Analyzing the efficacy of the FFT in Image Denoising and DigitalWatermarking

Abstract: The FFT has been a staple in the field of mathematics and computer science for almost 60 years. And yet, it still endures as an efficient algorithm in a multitude of fields. However, as significant technical advances has been made since its inception the demand on methods constantly get higher and higher, and the FFT is seldom enough to solve the problems of this day and age on its own. So how does the FFT perform on its own with today’s standards? This thesis aims to use the FFT to create two algorithms, an Image Denoising algorithm and a Digital Watermarking algorithm respectively, and analyse the efficacy of the algorithms with today’s standards. The results showed that the FFT on its own competently tackles problems well, however with increased demands on the algorithms, the limitations of the FFT became apparent. This underscores the prevalent trend of integrating the FFT with other specializedmethods, ensuring its continued relevance in an era of continuously advancing technologicaldemands.