A pumping control unit is disclosed herein. The pumping control unit includes a processor coupled to a memory and a communication interface. The memory is configured to store an invariant matrix. The communication interface is configured to receive a plurality of measurements of a time-varying parameter for a rod pumping unit. The plurality of measurements is taken at a surface of a pumping site over a pump cycle for a sucker rod string. The processor is configured to gain access to the invariant matrix in the memory and the plurality of measurements from the communication interface. The processor is further configured to compute a Fourier coefficient array based on the invariant matrix and the plurality of measurements. The processor is further configured to compute a time-varying downhole parameter based on the Fourier coefficient array and a sucker rod string model.