Bit depth and sample rate
The first thing to understand is that bit depth and sample rate only exist in digital audio.
In digital audio, bit depth describes amplitude (vertical axis) and sample rate describes frequency (horizontal axis). So increasing the number of bits we use increases the resolution of the sound’s amplitude, and increasing the number of samples per second increases the resolution of the sound’s frequency.
In an analog system (the natural world), the audio is continuous and smooth. In digital systems, smooth analog waveforms can only be roughly sampled and limited to a certain amplitude range. When sampling a sound, the audio is divided into small segments (samples) that are fixed at an amplitude level. The process of correcting a signal to a certain amplitude level is called quantization, and the process of creating a sample segment is called sampling.
In the graph below, a natural sine wave is displayed for up to 1 s, starting from 0 and ending at 1 s. The blue bars represent approximations of the digital quantization of the sine wave, and each bar is a sample, clipped to the approximate available amplitude level. (Of course, the graph is more incomplete than reality).
Depending on the choice made during recording, an audio of 1 s duration can have samples of 44.1K, 48K and, in the case of 24 bits, contains an amplitude level of -144 dB at 0 dB (- 96dB to 0dB for 16bit). The dynamic range resolution (the number of amplitude level units that can be used for a sample, ie the number of rectangles displayed) is 65536 at 16 bits and 16777216 at 24 bits.
Therefore, increasing bit depth can greatly improve amplitude resolution and dynamic range. So where does the increase in dynamic range appear? Since the amplitude cannot exceed 0dB, the added dB is distributed to samples with smaller amplitudes. So one can hear more small sounds (such as a reverb track stretching at -130dB) that would cut off at 16 bits, -96dB.
round and discard
In digital audio, each sample is analyzed, processed, converted to audio, and then played through speakers. When a sample is processed in your DAW (gain, distortion, etc.), they go through basic multiply and divide operations that allow you to change the digital representation of the sample. Very simply, if we don’t do the rounding process (the 1dB gain must be multiplied by 1.122018454), even 8 or 4 bits of sample precision will exceed the 24-bit space.
So since we only have 24 bits, these long numbers need to fit in this space. To do this, the DSP rounds or discards the least significant bit (LSB, the last digit in the number of bits, for example, the 16th digit in a 16-bit sample). Rounding is fairly straightforward and uses algorithms that you are familiar with. Discard discards the information after the least significant bit without analysis.
Both processes have certain errors, they will introduce errors into the equation, these errors accumulate through signal chain processing and are eventually reflected. On the plus side, the LSB is the digital bit with the smallest amplitude, so the error occurs at -96dB for 16-bit samples and -144dB for 24-bit samples. At the same time, the different structures and methods of digital signal processors will also lead to different results.
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