digitaltoana
Table of Contents
1 Main concepts
We describe an analogous signal using sample rate and bit depth. These two parameters define the analog to digital conversion that we are using. In short the sample rate determines how the frequencies are described digitally while the bit depth determines how the volumes are described digitally. Let's say that we want to describe digitally, and thus with an array of values, a continuous curve.
1.2 Sample rate
The sample rate is the inverse of the distance between two sampling points. The higher it is the nearer the two points will be. In order to describe properly the curve we need to have a sufficiently high sample rate. For an audio CD the sample rate is of 44.1 Kilohertz.
1.3 Bit depth
In order to describe a physical signal we need to know what we are measuring and, in particular, the scale that we are using. Dealing with an audio signal the altitude of the curve will describe the volume of our signal. In order to represent it we need to choose a scale for the volumes. The range of volumes that we can describe is the bit depth. If we have an higher bit rate we have more different volumes avaible for the sound that we want to describe, i.e. we can better approximate the current volume. The higher the bitrate the more accurately we can communicate how loud the volume of the real sound was before the conversion. In a more scientific way the bit depth is the amount of computer bits used for each plane wave composing the spectrum that you are hearing (8 bits, 16 bits, 24 bits and 32 bits).
1.4 Bit rate
The bit rate describe the speed at which the data need to be processed to play the audio file: 320 Kbps MP3 means that 320000 bits are processed per second. The bit rate can be obtained from the bits depth, the number of bits per sample wave, multiplied for the sample rate multiplied for the number of channels (mono, stereo…). For example if we need to play an audio CD:
| bits depth | sample rate | number of channels | bit rate |
| 16 | 44100 | 2 | 2 × 16 × 44100 = 1411200 |
1.5 Why 24 bit depth elaboration is important even for 16 bits audio signals
If you have a digital volume control set to 10% two adjacent samples: 41 and 48 will be scaled to 4.1 and 4.8. In a 16 bits song this is truncated to 4 loosing the differences between these samples.
1.6 An important theorem…
The Nyquist-Shannon sampling theorem states that a sample rate that is twice the highest frequency of the signal is sufficient to describe it completely with its analogous description. We are actually using the result of this theorem to choose the sampling rate of the CDs. In fact most humans (?) can hear from 20 Hertz to 20 KiloHertz, therefore, choosing a sample rate of 44.1 Kilohertz we are sure to get perfectly the part of the audio signal that we can actually hear.
