Once the signal is properly filtered, we need to change it back to time-domain, and we do this by using a second transformation function. Now we are able to listen our record, filtered of (any) noise. If we are satisfied with the quality of the recording, we can burn the CD; otherwise, we could repeat the above procedure, until results are exactly what we expect them to be. Digital Signal Processing ends here.

{mosgoogle}Now, we have a CD holding a digital signal--an audio file in this particular case. It happens that our audio digital file takes too many memory bytes to store, and we cannot afford this. We want our digital file to use the smallest amount of memory, so that we can transfer the file quickly over the Internet, or we would like to store as many records as we can in a small MP3 player, for example. For this we need a “compression” technique, and, implicitly, an “encryption” one.

There are very many compression/encryptions methods available, and very many will be developed into the future. Basically, the digital signal is in fact a series of integers--an integer is 2 bytes; one byte is 8 bits; each bit is either 0 or 1--and each integer represents one mathematical value in the range of 0 to 65535. Now, we see that each digit in the range 0 to 65535 is repeated a number of times, in the entire digital audio file. This information is very important, because it helps us to convert our series of integers into a mathematically encrypted structure, by means of a software compression/encryption “key”. Instead of using, for example, the integer 23501 for 1522 times in our digital audio file, we use only the information about that integer, meaning that we store only the value 1522, one single time, corresponding to the integer 23501.

The compression/encryption key--this is in fact another mathematical algorithm--it is responsible for taking the initial digital file and breaking it into frames of integers; for replacing each integer with the number of times it is used; and for storing the code needed to reconstitute the initial series of integers, which is the original digital file. Commonly, the key works with a special memory structure, named a “binary-tree”. In this binary-tree, the position of each number represents how many times an integer appears in the entire file, and it also holds the information needed to reconstitute the frames, and then the entire audio digital file.