Digital sound
Unlike the analog signal, the digital signal does not simulate acoustic sound.
Digital sound assigns digital values to individual points in time that reflect the height of the amplitude at a given point. The second difference between digital and analog audio is that digital audio is discrete.
As you know, digital information is stored in bytes, each of which consists of 8 bits. A bit is the smallest unit of digital information that can take only two values: zero or one.
So how do you convert a continuous analog signal into a sequence of zeros and ones, and even link this information correctly to the timeline? Converting audio to digital format is divided into two operations: sampling and quantizing. Sampling – sampling and quantization time – amplitude. It is these operations that your audio interface performs.
Any audio interface has an ADC (analog-to-digital converter) and a DAC (digital-to-analog converter). Let’s consider how audio recording works when used to record a microphone and a computer with an audio interface attached.
When you speak, your voice creates fluctuations in air pressure, which the microphone picks up and translates into an alternating voltage electrical signal. The received electrical signal is very weak, so it is amplified and then sent to the audio interface for digital conversion. Based on its internal clock, the ADC divides time into many different points. Time sampling occurs according to the set frequency, which indicates how many dots will be divided by 1 second of sound. At each received time point, the ADC measures the voltage of the input signal and assigns the corresponding digit to the amplitude value. The data obtained as a result of this conversion can be saved on a computer.
Digital sound
When you start playing the audio file, the reverse process will start. The digital information will be sent from the computer to your audio interface. Your DAC will provide a reverse conversion of the received information into a continuous electrical signal with alternating voltage. The signal will then be amplified and reproduced through your speaker system.
So what is the sample rate to get digital sound that can then be converted back to analog? According to Kotelnikov’s theorem, each band-limited signal can be sampled and then recovered in digital form, as long as the sample rate is at least twice the highest frequency of the original signal.
This means that our signal must have a maximum frequency that will never be exceeded. When we set the highest frequency, all that remains is to multiply it by two and get the desired sample rate. Also, according to the theorem, all frequencies above half the sample rate must be removed from the input signal.
Since a person hears sounds from 20 Hz to 20 kHz, a sample rate of 40 kHz should be adequate to encode any sound audible to a person. With a small margin for the filter, which is calculated before converting to digital format, in the CD audio standard, sounds above 22,050 Hz are cut off and the sample rate is 44,100 Hz.
Now let’s see exactly what numbers the ADC assigns to the amplitude values when converting an analog signal.
The computer can assign a finite number of values to the amplitude. As mentioned above, any information in a computer is a sequence of bits, each of which takes on values of zero or one.
A numeric expression of n bits assumes 2 n different variants of values, that is, 2 n different variants of sequences of zeros and ones. The table shows the sequence options for n = 2,3,4.
