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Solving for the Minimum Mean Squared Error Weights

February 2, 2019 by 3200 Creative

Solving for the Minimum Mean Squared Error Weights

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  1. Question 1 of 5
    1. Question

    If  {\bf R} = \frac{1}{L} \sum_{n= l_1}^{l_1+L-1} {\bf x}[n] {\bf x}^T[n],  {\bf p} = \frac{1}{L} \sum_{n= l_1}^{l_1+L-1} d[n]{\bf x}[n] and  \sigma_d^2 = \frac{1}{L} \sum_{n= l_1}^{l_1+L-1} d^2[n] as defined in the video, then the vector of optimum weights {\bf w} is expressed as

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  2. Question 2 of 5
    2. Question

    The mean-squared error is a quadratic function of the filter weights.

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  3. Question 3 of 5
    3. Question

    The matrix {\bf R}, vector {\bf p} and scalar \sigma_d^2 defined in question 1 correspond to sample estimates of the correlation matrix {\bf R} = E\{{\bf x}[n]{\bf x}^T[n]\}, cross-correlation vector  {\bf p} = E\{{\bf x}[n] d[n]\}, and second moment  \sigma_d^2 = E\{d^2[n]\}.

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  4. Question 4 of 5
    4. Question

    The solution to the system of L>N equations in N unknowns {\bf X}^T{\bf w} \approx {\bf d} where {\bf X}^T is L by N, {\bf w} is N by 1, and {\bf d} is L by 1 may be expressed as…

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  5. Question 5 of 5
    5. Question

    The MMSE filtering problem is similar, but not equivalent to a least squares problem involving L>N equations in N unknowns.

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Course Lessons

  • Introduction to Minimum Mean-Squared Error Filtering

  • Solving for the Minimum Mean-Squared Error Weights

  • Solving Least-Squares Problems with Gradient Descent: the Least Mean-Square Algorithm

  • Convergence, Tracking, and the LMS Algorithm Step Size

Courses

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  • The Z-Transform

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  • Random Signal Characterization

  • Basis Representations of Signals

  • Estimation of Power Spectra and Coherence

  • Introduction to Signal Estimation and Detection Theory

  • MMSE Filtering and Least-Squares Problems

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