Shift Walsh matrix and delay-differential equations

Shift Walsh matrix is first introduced. The
m \times m
shift Walsh matrix is formed from the
m \times m
Walsh matrix by shifting the columns of the Walsh matrix to the right, dropping the last
k(m \geq k > O)
columns and assigning first
k
columns of the new matrix as zero elements. Delay Walsh functions can be expanded in terms of Walsh functions using shift Walsh matrix. Therefore, linear delay-differential equations can he analyzed by Walsh series approximation. The method is most useful for time-varying systems.