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For any industry the efficiency and performance of rotating machinery/mechanical systems is a major concern. Bearings and gears are two essential parts in a rotating machinery and any defects in these components can lead to a major breakdown of the system thus causing large economical loss for the company. An appropriate machine condition monitoring system is essential in such scenarios for identifying the health of the machines. Therefore in this paper fault diagnosis of rotating mechanical systems is performed as a feature dependent-pattern classification problem. The machine is made to run in different good as well faulty conditions and the vibration signals are collected. Then chebfunction coefficients are extracted from the vibration signals as part of the feature extraction process. Finally, the extracted features are classified using regularized least squares (RLS) for identifying the good and faulty bearing as well as gear conditions of the machine. The evaluations are performed using different kernel functions and the average accuracy reported is 98% for bearing and gear data. The various experiments performed claims that the proposed system can be used for real-time fault diagnosis in rotating mechanical systems with sufficient accuracy.