Toeplitz Matrix

By: - Vivek Raj

Toeplitz Matrix: - A Toeplitz matrix is an n × n matrix Tn = [tk,j ; k, j = 0, 1, . . . , n − 1] where tk,j = tk-j .

Signal processing theory such as prediction, estimation, detection, classification, regression, and communications and information theory are most thoroughly developed under the assumption that the mean is constant and that the covariance is Toeplitz, i.e., KX(k, j) = KX(k − j), in which case the process is said to be weakly stationary.

Toeplitz matrices also arise in solutions to differential and integral equations, spline functions, and problems and methods in physics, mathematics, statistics, and signal processing.

Matlab Code to find inverse of Toeplitz Matrix: -

To solve any Matrix equation of type AX=B, we need to find inverse of A if we know matrix B to find “X”.

I have written a matlab code to find out inverse of Toeplitz matrix [10 x 10]. I have also multiplied original matrix and inverse matrix to check whether I get

Identity matrix or not and I got the expected Result. Matrix that I have taken for example is:-

C= Column entry = [1 2 3 0 0 0 0 0 0 0] R= Row entry = [1.5 2.5 3.5 0 0 0 0 0 0 0]