アナログとデジタル
father
Before discussing the encoding of sound, let me explain the difference between analog and digital using a clock as an example. An analog clock represents the passage of time through the continuous rotation of its hands, while a digital clock displays time using numbers. Since the hands of an analog clock move continuously, it is possible to discern the time between minutes by reading the position of the hands to some extent. However, with a digital clock, finer information than the displayed value cannot be determined. If seconds are displayed, one can know the exact time momentarily, but within that one second, there are infinite moments, and it is impossible to express all of them numerically. To represent continuous phenomena digitally, there is a series of processes: first, sampling at certain intervals, then outputting values for each of those segments (quantization), and finally displaying them (encoding).
Oto-kun
Hmm. The term 'digital' is often used, but it refers to values that are taken from continuous phenomena. So, to digitally record music means to sample, quantize, and encode the continuous changes in sound.
father
That's right, when it comes to music, comparing analog and digital is easily illustrated by records and CDs. Records and cassette tapes record sound waves in their original form. The principle of records is fundamentally the same as that of the wax cylinder invented by Edison, where sound waves are etched into grooves in the same shape as the waves, and a needle extracts the sound. CDs, on the other hand, record sound in a completely different way. The sampling interval mentioned earlier regarding the clock is about 23 microseconds, which means 44,100 times per second. This sampling interval determines the upper limit of the pitch of the sound when played back, and signals that include frequencies up to X Hertz should be sampled at a fineness of more than twice that (2X).
Oto-kun
Dad taught me before that the upper limit of what humans can hear is 20,000 Hertz, right? So does that mean that a CD contains all the sounds that humans can hear?
father
That's right, one of the records contains all sounds because it has not been sampled.
Oto-kun
But usually, CDs are said to have better sound quality; why is that?
father
You see, the secret lies in quantization, that is, the process of converting sampled sound into numerical values. Let's draw a little picture. Suppose the original sound waveform looks like this. (Figure 1) This is continuous, so it's an analog waveform. We sample this at 44100 Hertz (44100 times per second). (Figure 2) Then we quantize it. (Figure 3) The width of the waveform during this quantization is represented by integers between -32768 (-2 to the power of 15) and 32767 (2 to the power of 15 minus 1). You may have seen specifications for audio equipment that mention 16-bit or 24-bit dynamic range. The number of bits is represented in binary, so in the case of a CD, there is a range of 2 to the power of 16, which is why it is referred to as 16-bit.
Oto-kun
What does the fact that CDs have better sound quality than records have to do with anything?
father
Regardless of whether the sound is good or not, CDs likely have less noise. The dynamic range of 16-bit audio is about 96 decibels, which is slightly narrower than the range of sound intensity that humans can perceive, but considering the sound being played and the ambient noise (background noise), it is usually wide enough that one can say the noise is at a level that is not audible.
Oto-kun
I have never directly heard the sound of a record, but I have heard the sound of records being played on television. There was a noise that sounded like 'zaa', but that is the difference between CDs and records.
father
That's right, records are great when they're new, but even a small scratch can cause a popping noise. CDs don't have this issue and are convenient because you can easily skip tracks. However, there are still many so-called analog enthusiasts who enjoy the act of placing the needle on a record and the nostalgic sound that comes with it, claiming that records sound better than CDs. The quality of sound is largely a matter of personal preference, so it can't be measured simply by frequency or level.