Coronary artery disease (CAD) has recently emerged as a predominant source of morbidity and death worldwide. Assessing the existence and severity of CAD in people is crucial for determining the optimal treatment strategy. Currently, computed tomography (CT) delivers excellent spatial resolution pictures of the heart and coronary arteries at a rapid pace. Conversely, several problems exist in the analysis of cardiac CT images for indications of CAD. Research investigations employ machine learning (ML) and deep learning (DL) techniques to achieve high accuracy and consistent performance, hence addressing existing restrictions. This research proposes convMixer with median filter and morphological operations for the classification of the coronary artery disease from computed tomography angiography images. A total of 5,959 CT angiography images were used for classification. The model achieved an accuracy of 96.30%, sensitivity of 94.39%, and specificity of 99.16% for combination of the morphological operations and convMixer, 88.92% of accuracy and 89.56% of sensitivity, and 93.10% of specificity for the combination of median filter and convMixer and 94.63% of accuracy, 95.82% of sensitivity, and 93.10% of specificity for convMixer. The findings indicate the viability of automated non-invasive identification of individuals necessitating invasive coronary angiography images and maybe future coronary artery operations. This may potentially decrease the number of people who receive invasive coronary angiography images. Lastly, post-image analysis was conducted using DL heat maps to understand the decisions made by the proposed model. The proposed integrated DL intelligent system enhances the efficiency of illness diagnosis, reduces manual involvement in diagnostic processes, supports medical professionals in diagnostic decision-making, and offers supplementary techniques for future medical diagnostic systems based on coronary angioplasty.