In recent years, Doppler radar has been used as a sensing modality for human gait recognition, due to its ability to operate in adverse weather and penetrate opaque obstacles. Doppler radar captures not only the speed of the target, but also the micro-motions of its moving parts. These micro-motions induce frequency modulations that can be used to characterise the target movements. However, a major challenge in Doppler signal processing is to extract discriminative features from the radar returns for target classification. This study presents a feature extraction method for classification of human motions from the micro-Doppler radar signal. The proposed method applies the log-Gabor filters at multiple spatial frequencies and orientations on a joint time-frequency representation. To achieve invariance to the target speed, features are extracted from local patches along the torso Doppler shift. Then, the (2D)2PCA (two-directional two-dimensional principal component analysis) method is applied to create a compact feature vector. Experimental results based on real radar data obtained from multiple human subjects demonstrate the effectiveness of the proposed approach in classifying arm motions.