China
Africa
Explore chapters and articles related to this topic
Fundamentals of Speech Processing
Published in Shaila Dinkar Apte, Random Signal Processing, 2017
We can observe that the diagonal elements are γxx. When the displacement is 0, naturally the correlation is 1. The off-diagonal elements represent the correlation with offset as 1, 2, …, etc., … P. We can verify that the matrix element in the second row and first column is the same as the element in the first row and second column; the matrix element in Pth row and first column is the same as the element in the first row and the Pth column, etc. The matrix is symmetric. If the matrix is symmetric and diagonal elements are equal, then it is called the Toeplitz matrix. By exploiting the property of the Toeplitz matrix, a recursive procedure can be formulated for the calculation of predictor coefficients. This recursive algorithm is a well-known Levinson–Durbin algorithm. Levinson recursion or Levinson–Durbin recursion are procedures in the linear algebra to recursively calculate the solution to any equation involving a Toeplitz matrix.
Deconvolution of blast vibration signals by wiener filtering
Published in Inverse Problems in Science and Engineering, 2018
Using Equations (13) and (14), the autocorrelation sequence of input, r[n], and the cross-correlation sequence between input and desired output, g[n] are calculated. Substituting r[n] and g[n] into Equation (16) and solving the system, the Wiener filter, f[n], is obtained. To solve Equation (16), either Levinson recursive algorithm [9] or matrix operations can be used and they give the same results after comparison. Levinson recursion is a recursive procedure to solve equations in form of Toeplitz matrix. However, for large matrix data, the matrix inverse operation is not an optimum choice, and the Levinson algorithm is preferred. For consistency of results, Levinson recursive algorithm was employed throughout the paper in despite the size of the matrix. By following the previously described procedure, a Wiener filter can be calculated. Then, according to Equation (5), applying the estimated filter f[n] to the measured signal y[n], it is possible to calculate the synthetic signature . The three measured signature holes are compared to the calculated synthetic signature waveform in Figure 7(a) and (b), respectively.