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The process of audio signal classification (ASC) involves the extraction of features from sound and the use of these features to identify the class it belongs to. There are many possible applications for ASC including for example speech recognition, audio database creation and information retrieval, health condition monitoring, audio scene analysis, etc. While relevant features have been well studied and identified for speech signals, they are relatively less studied for other types of audio signals. Considering the fact that different classes of audio signals have their own unique characteristics, the idea of class-dependent feature selection and classification is examined in this paper. In particular, the paper uses a class-dependent method based on a proposed scatter-matrix based class separability ranking measure to select a highly relevant feature subset for each type of the audio signals. An effective training model is also incorporated into the proposed method. The support vector machine with radial basis function kernel is then used as the classifier. Experiments have been conducted on speech and two other types of audio sounds, i.e., coughing and the sound generated when a cup touches a plate or vice versa. Compared to some recently published methods, the proposed class-dependent ASC method requires fewer features and is able to achieve the same or better classification accuracy.