The fractal compression technique had been growing rapidly during the past two decades. It is mainly studied on images. Many researchers had studied and improved the fractal image encoding and had gotten a lot of achievement. The greater success of this method when applied to images encouraged several researchers to explore its applicability on other types of data (such as on audio data). So, one can consider the fractal audio compression as an advanced step in the life cycle of the fractal coding. However, the earlier few researches in fractal based audio compression has left a great bruit about this method, primarily its long encoding time even for small audio files. So the core of this book is speeding up the encoding time by employing the moment descriptors concept to index the blocks of the domain and range pools