The paper presents an investigation into a time-frequency (TF) method for extracting features from the electroencephalogram (EEG) recorded from subjects performing imagination of left- and right-hand movements. The feature extraction procedure (FEP) extracts frequency domain information to form features whilst time-frequency resolution is attained by localising the fast Fourier transformations (FFTs) of the signals to specific windows localised in time. All features are extracted at the rate of the signal sampling interval from a main feature extraction (FE) window through which all data passes. Subject-specific frequency bands are selected for optimal feature extraction and intraclass variations are reduced by smoothing the spectra for each signal by an interpolation (IP) process. The TF features are classified using linear discriminant analysis (LDA). The FE window has potential advantages for the FEP to be applied in an online brain-computer interface (BCI). The approach achieves good performance when quantified by classification accuracy (CA) rate, information transfer (IT) rate, and mutual information (MI). The information that these performance measures provide about a BCI system is analysed and the importance of this is demonstrated through the results.