Shift Walsh matrix and delay-differential equations

Shift Walsh matrix is first introduced. The shift Walsh matrix is formed from the Walsh matrix by shifting the columns of the Walsh matrix to the right, dropping the last columns and assigning first 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.