Definition

In digital audio, the bit depth is the number of information bits of each sample and is closely linked to the resolution of the audio. Unlike an analog signal, which is periodic and is composed of infinite points, digital audio is a discrete signal since it is composed of a finite number of points. Use binary numbers (bits) to determine the number of available states to represent the strength of each audio sample and thus represent the signal. “The quality of the representation increases, in general, when this number of states is increased. For example, […] high-fidelity music recording is obtained on a CD with 65,536 amplitude levels. The number of possible states of a binary system of n digits (n bits) is E = 2 ^ n. ” 1. In summary, it is the resolution, in terms of amplitude, that will have a digitized signal. Determine the dynamic range of that signal. In the following image we can see how a signal is represented in 4 bits of depth. 4 bits generate 16 possible values ​​on the vertical axis.

Aspects to consider

The accuracy of each sample is determined by its bit depth. Then, the higher the bit depth, the higher the resolution in the digitized signal. In addition, the greater the bit depth, the greater the dynamic range for the signal because it will have more points to represent the amplitude of each audio sample. It follows that low levels of bit depth can affect the shape of the wave and thus not achieve a good representation of the original wave because there are fewer possible points to represent it. For example, in the following graph we can see a sinusoid represented with different bit depths. A depth of 1 bit will generate a wave more similar to the square wave (depending on the quantification) because we only have two possible points on the vertical axis.

Requirements

A very important aspect to keep in mind is that at greater bit depth we will need more resources to process the audio and more memory to save it. This is because we will have more information. The size of our audio file will be given by the following account:

Bit number * Sample rate * number of seconds duration [* 2 (if stereo signal)]

Then, for example, the size of a second of audio on a CD, which works with a depth of 16 bits and a sampling frequency of 44,100Hz / second will be given by the following account:

1 second = 16 * 44100 * 2 (since it is stereo)

1 second = 1411200 bits (0.1764 Mb)

In sound and audio software and hardware specifications we are often told about processing capacities of up to 96kHz and 64bit operation, but what do these issues really mean? And how do they affect the quality of our sound?

Sample Rate and Frequency Range

The sampling rate is the frequency with which the A / D converter (analog to digital) measures the levels of a signal, the samples are broadly analogous to a series of snapshots. If the converter takes ten samples of the signal every second, it would have a sampling rate of 10 Hz.
The frequency range that an A / D converter (present on a sound card for example) can capture is determined by the sampling frequency, or sampling rate. However, in this there is a strict law that may seem unintuitive: the maximum frequency that can be captured is only half of the sampling frequency. A sampling rate of 10 Hz can capture a maximum frequency of 5 Hz, not 10 Hz. The reason is that, without double the samples of a sound source, some of the oscillations of the signal are lost.
But what happens if there are frequencies higher than the capacity of our sampling frequency in the captured analog audio signal? Aliasing then occurs, phenomena that occur when the highest sampling frequency that has been sampled is higher than the frequencies that can be accurately captured by the A / D converter. Aliasing adds distortion to the audio signal artificially, adding lower frequencies to higher partials. Aliasing can occur in a digital audio system as a result of a poorly designed A / D converter, but you are much more likely to hear it when you play high notes from a software-based synthesizer. If the synthesizer does not use an antialiasing technology, the high notes have the possibility of becoming random groups of tones that have no relation to the key note you are playing.

The researchers at Bell Laboratory are familiar with this problem since 1920 and conceptualized the principle as the Nyquist-Shannon sampling theorem. The theorem is simple: to sample the frequency value of x correctly, you need a sampling frequency of at least twice x. (The maximum frequency at which it can be sampled without aliasing at a certain sampling rate is thus the so-called Nyquist frequency.) So why do we need the sampling rate to be twice as fast as the most frequency? high to be recorded? Because each ordinary period of a waveform includes an upward and a downward oscillation. If the A / D converter takes less than two samples per period, it cannot capture the entire oscillation. In order to capture each “up” and “down” state, you need to take at least two samples from each period. Thus, the sampling rate has to be twice the highest frequency that must be recorded.

According to the Nyquist-Shannon theorem, to sample frequencies that are in the upper limit of the human ear (around 22000 Hz), you need a sampling frequency of around 44000 Hz, which is, not by chance, the rate Normal sampling for commercial audio CDs, 44100 Hz.

This obviously allows you to sample the frequencies from the top of the range of our ear, but what happens when the frequencies of the signal that reach the A / D converter exceed the maximum frequency limit of 22 kHz? They fold into the audible spectrum as distortion, so the A / D converters incorporate an anti-aliasing filter that eliminates these high partials, before the audio is converted to digital format.