Question

If the set of linear equations from the equation \(\sum_{k=0}^M b_k r_{hh} (k-l)=r_{dh} (l)\), l=0,1,…M are expressed in matrix form, then what is the type of matrix obtained?

(a) Symmetric matrix

(b) Skew symmetric matrix

(c) Toeplitz matrix

(d) Triangular matrix

I had been asked this question by my college director while I was bunking the class.

This interesting question is from FIR Least Squares Inverse Filters topic in section Digital Filters Design of Digital Signal Processing

Answer 1

Correct answer is (c) Toeplitz matrix

To elaborate: We observe that the matrix is not only symmetric but it also has the special property that all the elements along any diagonal are equal. Such a matrix is called a Toeplitz matrix and lends itself to efficient inversion by means of an algorithm.