In this work, we propose a combination of the Teager–Kaiser energy operator (TKEO) and the spiral phase transform (SPT) for robust instant energy estimation of amplitude-modulated and frequency-modulated (AM–FM) signals, where the energy extraction is followed by a high-frequency component, generally considered as noise. We demonstrate that this noise component can be subtracted mathematically using the SPT transformation applied to the AM–FM signal. The improvement in demodulation is tested using a simulated AM–FM image and evaluated by the image quality index. An experimental speckle fringe pattern obtained by digital speckle pattern interferometry on a hard disk is denoised using a multiband approach and demodulated using the proposed method.