Fourier Transforms in Image Compression: How Math Powers JPEG and MP3 Files

The use of Fourier Transforms for Image and Audio Compression is described in the research paper, specifically for their applications in JPEG and MP3. Compression of images removes redundant data, optimizing storage and transmission effectiveness, while compression of audio limits the inaudible frequencies in order to retain perceptual quality. The study cross-checks the mathematical foundation of the Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT), founded on their performance in converting components of signals into frequencies for purposes of compression. Two databases, an audio (Royalty-Free Audio) and an image (Live1-Classic5-BSDS500) database are used. Fourier-based compression techniques are employed by research study. The performances are verified using measures such as Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM). Outcomes indicate that increased compression ratios reduce file size without sacrificing sufficient quality, and that SSIM will increase with increasing Bits Per Pixel (BPP). The article identifies Fourier Transform-based compression as the best way to reconcile data reduction with perceptual/aoustic accuracy. Additionally, the research identifies current gaps in terms of areas of future work such as AI-improvement and live optimization on power-constrained hardware.