The differentiation and the integration of products are the essential procedures for product innovation. To understand the product innovation, the approaches using S-curve theory, which explain the evolution of a technological system, have been effective. However, the S-curve theory has the disadvantage that the validity of the analysis depends greatly on the number of data. In this paper, we propose a novel method for measuring and predicting the technological innovation and the product evolution based on the S-curve and wavelet transform to solve the problem. In order to confirm the effectiveness of the proposed method, we will conduct a case study using patents of air purifiers. Furthermore, we will define and support the differentiation and the integration of the mechanical structure using the proposed method. Our analysis shows that the differentiation and the integration of the mechanical structure occur as a life cycle extension after the main technologies enter the declining phase. Therefore, the incidental technologies should be introduced at the beginning of the declining phase of the main technologies.