8434 -2.1136 -3.5920 -8.4098 -4.7288 -1.3991 9.5390 7.2578

10.9235 5.9464 -1.9180 -6.7085 -6.6277 3.0723 10.3264 3.3078 -5.6364 -9.3671 10.9235 10.3264 5.9464 -1.9180 -6.7085 -6.6277 3.0723 -9.3671 3.3078 -5.6364

-5.3363 5.3470 8.2025 0.3092 -4.9505 -8.6505 0.1625 2.2958 8.1701 3.0291 -5.3363 -4.9505 -8.6505 5.3470 8.2025 0.3092 0.1625 2.2958 8.1701 3.0291

-7.7139 -7.3689 3.1425 10 3639 10.7804 -1.1927 -6.6937 -4 6271 5.3012 10.6891 -7.7139 -7.3689 -1.1927 -6.6937 3.1425 103,639 -46,271 10.7804 10.6891 5.3012

3.6113 -8.0459 -8.3748 -1.4583 6.6453 5.4941 0.0523 -7.8357 -4.7460 1.9324 3.6113 -8.0459 -8.3748 -1.4583 -7.8357 -4.7460 1.9324 6.6453 5.4941 0.0523

9.9685 3.7600 -4.6794 -3.7821 -2.9866 8.4182 6.1975 0.2506 -8.1656 -3.5612 9.9685 3.7600 8.4182 6.1975 0.2506 -4.6794 -3.7821 -2.9866 -8.1656 -3.5612

5.2344 9.9963 4.9838 -4.2224 -9.3746 -1.5908 11.0522 8.1827 -0.3214 -11.3551 5.2344 9.9963 4.9838 8.1827 -0.3214 -4.2224 -9.3746 -1.5908 11.0522 -11.3551

-5.7090 3.9121 10.9898 4.9617 -5.5324 -8.8929 -0 5175 3.6509 6.0837 -4.1507 10.9898 4.9617 -5.7090 3.9121 -5.5324 6.0837 -4.1507 3.6509 -8.8929 -05,175

-9.6138 -7.0414 1.9005 7.8731 2.8001 -9.9436 -3.8635 0.7394 7.1618 4.4641 -9.6138 -7.0414 -9.9436 -3.8635 1.9005 7.8731 2.8001 0.7394 7.1618 4.4641

-5.5749 -5.0750 -0.2420 8.9311 7.8683 -3.1123 -8.2853 -3.9400 7.0389 -5.5749 -5.0750 -0.2420 -3.1123 -8.2853 -3.9400 7.0389 8.9311 7.8683

10.5480 -1.8533 -6.4040 -4.8988 2.2594 10.1544 3.4588 -7.0473 -4.5673 2.2442 10.5480 -1.8533 -6.4040 -4.8988 -7.0473 -4.5673 2.2442 3.4588 2.2594 10.1544

7.0643 0.4916 -7.9303 -9.0185 -3.6419 10.7374 2.8766 -3.4085 -7.9242 -4.1593 7.0643 0.4916 -7.9303 -9.0185 -3.6419 -3.4085 -7.9242 -4.1593 10.7374 2.8766

12.1280 8.8361 -4.5713 -7.2804 -0.6050 9.6925 7.0833 -4.3910 -6.3754 -4.5601 12.1280 8.8361 9.6925 7.0833 -4.5713 -7.2804 -0.6050 -4.3910 -6.3754 -4.5601

7.4297 5.4252 2.0188 -9.0284 -4.3360 7.6200 7.3229 -4.9436 -12.5728 -2.1145 7.4297 5.4252 2.0188 -9.0284 -4.3360 7.6200 -2.1145 7.3229 -4.9436 -12.5728

5.5637 8.5401 1.7136 -6.6631 -1.2765 4.0440 7.4639 -2.6912 -6.4793 -0.9116 5.5637 8.5401 1.7136 4.0440 7.4639 -6.6631 -1.2765 -2.6912 -6.4793 -0.9116

4.9166 5.3861 0.0391 -8.9916 -1.4048 9.3942 8.6392 -3.3612 -7.6315 1.5476 4.9166 5.3861 9.3942 8.6392 0.0391 -8.9916 -1.4048 -3.3612 -7.6315 1.5476

6.5204 7.7742 -3.2388 -8.1871 -0.8108 8.1526 2.0246 -6.0797 -10.5661 1.4871 6.5204 7.7742 8.1526 2.0246 -3.2388 -8.1871 -0.8108 1.4871 -6.0797 -10.5661

9.2186 5.5257 -4.5861 -8.6051 3.1716 7.0179 1.8792 -11.9659 -5.1960 4.6238 9.2186 5.5257 -4.5861 -8.6051 3.1716 -5.1960 4.6238 7.0179 1.8792 -11.9659

5.7283 -0.7051 -7.5885 -2.3197 5.0188 3.8126 -7.7472 -10.5954 -1.0988 9.0560 5.7283 -0.7051 -7.5885 3.8126 -2.3197 5.0188 -1.0988 9.0560 -7.7472 -10.5954

9.4282 -7.6366 -6.7530 -0.1441 6.2347 6.3293 -7.4898 -8.3773 7.4215 10.9196 9.4282 -7.6366 -6.7530 -0.1441 -7.4898 -8.3773 6.2347 6.3293 7.4215 10.9196

-0.6563 -10.0258 -7.0634 5.2063 4.1700 -4 5047 -9 7464 3.0110 8.9456 -1.0764 -10.0258 -0.6563 -7.0634 5.2063 4.1700 -45047-97464 3.0110 8.9456 -1.0764

-7.6255 -6.1064 4.6809 9.7986 0.2727 -7.1591 -2.0645 8.5966 5.4061 -6.6128 -7.6255 -6.1064 -7.1591 -2.0645 4.6809 9.7986 0.2727 8.5966 5.4061 -6.6128

-5.1519 2.3441 10.1513 -1.4664 -9.9296 -5.3496 7.2690 4.9862 -3.7977 -6.7507 10.1513 -1.4664 -9.9296 -5.1519 2.3441 -5.3496 7.2690 -6.7507 4.9862 -3.7977

2.6090 10.2573 2.7362 -7.6729 -4.8024 6.0514 8.0016 -4.3617 -6.6826 0.6436 2.6090 10.2573 2.7362 -7.6729 -4.8024 -4.3617 -6.6826 0.6436 6.0514 8.0016

7.8355 -1.0709 -5.1317 -8.0022 6.8244 7.8394 -4.5072 -10.2087 3.1987 6.8365 7.8355 -1.0709 -5.1317 -8.0022 6.8244 7.8394 3.1987 6.8365 -4.5072 -10.2087

0.7438 -9.2962 -6.5043 5.7884 6.0699 -3.7352 -9.0128 3.2349 9.1212 -1.8822 0.7438 -9.2962 6.0699 -6.5043 5.7884 -9.0128 3.2349 -3.7352 9.1212 -1.8822

-8.3938 0.9678 8.9096 4.4859 -6.2075 -8.3266 5.0453 7.0283 -2.2446 -5.8717 -8.3938 0.9678 8.9096 4.4859 5.0453 7.0283 -2.2446 -5.8717 -6.2075 -8.3266

0.2013 9.0345 5.1134 -8.0785 -3.6290 5.9578 3.8150 -7.2473 -7.9194 3.0299 0.2013 9.0345 5.1134 5.9578 3.8150 -8.0785 -3.6290 -7.2473 -7.9194 3.0299

8.6715 -1.0583 -8.2097 1.7821 4.7751 -0.0638 -4.8038 -2.5960 11.3067 3.9246 8.6715 -1.0583 -8.2097 -0.0638 -4.8038 -2.5960 1.7821 4.7751 11.3067 3.9246

-6.8596 -2.0046 6.1195 3.8881 -3.5047 -6.5200 3.4206 7.2456 -6 6328 -10.4343 -6.8596 -2.0046 -3.5047 -6.5200 6.1195 3.8881 3.4206 7.2456 -66 328 -10.4343

3.3927 10.2978 -1.9740 -6.1521 0.5990 11.0394 1.5473 -8.5500 -7.0950 4.4865 3.3927 10.2978 -1.9740 -6.1521 -8.5500 -7.0950 4.4865 1.5473 0.5990 11.0394

4.6623 -6.3566 -4.0253 0.4709 4.4924 -1.6990 -2.6410 4.4095 9.1636 -4.4050 4.6623 -6.3566 4.4924 -4.0253 0.4709 -2.6410 4.4095 -1.6990 9.1636 -4.4050

-6.9789 6.8835 8.5786 -1.5593 -8.2582 0.8854 8.1078 0.8912 -6.2454 -6.9789 6.8835 -8.2582 8.5786 -1.5593 0.8912 -6.2454 0.8854 8.1078

2.8480 7.9728 0.8564 -9.7591 -0.6407 6.9144 1.1585 -9.1114 -1.7280 9.7898 2.8480 7.9728 0.8564 6.9144 1.1585 -9.7591 -0.6407 -9.1114 -1.7280 9.7898

0.5248 -8.5238 -3.2486 9.8546 2.1512 -6.6858 -2.4338 10.7942 2.5531 -6.9806 0.5248 -8.5238 -3.2486 9.8546 -2.4338 2.1512 -6.6858 2.5531 -6.9806 10.7942

-2.9785 8.0943 2.6007 -6.8424 -6.1788 6.3062 3.6731 -8.9769 -3.8224 9.4119 -2.9785 8.0943 -6.1788 2.6007 -6.8424 3.6731 -8.9769 6.3062 -3.8224 9.4119

1.9842 -9.2684 -1.2204 9.0432 2.1834 -7.3082 0.0313 7.6846 4.2083 -6.8879 1.9842 -9.2684 -1.2204 9.0432 -6.8879 2.1834 -7.3082 0.0313 7.6846 4.2083

0.2857 7.1488 3.0421 -10.5980 3.5601 6.4524 -1.0719 -10.3281 0.3100 4.2367 [0057]-2.9364 -7.7387 -1.5193 8.0523 -5.4848 -8.3136 8.0048 7.7579 -2.2467 -7.4223 0.2857 7.1488 3.0421 -10.5980 3.5601 -10.3281 6.4524 -1.0719 0.3100 4.2367 [0057] 8.0523 -2.9364 -7.7387 -1.5193 -2.2467 -7.4223 -5.4848 -8.3136 8.0048 7.7579

2.3898 5.5040 -5.8503 -8.7941 7.1427 6.3938 -8.0504 -4.2286 8.4934 4.2524 2.3898 5.5040 7.1427 6.3938 -5.8503 -8.7941 -8.0504 -4.2286 8.4934 4.2524

-9.8446 1.5934 6.2448 0.7170 -9.1071 -1.1677 9.6621 -1.2212 -9.4567 4.4592 -9.8446 1.5934 -1.1677 9.6621 -1.2212 6.2448 -9.1071 0.7170 -9.4567 4.4592

9.7930 -2.5714 -7.9682 7.1492 6.3094 -9.7990 -3.8944 6.6386 1.5734 -9.1559 9.7930 -2.5714 6.3094 -7.9682 7.1492 -3.8944 6.6386 -9.7990 1.5734 -9.1559

-1.9693 10.3395 -2.4379 -11.2701 1.1178 6.9584 -6.3599 -7.4362 6.0417 -11.2701 10.3395 -2.4379 -1.9693 -6.3599 -7.4362 6.0417 1.1178 6.9584

7.0178 -7.7777 -1.4494 8.8202 2.5661 -8.1632 1.4482 10.5969 -1.5509 -7.4751 7.0178 -7.7777 -1.4494 8.8202 -7.4751 2.5661 -8.1632 1.4482 10.5969 -1.5509

8.1284 8.2974 -7.8512 -2.6835 5.4007 -0.4628 -7.7867 -1.0579 5.9117 -0.9166 8.1284 8.2974 5.4007 -7.8512 -2.6835 -0.4628 -7.7867 -1.0579 5.9117 -0.9166

-8.7383 6.4730 7.3480 -7.4227 -4.8497 8.1005 2.2575 -7.1387 4.9974 -8.7383 6.4730 -4.8497 7.3480 -7.4227 2.2575 -7.1387 4.9974 8.1005

10.0538 -3.4447 -5.2959 4.6296 3.6622 -7.6437 1.9839 13.2039 -2.7565 -10.6727 10.0538 -3.4447 -5.2959 4.6296 -2.7565 3.6622 -7.6437 1.9839 13.2039 -10.6727

4.7283 4.8029 -9.4267 -5.1429 8.0628 0.0683 -10.3406 2.3855 7.1269 -8.8245 4.7283 4.8029 -9.4267 -5.1429 8.0628 0.0683 2.3855 7.1269 -8.8245 -10.3406

-3.8839 4.3120 0.5540 -6.5506 1.9608 8.0530 -5.8713 -6.2690 8.0448 4.1430 -3.8839 4.3120 -5.8713 -6.2690 0.5540 -6.5506 1.9608 8.0530 8.0448 4.1430

-12.0511 -4.2331 5.5976 -5.5837 -6.8598 9.1456 0.8963 -8.8348 1.7866 10.1223 -12.0511 -4.2331 -5.5837 -6.8598 5.5976 -8.8348 1.7866 9.1456 0.8963 10.1223

-6.0130 -6.5518 9.2246 -2.9344 -10.1999 3.6522 8.7256 -5.8725 -4.9227 7.6548 -6.0130 -6.5518 9.2246 -2.9344 8.7256 -5.8725 3.6522 -4.9227 7.6548 -10.1999

0.6535 -7.9786 4.4334 7.8801 -8.6174 -4.5211 7.9545 -4.3546 -9.2172 5.5691 0.6535 -7.9786 4.4334 -8.6174 7.8801 -9.2172 5.5691 -4.5211 7.9545 -4.3546

7.1747 -8.0327 0.3984 4.7100 -0.9968 -7.7870 10.9118 2.5527 -11.1381 2.7633 7.1747 -8.0327 0.3984 -7.7870 4.7100 -0.9968 2.7633 10.9118 2.5527 -11.1381

7.9501 -8.9759 -2.7860 8.7441 -0.2753 -8.0732 7.0108 7.1376 -10.0321 1.0147 7.9501 -8.9759 -2.7860 8.7441 -0.2753 1.0147 -8.0732 7.0108 7.1376 -10.0321

8.2495 -3.5758 -4.6487 6.4147 0.4380 -7.8627 4.9370 4.5576 -9.1727 1.4993 8.2495 -3.5758 -4.6487 6.4147 -9.1727 0.4380 -7.8627 4.9370 4.5576 1.4993

4.2623 -6.4757 -4.2793 7.1267 -3.3641 -6.6913 3.8110 4.7204 -5.0493 0.6936 4.2623 -6.4757 -4.2793 7.1267 -3.3641 4.7204 -5.0493 0.6936 -6.6913 3.8110

8.8144 -6.3843 -2.9382 11.1899 -2.5501 -7.4117 5 7313 2.6582 -7.5274 2.5724 8.8144 11.1899 -6.3843 -2.9382 -2.5501 -7.4117 -7.5274 2.5724 2.6582 57313

5.6066 -7.6553 -4.7531 9.7853 -5.1237 -5.4970 9.8261 0.3647 -6.2756 5.0601 5.6066 -7.6553 -4.7531 9.7853 -5.1237 0.3647 -6.2756 5.0601 -5.4970 9.8261

2.9082 -10.4344 1.7828 5.7229 -12.3336 1.4717 8.4369 -5.8995 -3.3740 11.1035 -10.4344 1.7828 5.7229 2.9082 1.4717 8.4369 -5.8995 -3.3740 11.1035 -12.3336

-1.2472 -5.2159 11.2790 4.0008 -9.5382 4.6330 5.0753 -10.7664 2.7382 3.3307 11.2790 -1.2472 -5.2159 4.0008 -9.5382 4.6330 5.0753 2.7382 3.3307 -10.7664

-7.7816 -2.4886 6.8166 -8.1045 -3.8757 8.5790 -1.7775 -6.4950 9.1349 1.8527 -7.7816 -2.4886 -8.1045 -3.8757 8.5790 -1.7775 6.8166 -6.4950 9.1349 1.8527

-6.4025 4.4336 0.8807 -9.4585 4.8291 5.1396 -7.6327 2.9445 4.9589 -8.5094 -6.4025 4.4336 -7.6327 0.8807 -9.4585 4.8291 5.1396 2.9445 4.9589 -8.5094

2.4424 8.7051 -8.0850 -1.0509 10.0909 -5.5604 -1.9577 6.6252 -10.7162 -2.2256 10.0909 2.4424 8.7051 -8.0850 -1.0509 -5.5604 -1.9577 6.6252 -2.2256 -10.7162

8.3228 -0.8360 -6.5001 7.2694 -2.7292 -5.1417 10.1172 0.0891 -6.8816 11.0712 8.3228 -0.8360 -6.5001 7.2694 -2.7292 0.0891 -6.8816 -5.1417 10.1172 11.0712

1.8128 -7.0769 6.0054 0.9219 -6.5422 3.0692 3.7247 -5.8588 3.8229 1.4760 1.8128 -7.0769 6.0054 -5.8588 0.9219 -6.5422 3.0692 3.7247 3.8229 1.4760

-7.4896 3.7401 3.7724 -13.9271 4.6634 6.4029 -7.8570 3.1437 3.2542 -7.3002 -7.4896 3.7401 3.7724 -13.9271 4.6634 6.4029 3.1437 3.2542 -7.3002 -7.8570

3.9021 6.8324 -10.6548 1.1327 2.1733 -7.9796 1.9941 4.9268 -9.1913 -0.3485 -10.6548 1.1327 3.9021 6.8324 1.9941 4.9268 2.1733 -7.9796 -9.1913 -0.3485

5.4754 -9.9199 2.6348 7.1139 -10.7765 5.5345 5.8524 -8.3726 2.6696 4.9874 5.4754 -9.9199 5.8524 -8.3726 2.6348 7.1139 5.5345 2.6696 4.9874 -10.7765

-11.7234 5.2617 4.8669 -6.4090 4.8517 0.8279 -11.1032 4.3336 2.9443 -11.7234 5.2617 4.8669 -6.4090 4.8517 0.8279 4.3336 2.9443 -11.1032

-10.5809 12.6243 1.2923 -9.1553 7.6740 -0.0864 -10.3077 7.1322 1.6754 -4.0189 -10.5809 12.6243 1.2923 -9.1553 7.6740 -0.0864 1.6754 -4.0189 7.1322 -10.3077

12.0049 -2.5810 -6.9641 6.7100 -4.4771 -3.0482 6.9879 -0.4643 -1.4104 7.2220 12.0049 -2.5810 -6.9641 -4.4771 -3.0482 6.9879 -0.4643 6.7100 -1.4104 7.2220

-11.0736 -0.3027 3.1477 -13.4273 2.6889 1.7676 -9.0924 3.0181 3.1744 -6.1674 -11.0736 -13.4273 2.6889 -0.3027 3.1477 -6.1674 1.7676 -9.0924 3.0181 3.1744

6.8160 4.0940 -7.0509 6.2824 0.9006 -3.3878 8.2637 -4.9580 -3.2481 10.5308 6.8160 4.0940 -7.0509 6.2824 -3.3878 8.2637 -4.9580 0.9006 -3.2481 10.5308

-8.2105 -3.3148 8.1923 -8.6149 1.2212 3.7588 -5.6479 4.3956 -2.9892 -8.4072 -8.2105 -3.3148 8.1923 -8.6149 1.2212 -8.4072 3.7588 -5.6479 4.3956 -2.9892

8.6557 -1.1503 -4.9821 12.1615 -3.1649 -1.2539 10.5550 -8.3452 -0.4177 6.6400 8.6557 -1.1503 -4.9821 -3.1649 -1.2539 10.5550 12.1615 -0.4177 6.6400 -8.3452

-10.1547 3.2020 0.8712 -9.2281 8.4370 -1.0420 -4.7692 13.2513 -3.0937 -2.0347 -10.1547 3.2020 0.8712 -9.2281 8.4370 -1.0420 -4.7692 -3.0937 -2.0347 13.2513

10.0263 -8.3902 0.8310 5.0096 -8.8817 6.0063 2.4374 -10.3827 8.4896 -0.7046 10.0263 -8.3902 0.8310 -8.8817 5.0096 -0.7046 8.4896 6.0063 2.4374 -10.3827

-1.9322 9.9599 -5.5981 1.3213 6.4105] -1.9322 9.9599 -5.5981 1.3213 6.4105]

[0058] 发明具体实施步骤如下: [0058] The following specific embodiment of the invention the step of:

[0059] 步骤一、对采样所得的采样结果r (η)进行归一化。 [0059] Step a, the sampling results obtained sampling r (η) are normalized. 实现步骤为: Implementation steps are:

[0060] 首先,求取采样结果r (η)的绝对值最大值^ax ;其次,按如下式对r (η)进行归一化,即 [0060] First, the maximum absolute value of the sample is obtained results r (η) a ^ ax; Secondly, according to the following formula to r (η) is normalized, i.e.,

[0061] x(n) = r(n)lxm^[0062] i(n)即为r(n)归一化后的数据。 [0061] x (n) = r (n) lxm ^ [0062] i (n) is the r (n) of a normalized data.

[0063] 步骤二、对归一化后的数据珂η),按照希尔伯特黄变换中的经验模式分解算法进行分解和希尔伯特变换,得到希尔伯特谱Η(ω,η)。 [0063] Step II [eta] Ke data after normalization), according to the Hilbert-Huang Transform empirical mode decomposition algorithm decomposition and Hilbert transformation, Hilbert spectrum Η (ω, η) . 实现步骤为: Implementation steps are:

[0064] Α、根据希尔伯特黄变换的经验模式分解,将数据分解为M个内蕴模式函数(IMF) Ci (η)分量之和,即 [0064] Α, experience Hilbert-Huang Transform mode decomposition, decomposing the data into M intrinsic mode function (IMF) Ci (η) and the components, i.e.,

[0065] [0065]

Figure CN101527698BD00111

[0066] 其中,ι·Μ(η)为分解后的剩余分量,M为分解得到的内蕴模式函数的个数,M的值根据对ι·Μ(η)的大小要求来确定。 Number [0066] wherein, ι · Μ (η) for the remaining components after the decomposition, M is decomposed intrinsic mode function, the value of M is determined according to the size requirements ι · Μ (η) of.

[0067] B、对每一个内蕴模式函数分量进行希尔伯特变换,得到相应的解析信号,将所得 [0067] B, for each of the components intrinsic mode function Hilbert transform, the corresponding analytic signal, the resulting

到的M个解析信号带入 Parsing the signal into the M

Figure CN101527698BD00112

,得到: ,get:

Figure CN101527698BD00113

[0071] 其中,Htci (η)]为Ci (η)的希尔伯特变换,a, (η)为Ci(Ii)解析信号的瞬时幅度, fi(n) ^ci(Ii)的瞬时频率,θ“η) ^ci(Ii)的瞬时相位。Ts为采样间隔,i为内蕴模式函数分量的序号,即i = 1〜M ;b为采样点序号,b = 1〜η ;n为第η个采样点。 [0071] wherein, Htci (η)] is Ci (η) of the Hilbert transform, a, (η) is the instantaneous amplitude Ci (Ii) of the analytical signal, fi (n) ^ ci (Ii) of the instantaneous frequency , θ "η) ^ ci (Ii) is the instantaneous phase .Ts i.e. i = 1~M sampling interval, i is the serial number of intrinsic mode function component,; b = 1~η b is the number of sampling points,; n is η of sampling points.

[0072] C、将每个解析信号〒(《)均表示成时间η、瞬时频率ω、幅值〜(η)的三维谱图,即希尔伯特谱Η(ω,η): [0072] C, each of the analytic signal 〒 ( ") are represented as time [eta], [omega] instantaneous frequency, amplitude ~ (η) of the three-dimensional spectrum, i.e., spectrum Hilbert Η (ω, η):

[0073] [0073]

Figure CN101527698BD00114

[0074] 其中,bi为开关因子,当ω = Coi时,I3i = 1,否则bi = 0。 [0074] wherein, BI is the switching factor, as when ω = Coi, I3i = 1, or bi = 0.

[0075] 步骤三、在希尔伯特三维谱图中,干扰的谱幅度明显大于噪声和直扩信号的谱幅度。 [0075] Step three, the three-dimensional Hilbert spectrum, the spectral amplitude is significantly larger than the interference and noise amplitude spectrum DSSS signal. 此时,根据得到的希尔伯特谱Η(ω,n)确定抑制噪声和直扩信号谱的门限电平,将高于门限电平的谱保留,将低于门限电平的谱清零,得到非平稳干扰的希尔伯特谱。 At this time, the obtained spectrum Hilbert Η (ω, n) is determined to suppress noise spectrum signal DS and the gate threshold level, the power spectrum above the threshold retention levels, will be below the threshold level spectrum cleared to give non-stationary interference Hilbert spectrum. 实现步骤为: Implementation steps are:

[0076]( 一)通过连续平均抑制(CME)算法,确定抑制噪声和直扩信号谱的门限电平,即 [0076] (a) by continuous average inhibition (CME) algorithm, and is determined to suppress gates noise spectrum DSSS signal threshold level, i.e.

[0077] ①将所有希尔伯特谱线作为初始谱线,并把它们放入集合I,得到所有希尔伯特谱线值的累加和,即Am。 [0077] ① all Hilbert spectrum as the initial spectrum, and put them into a collection I, to give all Hilbert spectral values ​​and accumulated, i.e., Am. 将Am除以希尔伯特谱线总数,求出希尔伯特谱线的均值Ε[ |Η(ω, η) I]: Am divided by the total number of lines Hilbert, Hilbert obtain mean spectrum Ε [| Η (ω, η) I]:

Figure CN101527698BD00115

[0080] 其中,M为内蕴模式函数分量的个数,N为采样点数。 [0080] wherein, M being the number of intrinsic mode function component, N is the number of sampling points.

[0081] ②根据希尔伯特谱线的均值Ε[|Η(ω,η) | ],采用下式估计希尔伯特谱线的标准差 [0081] ② The mean Hilbert spectrum Ε [| Η (ω, η) |], is estimated using the standard formula Hilbert difference spectrum

Figure CN101527698BD00121

[0083] 根据得到的标准差σ [|Η(ω,η) |],确定出门限η : [0083] The obtained standard differential σ [| Η (ω, η) |], is determined out limit η:

[0084] η = Ε[|Η(ω,η) |]+3 σ [|Η(ω,η) |] [0084] η = Ε [| Η (ω, η) |] +3 σ [| Η (ω, η) |]

[0085] ③将集合I中的希尔伯特谱线的模与门限η进行比较,大于该门限的希尔伯特谱线被认为是被干扰的希尔伯特谱线,从集合I中去除。 [0085] ③ The Hilbert spectrum I set in a mold with a threshold η is compared, is greater than the threshold are considered Hilbert lines interfered Hilbert lines, from the set I removed. 集合I被更新。 I is a collection of updates.

[0086] ④更新集合I后,更新Am和E [ IH (ω,n) I ],之后重复②和③,直到没有希尔伯特谱线的模大于门限η为止。 [0086] ④ updated collection I, and updating Am E [IH (ω, n) I], and after repeating ② ③, until the mold is not Hilbert spectrum far greater than the threshold η. 最终得到没有希尔伯特谱线的模大于门限η的集合Γ。 No Hilbert finally obtained spectrum mold set greater than a threshold η Γ.

[0087] ⑤以集合I '中的希尔伯特谱线,估计最终的门限η = Ε[|Η(ω, n) ]+3σ [|Η(ω,π)]。 [0087] ⑤ in sets I 'line in Hilbert, the final estimated threshold η = Ε [| Η (ω, n)] + 3σ [| Η (ω, π)].

[0088] (二)将高于门限η电平的希尔伯特谱保留,将低于门限η电平的希尔伯特谱清零,从而得到非平稳干扰的希尔伯特谱。 [0088] (ii) the level above the threshold η Hilbert reserved spectrum, the level is below the threshold η Hilbert spectrum is cleared, whereby the non-stationary interference Hilbert spectrum.

[0089] 步骤四、依照非平稳干扰的希尔伯特谱与频率之间的对应关系,求取出非平稳干扰的瞬时频率,由该瞬时频率决定自适应无限冲激响应(IIR)格型陷波器的参数。 [0089] Step 4 in accordance with the correspondence between the frequency spectrum of the Hilbert non-stationary interference request remove non-stationary interference instantaneous frequency, instantaneous frequency is determined by the adaptive infinite impulse response (IIR) lattice notch the wave parameters.

[0090] 假设以采样频率fs/2为归一化频率,量化单位为400,非平稳干扰希尔伯特谱对应的瞬时频率为fH,则实际非平稳干扰的瞬时频率f为: [0090] Assuming that a sampling frequency fs / 2 is the normalized frequency, a quantization unit 400, the non-stationary interference instantaneous frequency corresponding to the spectrum of the Hilbert fH, the actual non-stationary interference instantaneous frequency f is:

[0091] f = (fH/400) X (fs/2) [0091] f = (fH / 400) X (fs / 2)

[0092] 其中,fs为采样频率,fH为干扰归一化瞬时频率。 [0092] wherein, fs is the sampling frequency, fH is a normalized instantaneous frequency interference. 通过曲线拟合,得到干扰信号瞬时频率曲线,如图3所示,这比采用Wigner-Ville分布估计的瞬时频率精度更高。 By curve fitting to obtain an interference signal instantaneous frequency profile, as shown in Figure 3, instantaneous frequency estimation accuracy higher than that using the Wigner-Ville Distribution.

[0093] 步骤五、将采样所得基带接收数据与自适应陷波器冲激响应进行卷积运算,得到抑制非平稳干扰后的数据,将该数据和同步的PN码序列进行相关运算,可完成接收数据的解扩。 [0093] Step five, the resulting baseband reception data sampling and adaptive notch filter impulse response convolution operation is performed to obtain the data to suppress non-stationary interference, the PN code sequence synchronized data and performs a correlation operation to be completed Solutions of the reception data expander.

[0094] 所采用的无限冲激响应(IIR)格型陷波器结构如图4所示,由非平稳干扰的瞬时 By interfering nonstationary transient [0094] employed IIR (IIR) lattice notch filter structure shown in Figure 4

频率决定自适应格型无限冲激响应(IIR)陷波器的相关参数Vac^k1和%,即 Frequency determining adaptive lattice infinite impulse response (IIR) filter parameters of the notch Vac ^ k1 and%, i.e.,

「 η , 2r cos ω() "Η, 2r cos ω ()

[0095] [0095]

Figure CN101527698BD00122

Iar cos®n Iar cos®n

[0096] [0096]

Figure CN101527698BD00123

[0097] Ic1 = r2 [0097] Ic1 = r2

[0098] B1 = α V [0098] B1 = α V

[0099] 其中,r为极半径,可取r = 1 ;α为一个决定陷波器宽度和深度的参数,可取α =0.95; Oci为陷波频率,G^ = 2Jif/fs。 [0099] wherein, r is the polar radius, preferably r = 1; α is a parameter decision wave trap width and depth, preferably α = 0.95; Oci is a notch frequency, G ^ = 2Jif / fs. 从而可得自适应格型陷波器传递函数为 Whereby available adaptive lattice notch filter transfer function is

Figure CN101527698BD00124

[0101] 按照如图5所示的非平稳干扰抑制框图,将采样所得数据与自适应无限冲激响应(IIR)格型陷波器的冲激响应进行卷积,得到抑制非平稳干扰后的数据序列吖…,如表2所示,即 After [0101] in a non-stationary interference suppression block diagram shown in Figure 5, the sampling data obtained with an adaptive infinite impulse response (IIR) impulse wave lattice notch filter response of the convolution of suppressing non-stationary interference acridine ... data sequence, as shown in table 2, i.e.

[0102] s(n) = r(n)*h(n)[0103] 表2抑制非平稳干扰后的数据序列Mn) [0102] s (n) = r (n) * h (n) [0103] Table 2 the data sequence Mn suppressing non-stationary interference)

[0104] s(n)= [0104] s (n) =

Figure CN101527698BD00131

[0105] [0105]

Figure CN101527698BD00141

-0.5607 -0.0864 0.1431 4.1725 1.1886 -3.8942 -3.3439 1.0640 1.6413 3.1839 -0.5607 -0.0864 -3.8942 -3.3439 0.1431 4.1725 1.1886 1.0640 1.6413 3.1839

-0.2770 1.9908 -1.7039 -2.9555 0.3866 3.6250 1.2914 2.2537 -1.3046 0.0426 -0.2770 1.9908 -1.7039 -2.9555 -1.3046 0.0426 0.3866 3.6250 1.2914 2.2537

-0.0243 -1.0902 -2.2072 0.9034 -0.4306 -3.2123 2.2235 -2.0981 -1.0401 1.8911 -0.0243 -1.0902 -2.2072 -0.4306 -3.2123 2.2235 -2.0981 0.9034 -1.0401 1.8911

0.6723 0.6869 3.9780 2.5576 5.0169 0.6030 0.0169 2.0342 0.8157 0.0475 0.6723 0.6869 3.9780 2.5576 5.0169 0.6030 0.0169 2.0342 0.8157 0.0475

1.4780 -2.5796 0.9218 1.4956 -1.3242 -2.0461 2.2246 -2.2575 -0.8414 0.1631 1.4780 -2.5796 0.9218 -1.3242 1.4956 -0.8414 0.1631 -2.0461 2.2246 -2.2575

-1.1433 -2.5786 -0.4443 -0.3167 2.9208 -2.3090 1.6588 -3.7017 -2.7555 0.0606 -1.1433 -2.5786 -0.4443 -0.3167 2.9208 -2.3090 1.6588 -3.7017 0.0606 -2.7555

1.2101 -0.5816 0.6828 -1.6177 -3.1242 -3.0250 1.9279 -0.2136 -0.8642 1.6298 1.2101 -0.5816 0.6828 -1.6177 -3.1242 -3.0250 1.9279 -0.2136 1.6298 -0.8642

-3.7140 0.8625 -2.5548 -0.9989 2.1566 -2.5180 0.3755 0.1863 0.8941 0.6337 -3.7140 0.8625 -2.5548 -0.9989 2.1566 -2.5180 0.3755 0.1863 0.8941 0.6337

-0.5418 3.8901 -0.0676 0.5980 -0.0257 1.0428 -0.7689 0.6476 3.3596 2.0682 -0.5418 3.8901 -0.0676 0.5980 -0.0257 1.0428 -0.7689 0.6476 3.3596 2.0682

0.7889 -0.5863 -2.0051 -2.2172 -2.1488 0.8685 1.2152 -0.4534 -0.8081 0.2336 0.7889 -0.5863 -2.0051 -2.2172 -2.1488 -0.4534 -0.8081 0.2336 0.8685 1.2152

-1.6601 -1.7678 1.0057 0.1963 1.8860 1.6798 -3.1188 0.4186 3.1167 2.3255 -1.6601 -1.7678 1.0057 -3.1188 0.1963 1.8860 1.6798 0.4186 3.1167 2.3255

5.0322 0 9677 -2.1638 1.2268 0.9171 2.8250 -2.3201 -1.0369 -1.4921 -0.9316 5.0322 1.2268 0.9171 2.8250 09677 -2.1638 -2.3201 -1.0369 -1.4921 -0.9316

-3.6979 3.9410 -0.4565 -1.5042 -0.9721 1.4590 0.2516 -2.8398 2.5384 -0.3525 -3.6979 3.9410 -0.4565 -1.5042 0.2516 -0.9721 1.4590 -2.8398 2.5384 -0.3525

-0.6779 0.0540 0.3616 -3.9126 -2.3813 -0.6878 2.9451 1.0174 -3.3865 -2.1440 -0.6779 0.0540 -0.6878 2.9451 -2.3813 0.3616 -3.9126 1.0174 -3.3865 -2.1440

-0.0637 2.8331 0.9402 0.7887 -0.3792 -0.1799 -0.5648 2.3071 3.5302 1.6540 -0.0637 -0.3792 -0.1799 -0.5648 2.8331 0.9402 0.7887 2.3071 3.5302 1.6540

-0.2316 -1.4040 -0.2640 0.2936 -1.8931 1.9016 1.2401 0 7382 -2.5978 -1.1871 -0.2316 -1.4040 -0.2640 0.2936 -1.8931 1.9016 -2.5978 -1.1871 1.2401 07382

2.2637 -2.2266 1.9705 -1.5533 -2.1325 -2.5117 0.3127 1.2534 -1.1592 -0.7455 2.2637 -2.2266 1.9705 -1.5533 -2.1325 -2.5117 -1.1592 -0.7455 0.3127 1.2534

-0.8429 -0.2553 0.2471 -1.4426 0.0687 2.6930 -0.5291 -0.3508 2.1324 0.5481 -0.8429 -0.2553 0.2471 -1.4426 0.0687 -0.5291 2.6930 -0.3508 2.1324 0.5481

0.0037 2.5411 -2.1328 -3.6133 -0.7318 -0.7294 1.3903 -0.6412 -1.2030 -2.5803 0.0037 2.5411 -2.1328 -3.6133 -0.7318 -0.7294 1.3903 -0.6412 -1.2030 -2.5803

-3.1652 1.7651 -1.4507 2.6089 0.4412 -0.9628 -0.9758 -1.2787 0.1983 1.0778 -3.1652 1.7651 -1.4507 2.6089 -1.2787 0.1983 -0.9758 0.4412 -0.9628 1.0778

-0.9304 -1.9497 -1.6563 -0.6861 3.4903 -1.9946 -0.3639 -0.9380 -2.2593 5.0594 -0.9304 -1.9497 -1.6563 -0.6861 -1.9946 -0.3639 -0.9380 -2.2593 5.0594 3.4903

-1.0606 -3.0862 1.4669 -2.8833 1.5104 1.3394 -1.0724 0.0650 0.6135 -4.8850 -1.0606 -3.0862 1.4669 -2.8833 1.5104 -4.8850 1.3394 -1.0724 0.0650 0.6135

2.6077 1.0723 2.0640 1.8725 -2.5458 -1.4366 1.9065 -0.1520 -0.1965 -0.9373 2.6077 1.0723 2.0640 1.8725 1.9065 -0.1520 -0.1965 -0.9373 -2.5458 -1.4366

-3.0621 -0.9653 -0.0556 -0.9456 2.2120 -1.1377 0.0143 -5.4613 1.6337 4.3570 -3.0621 -0.9653 -0.0556 -0.9456 2.2120 -1.1377 0.0143 -5.4613 1.6337 4.3570

-0.0318 -1 4625 0.7422 2.1664 5.9519 2.7223 2.0187 -0.7688 0.1735 2.3026 -14625 -0.0318 2.0187 -0.7688 0.7422 2.1664 5.9519 2.7223 0.1735 2.3026

1.4052 -1.3974 -0.2556 -1.2710 -1.2844 -1.5225 1.9570 0.5640 0.6156 -1.9196 1.4052 -1.3974 -0.2556 -1.2710 -1.2844 -1.5225 1.9570 0.5640 0.6156 -1.9196

1.5106 0.2750 1.0029 4.4210 -1.9419 1.5916 -0.7383 1.5538 -0.2962 1.7380 1.5106 0.2750 1.0029 4.4210 -1.9419 1.5916 -0.7383 1.5538 -0.2962 1.7380

1.5879 1.8364 2.0949 1.6968 -1.5801 -1.0196 3.6019 1.4205 2.0418 -2.6604 1.5879 1.8364 2.0949 1.6968 3.6019 1.4205 2.0418 -2.6604 -1.5801 -1.0196

-0.8918 -1.2093 2.1087 2.9258 1.8503 -0.8976 -1.4825 -5.1207 0.3408 -0.3031 -0.8918 -1.2093 2.1087 2.9258 1.8503 -0.8976 -1.4825 -5.1207 0.3408 -0.3031

-0.8801 -4.2198 -4.6124 -0.1223 2.8271 -2.0463 2.3885 -2.7710 -1.3705 1.4176 -0.8801 -4.2198 -4.6124 -0.1223 2.8271 -2.0463 2.3885 -2.7710 1.4176 -1.3705

0.5161 2.5839 -0.7475 1.1811 2.6006 0.8265 0.0610 -1.7724 0.3223 3.3797 0.5161 2.5839 1.1811 2.6006 0.8265 -0.7475 0.0610 -1.7724 0.3223 3.3797

-0.3478 2.1780 -0.4282 -2.9356 2.0875 2.6352 0.5554 1.7879 -0.9578 -1.2963 -0.3478 2.1780 -0.4282 -2.9356 -0.9578 -1.2963 2.0875 2.6352 0.5554 1.7879

-2.1113 -1.4089 -2.1176 -5.5317 2.5363 -1.3974 2.2116 -0.0945 -4.3345 4.3167 -2.1113 -1.4089 -2.1176 -5.5317 2.5363 -1.3974 2.2116 -0.0945 4.3167 -4.3345

3.2732 -0.1160 1.5321 0.6438 1.8222 0.7306 -0.4722 2.5859 -2.8640 3.2732 -0.1160 1.5321 -0.4722 2.5859 -2.8640 0.6438 1.8222 0.7306

-0.1054 -1.3363 5.3062 -0.4923 -1.7335 0.7165 0.2334 -2.3698 -3.7998 0.5855 -0.1054 -1.3363 5.3062 -0.4923 0.2334 -1.7335 0.7165 -3.7998 0.5855 -2.3698

-1.9466 1.3842 4.6551 2.2622 1.5291 -3.0288 0.6873 0.0504 1.9799 -1.9466 1.3842 -3.0288 4.6551 2.2622 1.5291 0.6873 0.0504 1.9799

1.2602 -2.1171 -0.6926 3.3672 -1.1597 0.1203 2.3162 3.0396 0.6913 1.2602 -2.1171 -0.6926 3.3672 -1.1597 0.1203 2.3162 3.0396 0.6913

0.5247 2.1137 -1.3282 3 1004 1.8169 -0 4863 -1.4711 0.0856 -1.8213 -0.0235 -1.3282 0.5247 2.1137 31,004 1.8169 -1.4711 0.0856 -1.8213 -0.0235 -04,863

-3.6572 -0.7970 0.7649 3.2595 2.6696 -2.3096 -0.5008 -1.3831 1.2304 -4.0620 -3.6572 -0.7970 0.7649 3.2595 2.6696 -2.3096 -0.5008 -1.3831 1.2304 -4.0620

-0.3156 -1.2066 -2.0771 1.1662 0.9136 0.0933 -2.2133 -2.0634 -3.5293 -2.8028 -0.3156 -1.2066 -2.0771 1.1662 0.9136 0.0933 -2.2133 -2.0634 -3.5293 -2.8028

-1.8601 0.6718 6.0226 -0.9315 0.3984 -3.6240 -2.4023 5.5438 0.4279 -3.4692 -1.8601 0.6718 -2.4023 6.0226 -0.9315 0.3984 -3.6240 0.4279 -3.4692 5.5438

1.8362 3.1301 1.5713 -0.9808 -5.1418 -2.9832 -1.7400 0.8852 -1.7183 1.8362 3.1301 1.5713 -0.9808 -5.1418 -2.9832 -1.7400 0.8852 -1.7183

1.1566 -0.0574 -2.8837 0.6793 -1.1593 -1.5018 2.2474 3.2054 1.7261 -1.1721 1.1566 -0.0574 -2.8837 0.6793 -1.1593 1.7261 -1.1721 3.2054 -1.5018 2.2474

0.2567 1.1132 0.0539 1.8328 -1.6652 1.8461 -0.8016 -1.1794 -2.8055 -0.6024 0.2567 1.1132 0.0539 1.8328 -1.6652 1.8461 -0.8016 -1.1794 -2.8055 -0.6024

-0.7115 1.9517 0.9207 -0.2160 1.6748 2.4834 0.9410 -1.3360 -1.2556 -0.7115 1.9517 -1.3360 0.9207 -0.2160 1.6748 -1.2556 2.4834 0.9410

1.9346 0.7391 1.2700 -1.7645 -0.7571 -1.6262 3.2338 -4.9769 -0.1864 2.1269 [0107]0.6726 -2.7008 0.4204 -1.7820 1.0068 -0.7883 -4.1582 -2.0537 1.0909 2.4728 1.9346 0.7391 1.2700 -1.7645 -0.7571 2.1269 -1.6262 3.2338 -4.9769 -0.1864 [0107] 0.6726 -2.7008 0.4204 -1.7820 1.0068 -0.7883 -4.1582 -2.0537 1.0909 2.4728

-2.2123 -0.8045 1.0016 -0.1509 0.2929 1.5369 0.3814 1.8360 1.6505 -2.2123 -0.8045 1.0016 -0.1509 0.2929 1.5369 0.3814 1.8360 1.6505

-3.5152 -1.3951 0.2879 2.3983 1.9957 -2.3437 0.7863 5.4911 0.2701 -3.5152 -1.3951 -2.3437 0.2879 2.3983 1.9957 0.7863 5.4911 0.2701

-1.5715 -1.8840 -0.1149 -0.4480 -2.5283 -2.6388 1.8724 2.9280 -0.4457 -0.3560 -1.5715 -1.8840 -0.1149 -0.4480 -2.5283 -2.6388 -0.4457 -0.3560 1.8724 2.9280

-3.4515 0.4721 3.1844 -1.6097 3.8268 1.3818 0.5248 1.9706 -0.5419 -3.4515 0.4721 -1.6097 3.1844 3.8268 1.3818 0.5248 1.9706 -0.5419

-1.0245 2.2910 -0.7747 -1.2200 0.7011 -3.1308 -3.2657 0.6767 2.4100 -0.3347 -1.0245 2.2910 -0.7747 -1.2200 0.7011 -3.1308 0.6767 -3.2657 2.4100 -0.3347

2.2020 0.0528 2.8268 1.0094 -0.1367 -5.4125 -3.7035 1.5070 1.1009 2.2020 0.0528 2.8268 1.0094 1.5070 1.1009 -0.1367 -5.4125 -3.7035

0.1052 -6.4304 -0.3235 4.0828 2.6984 -0.4723 3.6339 -0.0845 -0.7181 3.0838 0.1052 -6.4304 -0.3235 4.0828 -0.0845 2.6984 -0.4723 3.6339 -0.7181 3.0838

1.9279 2.0161 -1.1600 -1.9811 0.7070 3.0786 1.3509 1.4059 0.4235 2.0353 1.9279 2.0161 -1.1600 -1.9811 0.7070 3.0786 1.3509 1.4059 0.4235 2.0353

-2.1149 -1.2598 -0.9602 1.3387 -1.3262 -1.5097 1.8844 -0.0635 -0.4491 -2.4918 -2.1149 -1.2598 -0.9602 1.3387 -1.3262 -1.5097 1.8844 -0.0635 -0.4491 -2.4918

1.7524 1.0262 1.5730 -1.1350 2.6968 1.1212 1.3804 -1.4670 -0.1428 1.7524 1.0262 1.5730 2.6968 1.1212 1.3804 -1.4670 -0.1428 -1.1350

1.0276 1 4019 -4 6379 -1 8358 1.8611 -0.9650 -2.0615 1.2463 0.3115 -0.9165 14019-46379-1 1.0276 8358 1.8611 1.2463 0.3115 -0.9165 -0.9650 -2.0615

0.1342 0.5417 1.2499 1.2968 0.6239 -0.8262 4.1893 1.5569 0.1535 -1.1344 0.1342 0.5417 1.2499 1.2968 0.6239 4.1893 1.5569 0.1535 -1.1344 -0.8262

3.7919 -2.4682 2.5229 -1.8217 0.9150 -2.4047 -2.3307 -3.6800 0.2407 -0.5035 3.7919 -2.4682 2.5229 -1.8217 0.9150 -2.4047 -2.3307 -3.6800 0.2407 -0.5035

-5.4363 1.1629 -1.3229 -1.7960 2.9347 1.6972 3.8737 -1.9520 -4.0809 -5.4363 1.1629 -1.3229 1.6972 -1.7960 2.9347 -4.0809 3.8737 -1.9520

0.6829 0 8885 -4.8460 -0.1111 3 0373 -0.2812 -1.7684 0.2980 2.9306 08885 -4.8460 0.6829 -0.1111 -0.2812 -1.7684 0.2980 2.9306 30373

-1.3810 1.7839 -2.3706 2.1663 -0.9585 -3.8727 1.8777 2.5669 -2.1795 -1.3810 1.7839 -2.3706 2.1663 -0.9585 1.8777 -3.8727 2.5669 -2.1795

-0.4957 3.2650 3.6621 -2.3413 0.0966 1.9222 -1.7899 -1.0567 -2.1743 0.5557 -0.4957 3.2650 -1.7899 3.6621 -2.3413 0.0966 -1.0567 1.9222 -2.1743 0.5557

-0.3207 -2.9103 1.6565 0.2696 -3.0644 -3.5725 -0.4471 -0.1953 -1.6185 -1.6362 -0.3207 1.6565 -2.9103 0.2696 -3.0644 -3.5725 -0.4471 -0.1953 -1.6185 -1.6362

2.9913 0.8257 0.6163 -0.2446 3.0008 0.8001 -1.1573 2.4232 3.2856 2.9913 0.8257 0.6163 3.0008 0.8001 -1.1573 2.4232 -0.2446 3.2856

-0.4006 1.5614 3.1263 0.4427 0.3205 -3.7527 -0.6979 1.0626 -3.6340 -2.0795 -0.4006 1.5614 3.1263 0.4427 0.3205 1.0626 -3.6340 -2.0795 -3.7527 -0.6979

3.8163 -2.4107 0.0172 2.9042 0.5556 -2.7836 -0.5689 2.8684 1.3142 3.8163 -2.4107 -2.7836 -0.5689 0.0172 2.9042 0.5556 2.8684 1.3142

1.7497 2.8997 2.5594 0.0401 -3.0494 1.0703 0.7097 1.5975 5.0939 0.9403 1.7497 2.8997 2.5594 0.0401 1.0703 0.7097 1.5975 5.0939 0.9403 -3.0494

-3.4545 -1.7126 -0.2930 -1.1700 -3.3475 -1.0867 1.5849 -1.8767 -2.4559 0.4139 -3.4545 -1.7126 -0.2930 -1.1700 -3.3475 -1.0867 1.5849 -1.8767 0.4139 -2.4559

-1.4407 -0.2351 -4.7484 0.6140 2.0343 -1.6829 1.2068 0.6198 -2.1433 -1.4407 -0.2351 -4.7484 0.6140 -2.1433 2.0343 -1.6829 1.2068 0.6198

-0.2594 3.5052 -3.4070 -7.2414 -2.1728 0.2351 -1.9857 1.0344 -0.3445 -0.2594 3.5052 -3.4070 -7.2414 -2.1728 0.2351 -1.9857 1.0344 -0.3445

-0.0450 -1.1857 2.7224 0.4755 -2.0233 0.5209 -3.3673 -1.3145 -0.7038 -0.0450 2.7224 -1.1857 0.4755 -2.0233 0.5209 -3.3673 -1.3145 -0.7038

1.8794 1.9188 -1.8037 -1.5907 2.0766 0.4285 -1.1584 2.4177 -0.1914 -3.3032 1.8794 1.9188 -1.8037 -1.5907 2.0766 -3.3032 0.4285 -1.1584 2.4177 -0.1914

-1.2293 -0.9898 -2.0002 -1.8744 3 7868 1.1983 -0.9258 -3.6920 4.8439 -1.2293 -0.9898 -2.0002 -1.8744 -0.9258 -3.6920 4.8439 1.1983 37868

-2.9021 2.6905 2.1515 -2.3625 -1.7575 1.5165 -0.8279 -1.0104 -0.5623 3.3562 -2.9021 2.6905 -2.3625 2.1515 -1.7575 1.5165 -0.8279 -1.0104 -0.5623 3.3562

-0.8883 -0.6306 4.4565 -0.6910 -1.5867 0.3871 3.7285 -1.1587 -2.7359 -0.8883 -0.6306 4.4565 -0.6910 0.3871 -1.5867 3.7285 -1.1587 -2.7359

2.4789 -0.1853 -1.7253 1.0442 -0.3994 -0.5351 -3.2535 0.2789 -1.4776 -1.4858 2.4789 -0.1853 -1.7253 -0.3994 -0.5351 -3.2535 0.2789 -1.4776 1.0442 -1.4858

-0.6846 -0.0204 -3.3745 2.7392 3.2304 -2.5393 2.9568 0.6948 -1.6174 3.2138 -0.6846 -0.0204 -3.3745 2.7392 -1.6174 3.2304 -2.5393 2.9568 0.6948 3.2138

1.5978 -1.9486 -2.1422 2.4513 0 3693 -2.5578 1.3028 0.3463 -6.0514 1.5978 -1.9486 -2.1422 2.4513 -2.5578 1.3028 0.3463 -6.0514 03693

2.5352 0.9259 -2.3661 1.4930 3.1729 0.2501 -2.2607 1.7664 -2.4153 -3.0087 2.5352 0.9259 1.4930 3.1729 -2.3661 0.2501 -2.2607 1.7664 -2.4153 -3.0087

0.9646 -4.1989 -0.0164 1.0277 1.3041 -1.3579 2.4165 3.4394 0.1884 0.9646 -4.1989 1.0277 -0.0164 1.3041 -1.3579 2.4165 3.4394 0.1884

2.7061 5.4573 -1.6354 -2.6171 2.6761 -1.7484 -1.9035 -2.1971 1.0544 -4.3037 2.7061 5.4573 2.6761 -1.6354 -2.6171 -1.7484 -1.9035 -2.1971 1.0544 -4.3037

-0.6129 -0.6562 -2.6502 -0.0530 3.8815 -2.4094 0.3456 4.9070 0.0592 -0.6129 -0.6562 -2.6502 -0.0530 3.8815 -2.4094 0.3456 4.9070 0.0592

-3.5924 1.0712 -1.8992 -1.7899 2.9890 0.7897 -1.8489 0.6863 -0.1511 -0.5193 -3.5924 1.0712 -1.8992 2.9890 -1.7899 0.7897 -1.8489 0.6863 -0.1511 -0.5193

2.9037 0.0541 -2.1456 2.8315 1.9028 -0.9942 -1.5594 -4.4939 -0.0052 -0.3467 2.9037 0.0541 2.8315 1.9028 -2.1456 -0.9942 -1.5594 -4.4939 -0.0052 -0.3467

4.7986 -2.7795 -1.4261 1.1918 -0.1403 1.6854 2.9686 -0.8260 2.7903 3.5628 4.7986 -2.7795 1.6854 -1.4261 1.1918 -0.1403 2.9686 -0.8260 2.7903 3.5628

-0.0012 -2.0691 1.3872 0.9547 -4.3556 3.2077 1.7907 -2.6193 ϋ.0919 -0.0012 -2.0691 1.3872 0.9547 -4.3556 3.2077 1.7907 -2.6193 ϋ.0919

0.0419 -2.1806 1.9087 -6.3036 -1.0734 3.7568 0.5725 -2.1632 0.0450 0.9962 0.0419 -2.1806 1.9087 -6.3036 3.7568 -1.0734 0.5725 -2.1632 0.0450 0.9962

-1.1284 3.6214 -2.3220 -3.8290 -1.5573 0.3177 -2.8617 1.4752 -1.0018 -1.1284 3.6214 -2.3220 -3.8290 -1.5573 0.3177 -2.8617 1.4752 -1.0018

-5.2222 1.9437 -1.8028 -2.1566 3.6936 -2.4337 0.4565 2.6265 0.2843 -2.9739 -5.2222 1.9437 -1.8028 -2.1566 3.6936 -2.4337 0.4565 2.6265 0.2843 -2.9739

2.1770 -3.2694 -0.8946 2.6227 2.2047 -1.7849 -0.5161 -3.2162 -3.0939 2.6476 [0108]-2.9873 4.7168 2.3324 -1.8029 -1.3412 2.2748 -3.9140 -2.3301 5.3147 2.1770 -3.2694 -0.8946 -1.7849 -0.5161 -3.2162 -3.0939 2.6227 2.2047 2.6476 [0108] 2.3324 -1.8029 -2.9873 4.7168 -1.3412 2.2748 -3.9140 -2.3301 5.3147

1.4466 2.8410 2.5500 -3.1599 -2.6481 1.8601 -1.0399 -1.5141 7.0468 -1.2514 1.4466 2.8410 2.5500 -3.1599 -2.6481 1.8601 -1.0399 -1.5141 7.0468 -1.2514

0.1436 -3.2001 -2.4799 -2.6624 -4.9070 -1.9544 -1.9313 -0.4288 -3.6499 2.0892 0.1436 -3.2001 -2.4799 -2.6624 -4.9070 -1.9544 -1.9313 -0.4288 -3.6499 2.0892

1.5460 -0.9132 5.6283 -0.8979 -2.0784 4.5099 0.7236 0.2083 0.6952 1.5460 -0.9132 5.6283 -0.8979 -2.0784 4.5099 0.7236 0.2083 0.6952

-1.9419 3.2504 -0.6942 -4.8827 2.2189 -0.1021 -3.0035 0.2297 2.6337 -1.9419 3.2504 -0.6942 -4.8827 2.2189 -0.1021 -3.0035 0.2297 2.6337

-2.0895 -3.1374 -2.1365 0.5878 2.4378 -1.1765 3.9839 3.4030 -0.7169 -2.0895 -3.1374 -2.1365 0.5878 -0.7169 2.4378 -1.1765 3.9839 3.4030

3.5983 0.0458 -3.7113 2.1902 -1.4347 -3.3217 0.1195 -2.0598 -0.1153 3.5983 0.0458 -3.7113 2.1902 -1.4347 -3.3217 0.1195 -2.0598 -0.1153

2.5629 -0.7023 4.6056 4.2448 -2.1725 3.1395 0.7018 -3.7879 1.7755 2.5629 -0.7023 4.6056 -3.7879 4.2448 -2.1725 3.1395 0.7018 1.7755

-0.2795 -1.8973 4.0813 -4.5623 -0.7481 5.2127 -0.2737 2.3272 3.0435 -2.1565 2.5755] -0.2795 -1.8973 4.0813 -4.5623 2.3272 -0.7481 5.2127 -0.2737 3.0435 -2.1565 2.5755]

[0109] 吖…的频谱图如图6所示,可见已将非平稳干扰的频谱抑制。 [0109] acridine ... spectrum shown in Figure 6, the visible spectrum has a non-stationary interference suppression. 将数据〗(《)和同步的PN码序列进行相关运算,就可完成对抑制干扰后的基带接收数据的解扩。 〗 Data ( ") PN code sequence and performs a correlation operation is synchronized, can be completed despread baseband reception data to suppress the interference.

Claims (1)

1.基于希尔伯特黄变换和自适应陷波的非平稳干扰抑制方法,其特征在于具体步骤如下:步骤一、对基带接收数据的采样结果进行归一化;步骤二、对归一化后的数据,按照希尔伯特黄变换中的经验模式分解算法进行分解和希尔伯特变换,得到希尔伯特谱,具体实现步骤为:A、根据希尔伯特黄变换的经验模式分解,将经步骤一得到的归一化后的数据玛《)分解为M个内蕴模式函数(IMF)Ci(n)分量之和,即M 1. Based on the non-stationary interference Hilbert-Huang Transform and adaptive notch suppression method, comprising the following steps: a step of sampling results baseband reception data is normalized; Step two, the normalized after the data, according to the Hilbert-Huang transform empirical mode decomposition algorithm decomposition and Hilbert transformation, Hilbert spectrum, specific implementation steps of: a, according to the empirical mode decomposition Hilbert transform yellow , the data obtained by a step of Mary "after normalization) is decomposed into M intrinsic mode function (IMF) Ci (n) and the sum component, i.e., M
Figure CN101527698BC00021
Figure CN101527698BC00022
其中,rM(n)为分解后剩余分量,M为分解得到的内蕴模式函数的个数,M的值根据对rM(n)的大小要求来确定;B、对每一个内蕴模式函数分量进行希尔伯特变换,得到相应的解析信号,将所得到的MM个解析信号带入拜= + &㈨中,表示为 Wherein, rM (n) is the residual component decomposition, M is the number of intrinsic mode decomposition function, the value of M is determined according to the size requirements of rM (n) a; B, a function of each component of the intrinsic mode Hilbert transform, the corresponding analytic signal, the resulting signal is parsed into a prayer MM = ix + in, expressed as
Figure CN101527698BC00023
其中,HtCi (η)] ^Ci(Ii)的布尔伯特变换,Bi(Ii) ^Ci(Ii)解析信号的瞬时幅度,^ (η) 为Ci(Ii)的瞬时频率,θ Jn)为Ci (n)的瞬时相位,Ts为采样间隔,i为内蕴模式函数分量的序号,即i = 1〜M;b为采样点序号,b = 1〜η ;n为第η个采样点;C、将巧《)表示成时间η、瞬时频率ω、幅值〜(η)的三维谱图,即希尔伯特谱Η( ω,η): Wherein, HtCi (η)] ^ Ci (Ii) Boolean Hilbert transform, Bi (Ii) ^ instantaneous magnitude Ci (Ii) of the analytical signal, ^ (η) of Ci (Ii) of the instantaneous frequency, θ Jn) of Ci (n) instantaneous phase, Ts of the sampling interval, i is the serial number of intrinsic mode function component, i.e., = 1~M i; b is a number of sampling points, b = 1~η; n η for the first sampling points; C, the clever ") is represented as the time [eta], [omega] instantaneous frequency, amplitude ~ (η) of the three-dimensional spectrum, i.e., spectrum Hilbert Η (ω, η):
Figure CN101527698BC00024
其中,1^为开关因子,当ω = Coi时,bi = l,否则bi = 0;M代表内蕴模式函数分量的个数,i为内蕴模式函数分量的序号,即i = 1〜M ;步骤三、根据得到的希尔伯特谱确定抑制噪声和直扩信号谱的门限电平,将高于门限电平的谱保留,将低于门限电平的谱清零,得到非平稳干扰的希尔伯特谱,具体实现步骤为:(一)通过连续平均抑制算法,确定抑制噪声和直扩信号谱的门限电平,即①将所有希尔伯特谱线作为初始谱线,并把它们放入集合I,得到所有希尔伯特谱线值的累加,将A1J*以希尔伯特谱线总数,求出希尔伯特谱线的均值Ε[|Η(ω,η)]: Wherein 1 ^ is a switch factor, when ω = Coi time, bi = l, or bi = 0; intrinsic mode function component representative of the number of M, i is the number of intrinsic mode function component, i.e., i = 1~M ; step three, according to the determined spectrum obtained Hilbert inhibition gate signal DS and noise spectrum threshold level, higher than the threshold level reserved spectrum, the spectrum will be lower than the threshold level is cleared to give nonstationary interference Hilbert spectrum, specific implementation steps :( a) by inhibiting the running average algorithm, and determining the level of the noise suppressing signal spectrum DS threshold, i.e., ① all lines as the initial Hilbert line, and put them into a collection I, to obtain all the accumulated values ​​of the Hilbert lines, the total number of the Hilbert A1J * lines, mean spectrum determined Hilbert Ε [| Η ( ω, η)]:
Figure CN101527698BC00025
其中,M为内蕴模式函数分量的个数,N为采样点数;②根据希尔伯特谱线的均值Ε[|Η(ω,n) | ],采用下式估计希尔伯特谱线的标准差σ [|Η(ω,η)]: Wherein, M being the number of intrinsic mode function component, N is the number of sampling points; ② spectral lines from the mean Hilbert Ε [| Η (ω, n) |], is estimated using the formula Hilbert line the standard deviation σ [| Η (ω, η)]:
Figure CN101527698BC00031
③将集合I中的希尔伯特谱线的模与门限η进行比较,大于该门限的希尔伯特谱线被认为是被干扰的希尔伯特谱线,从集合I中去除,集合I被更新;④更新集合I后,更新Am和E [ IH (ω,η) I ],之后重复②和③,直到没有希尔伯特谱线的模大于门限Π为止,最终得到没有希尔伯特谱线的模大于门限n的集合Γ ;⑤以集合I'中的希尔伯特谱线,估计最终的门限η =Ε[|Η(ω,π)|]+3σ[|Η(ω, n)|];(二)将高于最终门限n电平的希尔伯特谱保留,将低于门限n电平的希尔伯特谱清零,从而得到非平稳干扰的希尔伯特谱;步骤四、依照非平稳干扰的希尔伯特谱,求取出非平稳干扰的瞬时频率,由该瞬时频率决定自适应无限冲激响应格型陷波器的参数,由此得到自适应陷波器冲激响应;步骤五、将步骤一中的采样结果与自适应陷波器冲激响应进行卷积运算,得到抑制非平稳干 ③ The set I is Hilbert spectrum mode and compares a threshold η, greater than the threshold line is considered to be a Hilbert Hubert disturbed line is removed from the set I, a collection of I is updated; ④ I set update, updating Am and E [IH (ω, η) I], and after repeating ② ③, until no Hilbert modulus greater than the threshold line Π far, no finally obtained Hill Burt mold spectrum than the threshold n is set Γ; ⑤ in sets I 'line in Hilbert, the final estimated threshold η = Ε [| Η (ω, π) |] + 3σ [| Η ( [omega], n) |]; (ii) the threshold will be higher than the final level n Hilbert spectrum reserved, will be below the threshold level of the n Hilbert spectrum is cleared, whereby the non-stationary interference Hill Burt spectrum; step 4 in accordance with the Hilbert nonstationary interference spectrum, the instantaneous frequency seeking remove interfering non-stationary, the instantaneous frequency is determined by parameters of an infinite impulse response adaptive lattice notch filter, thereby obtaining a self- adaptation impulse response notch filter; five steps, a step of sampling results of the adaptive notch filter impulse response convolution operation, is suppressed nonstationary dry 后的数据,将该数据和同步的PN码序列进行相关运算,完成接收数据的解扩。 After the data, the data and the PN code sequence synchronized correlation is performed to complete despreading the received data. 3 3
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