Accurate detection of low-level targets is a challenging problem since the invention of radar. Many techniques have been developed to improve the detection quality, one of which is Detection in the Moments Space (DMS). So far, this technique has only been implemented using the amplitude of the received signal as an input parameter. In this research, DMS is implemented for the first time using the instantaneous frequency (IF) of the signal. The main motivation for this proposal was the expected improvement in the detection of low-level mobile targets. Although the superiority of the new detector is shown in several cases, the behavior obtained for certain target speeds turned out to be an unexpected finding. Experiments conducted on real signals and simulated moving targets indicate the need for further studies on the use of IF and spectral information in combination with DMS, as well as their usefulness for detecting moving targets compared to the detector using only moments of the amplitude.