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7.3.3 Causal Wiener Filter

7.3.3 Causal Wiener Filter. Causal 이란 , 미래의 입력이 과거와 현재의 출력에 영향을 미치지 못하고 , 과거와 현재의 입력만이 출력에 관여하는 것이다. Wiener Filter Signal 과 noise 는 spectral characteristics or autocorrelation, crosscorrelation 을 알고 있는 random processes 이다 . 2. filter 성능은 minimum mean-square error 로 판정한다 .

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7.3.3 Causal Wiener Filter

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  1. 7.3.3 Causal Wiener Filter Causal이란, 미래의 입력이 과거와 현재의 출력에 영향을 미치지 못하고, 과거와 현재의 입력만이 출력에 관여하는 것이다. • Wiener Filter • Signal과 noise는 • spectral characteristics or autocorrelation, crosscorrelation을 알고 있는 • random processes이다. • 2. filter 성능은 minimum mean-square error로 판정한다. • 3. A solution based on scaler methods that leads to the optimal filter • weighting function 20067168 김정중 제어계측공학과 전력전자연구실

  2. x(n) = d(n) + v(n) System function is given in Eq. (7.53) • If v(n) is uncorrelated with d(n) • Then Pdx(z) = Pd(z) Power Spectrum of x(n) is

  3. Although Eq.(7.32) In the frequency domain, Eq.(7.33) Frequency response of the IIR Wiener filter is System function Px(z) is a power spectral density Pdx(z) is a cross-power spectral density

  4. V(n) : unit variance white noise d(n) : AR(1) process W(n) is white noise with Variance therefore Example 7.3.2

  5. From page. 357 위 식에 대입 From Eq. 7.61

  6. Form Eq. 7.60 For Second-order FIR Wiener filter, mean square error = 0.4048 : only slightly improve

  7. error This error, called the innovations process Corresponds to that part of x(n) cannot be predicted. The estimate d(n) is modified by adding a correction, which is the innovations process after it has been scaled by a gain, K, referred to as the Kalman Gain. We will soon discover in Section 7.4.

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