As low-cost drones become more accessible, they pose various safety, security, and privacy threats. As such, it becomes increasingly important to detect their presence, locate and track their positions, and classify their types in real time. In this paper, we perform time-frequency analyses of drone Doppler and micro-Doppler signatures to provide enhanced drone detection and feature extraction capabilities. The analyses are based on the combined use of spectrogram and inverse Radon transform (IRT). The paired property of propeller blades associated with a rotor is further utilized to compute the IRT product for enhanced performance. It is demonstrated that the IRT and IRT product images, when expressed in terms of the rotation frequency and blade position phase, provide flexibility and effectiveness for the presentation and estimation of these parameters.