Frequency used for audio (sample rate, PCM, DSD, etc.)

On this occasion, I would like to explain the frequencies used in digital audio and their meanings.

Recently, the high-resolution sound source has increased, such as 192KHz Toka, 11.2MHz, as the frequency has been written or will, what frequency?
I would like to explain the frequency used for said audio taking as an example the Combo384 installed in the USB-DAC used in LV2.0.
1. 1. What is the sampling frequency?
Music distribution is becoming mainstream these days, but audio was first digitized on CDs, which are still on the market.
You often hear that the sample rate of a CD is 44.1 KHz. Since digital signals are basically 0 or 1, to reproduce up to the 20 KHz limit that can be heard by the human ear, a resolution of twice that frequency is required. Furthermore, the frequency was decided to be 44.1 KHz taking into account the digital signal processing margin. Since a music signal is a set of sine waves, it is 44.1 KHz that can fluctuate at a maximum frequency of 20 KHz.
2. What are 16 bits and 24 bits?
As you may hear often, CDs are sometimes described as 44.1KHz / 16bit. This 16 bit is the volume of the sound. Since 16 bits can express the size of 2 raised to 16, there are 65536 different sizes.
Converting this to dB is 20LOG (65536), which is approximately 96 dB. The dynamic range of a CD (the difference between low and loud sounds) is 96 dB.
For DVD and Hi-Res, it can be 24-bit, but in this case, it’s 16.77 million steps of 144 dB.
3. 3. PCM format
So what is the actual signal? In the case of the PCM format, the standard called I2S, which can support up to 32 bits in sample rate, is common. In the case of a CD, being stereo, the data has a frequency of 44.1 KHz with 2 channels (L, R) alternately of 32 bits (although in reality 16 bits are used).
Therefore, to process this digitally, a processing capacity of 44.1KHz x 2CH x 32bit = 2.8224MHz is required.
Let’s actually look at the output of COMBO384.
image049
This is a signal that the yellow is called 2CH (L · R) are switched LRCLK (or FSCLK), the LR set 44.1KHz has been sent to each.
The blue color below is divided into 32 bits by the DATA line, and DATA L and R are output.
4. COMBO 384 audio
Looking at the COMBO384 instruction manual
image021
The first thing that stands out is the OSCILLATOR SG (oscillation) item, which lists two types of frequencies.
They are 24.5760MHz and 22.5792MHz.
COMBO384 is equipped with these two as reference frequencies for audio.
5. Master clock
The reference frequency mentioned above is called the master clock. In the schematic, it is written as MCLK.
Let’s take a look at the actual waveform.
image033
MCLK 22.5792 MHz
image031
MCLK 24.5760 MHz
[Caution] Due to the frequency bandwidth performance of the oscilloscope, it is displayed as a trapezoid, but it is actually a square wave.
The difference between the two is due to the difference in the format of the music played.
From the left 22.5792MHz is, CD (44.1KHz when playing), the right side of the 24.5760MHz is, DVD (48KHz) when playing.
In digital processing, it is easy to reduce this reference frequency (master clock) to 1/2, 1/4, etc., but creating a completely different frequency is problematic. Reducing the frequency to 1/2 in this way is called frequency division.
Now let’s divide.
22.5792 MHz / 32/2 = 352.8 kHz
22.5792 MHz / 2 = 11.2869 MHz / 32/2 = 176.3 kHz
22.5792 MHz / 4 = 5.6448 MHz / 32/2 = 88.2 kHz
22.5792MHz / 8 = 2.8224 MHz / 32/2 = 44.1 kHz
24.5760 MHz / 32/2 = 384 kHz
24.5760 MHz / 2 = 12.288 MHz / 32/2 = 192 KHz
24.5760MHz / 4 = 6.144 MHz / 32/2 = 96 KHz
24.5760MHz / 8 = 3.072 MHz / 32/2 = 48 KHz
What about that. I think the frequencies that I have seen have come out.
/ 32/2 is for the 32-bit LR2 channel that came out earlier.
On the left side, you can see that the frequency comes from the CD’s 44.1KHz.
The right side is the 48KHz based frequency used in DVD and broadcast.
Also, although the method is different from PCM, the number on the left appears as the DSD sample rate, so you can see that it is based on CD.
DSD64 2.8224 MHz, DSD128 5.6448MHz, DSD256 11.2896MHz DSD512 22.5792MHz
All of these are based on this master clock frequency.