Raga is an essential element in Carnatic music. It represents a unique melodic framework that defines the mood, emotion, and character of a Carnatic music song. However, the subtle and very minute variations within the ragas can be understood and the raga can be classified only by professionals. The presence of Gamakha which are sudden oscillatory movements in the pitch distribution, is a significant challenge for the automated raga classification system. For the task of automated raga classification and overcoming the challenges in it, the proposed work uses a novel approach using audio signal processing (ASP) and deep learning (DL) techniques. Feature extraction for capturing all the characteristics (pitch characteristics, tonal characteristics etc.) is done and Various deep learning models (Artificial Neural Networks, Long Short-term memory, and Bi-LSTM) are trained to classify ragas accurately. Our method uses the inherent capability of deep learning algorithms to learn subtle but complex patterns and capture the essence of ragas, achieving promising results in the raga classification task. Comp Music dataset for Carnatic music was used for this task and an accuracy of 96.43% was achieved by the Bi-LSTM model which outperformed the other two deep learning models by small margins. A comparison of the current work with previous work is also made.