Hand gesture recognition using radar often relies on computationally expensive fast Fourier transforms. This paper proposes an alternative approach that bypasses fast Fourier transforms using resonate-and-fire neurons. These neurons directly detect the hand in the time-domain signal, eliminating the need for fast Fourier transforms to retrieve range information. Following detection, a simple Goertzel algorithm is employed to extract five key features, eliminating the need for a second fast Fourier transform. These features are then fed into a recurrent neural network, achieving an accuracy of 98.21% for classifying five gestures. The proposed approach demonstrates competitive performance with reduced complexity compared to traditional methods