The rolling element bearing is one of the most significant components of any rotating machinery. However, the foremost cause of malfunction in any rotating machine is due to defects like cracks, dents, spall, pits, etc. in ball bearings. Early diagnosis of these bearing faults is highly essential to avoid an accidental shutdown of rotating machinery. In the present work, a novel technique of bearing fault diagnosis is proposed following double decomposition of the vibration activity. The experimentally recorded vibration signals are processed through two stages of decomposition viz. Empirical Mode Decomposition and Tunable Q-factor Wavelet Transform based Time-Frequency decomposition. Subsequently, sub-bands of decomposed time-frequency activity are acquired and discriminable features are computed. Fractal Dimension (FD) based features are extracted from each decomposed sub-band as complexity measures of time-frequency sub-bands. In order to classify bearing faults, a Support Vector Machine classifier is trained with acquired features and classification performance is evaluated. The results of classification reveal that the proposed double decomposition technique is a potential candidate in extracting viable vibration signatures for fault identification. The study is conducted on Case Western Reserve University bearing datasets.