A generalized formulation of the instantaneous frequency based on the higher order differential energy operator is proposed. The special cases of the general formulation are also presented. The proposed instantaneous frequencies are compared with existing methods in terms of computational requirements and error performance measured in the mean absolute error. The proposed methods are less expensive than the existing ones, but need more data samples to obtain a frequency estimation value. But, the number of data used is independent of the order of the energy operator. In terms of the estimation error performance, the existing DESA I and II algorithm show the best result under noise free situation, but the HODEO with order k=4 produces the best result under noisy situation. And the HODEO with order k=3 shows comparable result. Suitable post-processing like the median filtering may be added to improve further.