In this bachelor's thesis, we will define the Discrete Cosine Transform (DCT) and explain the fundamental principles behind its derivation. Additionally, we will explore its two-dimensional extension and demonstrate how to compute the two-dimensional form using the one-dimensional definition. We will provide an example of an algorithm for fast DCT computation, utilizing existing Fast Fourier Transform (FFT) algorithms. Similarly, we will introduce an example of an Integer DCT algorithm that works on simpler arithmetic operations. Furthermore, we will delve into the most common implementation of JPEG compression. We will explain the encoding process, transforming the original image into a bit string for storage and transmission. We will also describe the inverse process, i.e., decoding. To illustrate these processes, we will use an example involving a block of an image. Lastly, we will convert several images into the JPEG format, varying the quality levels, and subsequently assess their quality to determine the most suitable qualities for specific applications.
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