An extension of the 2-D discrete Teager-Kaiser energy operator and the 1-D higher-order energy operators to the 2-D continuous case is proposed. These 2-D continuous operators are flexible enough to apply a large class of image gradient filters, and consequently different discrete energy operators are derived. Particularly, the proposed model takes into account the diagonal directions, through the partial derivatives. The obtained operators are computationally very simple, like the classical 2D Teager-Kaiser operator, and are well suited for image-processing applications such as image demodulation or image contrast enhancement. Results of demodulation of synthetic and real images, to estimate envelope information, are presented to show the feasibility of the proposed operators.