Let’s proceed in order and start from the sampling frequency, defined as the number of times per second in which our AD converter will measure the electrical signal placed at its input: it is measured in Herz (Hz).
Obviously, the greater the number of “photographs” that we take of our electrical signal in one second, the greater its fidelity to the “original” sound wave. At the same time, obviously, our converter will be obliged to spend a greater amount of “energy” (faster information processing speed, greater storage space, etc.) which therefore translates into a different quality of components and obviously at a higher cost.
Sampling rate
On the left an analog wave (a sine wave) in the time / amplitude domain and an image of Vincent Van Gogh’s “Starry Night” which, for our teaching purposes, we intend to be very high resolution. On the right, a quick reconstruction of the same sampled analog waveform and the same photograph reproduced with a much smaller number of pixels.
Well, if it were that simple, there wouldn’t be a bit of fun. Let’s go back to the diagram of the AD converter at the end of the previous article. Surely you have noticed that the first block through which our signal passes is the so-called “Anti-aliasing filter”, nothing less than a low pass filter.
Coooooooooooosaaaaaaaaaaaaaaaaaa !? Do we want to faithfully reproduce our signal in the digital domain and the first thing we do is pass it through a filter to change its frequency component (remove all components above a certain frequency)?
Yes my dear … you need to share a minimum (but I swear, a minimum) of signal theory to tell you a bit about the “Nyquist-Shannon Sampling Theorem” (for the “fetishists” – no offense, for course …. I am also part of it: of the mathematical treatment, take a look at the related Wikipedia page where you can find a good perspective), based on which, to sample an analog signal without loss of information (that is, to be able to re-enter it – then convert it DA – into the analog domain without “noticeable” differences compared to the original signal) it is necessary that the number of samples taken per second (the sampling frequency) is at least twice the maximum present frequency into the signal to be sampled, Therefore, it is worth introducing frequencies in the digital signal that do not exist in the original analog signal (the calls, and hence the filter name, alias frequencies).
The aliasing phenomenon occurs because we do not have enough samples to describe the trend of the higher frequencies, which are therefore translated into the digital signal as lower frequencies, although nonexistent in the original signal. See this beautiful image always taken from the omniscient Wikipedia. In red the sinusoid sampled at intervals not sufficient to reconstruct it, and in blue the frequency alias (lower) that originates from the points we have taken.
Sampling rate
As we already know, the human ear is sensitive, at most (at an early age and in good hearing health), to frequencies around 20 KHz; In theory, our anti-aliasing filter should be set at 40,000 Hz and that should be our sample rate, but since it is practically impossible to build a filter with such a steep slope in analog, we opted for a filter with less steep slope and so both leaves the signal to sample frequencies slightly higher than 20,000 Hz (which we don’t hear, but there are), sampling at a slightly higher frequency. Therefore, the minimum sample rate used is equal to 44,100 samples per second.
Obviously, technological development and, nevertheless, the opinion and experience of many professionals (which I personally share very modestly) have in any case led to the awareness that, having set the minimum limit of 44,100 Hz (we will see later, it is the sampling frequency of the files that make up an audio CD), sampling at higher frequencies certainly leads to better results both from the point of view of signal manipulation (passing through a plug-in, the sum of two or more signals within a DAW, etc.) and from a listening point of view.
Later we will return to the topic, we will develop it further and we will begin to understand the logic with which the converter assigns a value in “machine language” to the different samples taken during the sampling phase.
