To store any real-world signal in a digital manner, the concern is ?At what point should samples of the signal be taken?? Every sample of the signal must be coded, which takes space on any storage medium. Every sample represents information, which must be processed by some future device in order to recreate the signal. Optimally, the fewest number of samples of a signal that yields the best recreation of the original signal is the optimal solution. This solution allows for the maximum amount of information to be stored on the media used. Fortunately, Harry Nyquist proved Augustin-Louis Cauchy?s sampling theorem in 1928, doing the theoretical work for us. To reproduce any signal without error, it must be sampled at a frequency that is at least twice as great as the highest frequency in the signal. Otherwise, an effect known as aliasing will occur, and add error to our result. To prevent aliasing from arising when we store the quantified signal values, a low-pass filter is used to eliminate frequencies greater than half the sampling frequency. The maximum frequency that can be accurately reproduced through sampling is known as the Nyquist frequency. It is completely dependent on the sampling frequency through Formula 2.
|
|
fs is the sampling frequency. fmax is the maximum frequency in the signal being sampled. |
It turns out that the maximum frequency the most sensitive people can hear is 20 kHz. People with good hearing and young people who don?t listen to too much loud music might be able to hear up to 20kHz, but for most of us our peak frequency is less. The sampling frequency needs to be at least twice that to get the original signal back, then. This yields a sampling frequency of 40 kHz. To prevent aliasing due to imperfect filters, professional recording studios sample at a higher rate of 44.1 kHz. This yields a maximum recordable signal frequency of 22.05 kHz. Any frequencies present in the signal when it is sampled will be aliased back into the signal, reappearing as unwanted noise. Therefor, the recording studios perform very expensive filtering on the signal before it is recorded or before it is sampled for storing in a digital format.