Digital Signals and Discrete Signals
We often use the word "digital era" to represent the present age but what on earth is digital? As digital originally means fingers or counting by fingers, digital signals are signal represented by numbers. Objects existing in the natural world such as temperature or velocity are represented as analog or continuous quantity. If we try to represent a quantity in the natural world as a number, we can represent only limited points out of unlimited possibilities. For example, if the least digit of your thermometer is 0.1, it cannot represent 18.63 or 24.93 degree C. Usually you do not care about that because the 0.1 is accurate enough for general use.
Let us consider music CD players. In the music CD, the audio signal is quantized in 16-bit numbers, or the instantaneous values are sorted to 65536 steps. The 16-bit accuracy is based on study results of human ears brought by a field of acoustics and the accuracy itself seldom causes a controversy.
Now, what is the issue? At first, see the following figure.
This figure shows that a sound wave (precisely electric signal representing it) is continuous while the digitized signal is discrete in the time. There are no other methods but the signal is sampled in the time domain at certain points and represented as a set of the sampled signals. The set of samples is called a discrete signal whether the amplitude is quantized or not.
If you click the button located on right side of the "Display Samples" in above figure, a sampled signal appears, and another sampled signal with higher density appears when you click it again. If you watch the analog signal and sampled signals, probably you can find that a peak existing between two contiguous sample points cannot be represented. You can also find that increasing the density of sampling or a smaller sampling period brings a better result. This has been theoretically proved as Shannon's Law: A discrete signal cannot represent frequency components exceeding the half of the sampling frequency.
However, Shannon's low is only a theoretical proof of sampling systems but it is not enough to prove that the music CD perfectly represent music. As some people doubt the accepted theory of acoustics that the maximum audible frequency for human beings is 20KHz, many people has the opinion that the music CD cannot provide musical information enough for human beings.
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