The student demonstrates a strong understanding of the mathematics associated with Fourier analysis as it pertains to image compression, ensuring that all included mathematics is relevant to the research. The student effectively explains subject-specific terms and concepts, enhancing comprehension for both knowledgeable readers and those less familiar with the topic. Additionally, the student integrates sources appropriately, commenting knowledgeably on their relevance, and demonstrates clear communication of mathematical operations, providing detailed steps that allow readers to follow along easily. Overall, the essay is structured and accessible, with well-explained terminology and definitions aiding in the reader's understanding of the subject matter.