Recursive method to obtain the differential and integral operators based on the Walsh series

An iterative method is presented for obtaining global-domain derivatives and integrals for Lebesgue-integrable signals. The classical method uses multiplication and inversion of large matrices to obtain them, also low-pass filter is implicitly applied to obtain the derivative, which can cause the loss of valuable information for certain applications. Both new operators, integral and differential, are defined in a recursive format which facilitates their application and reduces computational cost. The derivative operator is sensitive to discontinuities and abrupt changes of signals, making it useful for their analysis.