Electronics Project:Audio file compression

   Audio file compression using different techniques:

              The compression of digital audio data is an important topic. Compressing (reducing) the data storage requirements of digital audio allows us to fit more songs into our memory and download them faster. We will apply ideas from interpolation, least-squares approximation, and other topics, in order to reduce the storage requirements of digital audio files. All of our approaches replace the original audio signal by approximations that are made up by a linear combination of cosine functions.

Large storage requirements limit the amount of audio data that can be stored on compact discs, flash memory, and other media. Large file sizes also give rise to long download times for retrieving songs from the internet. For these reasons (and others), there is considerable interest in shrinking the storage requirements of sampled sound.

• ·         Least-squares data compression:

              Least-squares data fitting can be thought of as a method for replacing a (large) set of data with a model and a (smaller) set of model coefficients that approximate the data by minimizing the norm of the difference between the data and the model.

• ·         Digital filtering:

              The DCT algorithm can be used to not only interpolate data, but to compute a least-squares fit to the data by omitting frequencies. The process of computing a least-squares fit to digitized signals by omitting frequencies is called digital filtering. Digital filtering can reduce the storage requirements of digital audio by simply lopping off parts of the data that correspond to specific frequencies. Of course, cutting out frequencies affects the sound quality of data. However, the human ear is not equally sensitive to all frequencies. In particular, we generally do not perceive very high and very low frequencies nearly as well as mid-range frequencies. In some cases, we can filter out these frequencies without significantly affecting the perceived quality.

             Digital filtering is an effective technique for compressing audio data in many situations, especially telephony. Cutting out entire frequency ranges is rather a brute-force method, however. There are more effective ways to reduce the storage required of digital audio data, while also maintaining a high-quality sound. One idea is this: rather than cutting out “less-important” frequencies altogether, we could store the corresponding model coefficients with lower precision - that is, with fewer bits. This technique is called quantization. The “less-important” frequencies are determined by the magnitude of their DCT model coefficients. Coefficients of small magnitude correspond to cosine frequencies that do not contribute much to the sound sample. A key idea of methods is to focus the compression on parts of the signal that are perceptually not very important.