44100 Hz encoded in 24bit vs 16bit

Question

I'm learning the basics of audio recording and mastering and I was thinking to some of my purchased audio collection. I have some assumptions that I feel may be incorrect or incomplete and would like clarification.

It seems that as defined by the CDDA Red Book, CD quality is 16 bit with a maximum sample rate of 44.1 kHz. I understand 44.1kHz was chosen due to human hearing limitations so I assume 16 bit was chosen as the smallest encoding rate that can handle that sample rate vs acceptable data storage size (physical CD and play time).

As such, at sample rates greater than 44.1 kHz, is it fair to say that 16 bit cannot handle that amount of data being encoded?

Also, it seems that the higher the bit rate when mastering, the larger the dynamic range and the greater the reduction of degradation of audio when mixing different sources together. However, the intricacies of mixing down to a lower bit rate confuse me.

If the same master source is mixed down to 44.1 kHz, what benefit is there to using 24 bit rate encoding over 16 bit?

I assume at a digital level this is simply information stored in a file / physical media, so I would have assumed the the actual playback frequency of 44.1 kHz would be identical in both bit rates, except that the 24 bit rate would just have more data storage size (i.e. a bigger file size) with I assume mostly empty or padded data since the extra bits are not needed for such a small sample rate.

That said, it seems like in audio forums, many people anecdotally swear that 24 bit encoding even with a 44.1 kHz sample rate has a larger dynamic range over 16 bit. I get that good mastering (dithering etc) has probably the most impact, but I'm curious if this holds up from a 1s and 0s point of view.

Answer 1

It seems that as defined by the CDDA Red Book, CD quality is 16 bit with a maximum sample rate of 44.1 kHz. I understand 44.1kHz was chosen due to human hearing limitations so I assume 16 bit was chosen as the smallest encoding rate that can handle that sample rate vs acceptable data storage size (physical CD and play time).

The CDDA specification has a bit of history behind it. Two companies cooperated on creating the CD format: Philips and Sony. Each had their own ideas: Philips was working on a disc with 11.5 cm diameter (the same size as the diagonal of a Philips Compact Cassette), 14 bit resolution and 44 kHz sample rate. Sony was working on a 16-bit system with a 1-hour play time. One hour was felt to be slightly too short, which led to 12 cm diameter and 74 minutes of play time.

• the sample rate determines the highest frequency that can be encoded. You're correct in saying that the limit of human hearing (plus a small margin, to allow for analog filtering above 20 kHz) led to a sample rate slightly more than 40 kHz. The 44.1 kHz figure was chosen because this enabled the use of unmodified U-matic video recorders to store the digital recording (master): at this sample rate, 6 samples fit in each line of video.

• the bit depth is the resolution of each sample, which determines the dynamic range. Philips initially wanted 14 bits (and was already working on 14-bit DA converters), Sony was working on a 16-bit system. The first Philips CD-players used those 14-bit DACs running at 4x the sample rate ('oversampling'). 16 bits was on the edge of what was possible in those days.

Sample rate, bit depth, error correction and disc size combine to give a maximum play time.

As such, at sample rates greater than 44.1 kHz, is it fair to say that 16 bit cannot handle that amount of data being encoded?

Um, no. The two are independent. You can do 16-bit sampling at any frequency you want (as long as the hardware can physically keep up).

If the same master source is mixed down to 44.1 kHz, what benefit is there to using 24 bit rate encoding over 16 bit?

It gives you more flexibility in setting levels during recording. For audio consumption, 24-bit offers little to no benefit.

I assume at a digital level this is simply information stored in a file / physical media, so I would have assumed the the actual playback frequency of 44.1 kHz would be identical in both bit rates, except that the 24 bit rate would just have more data storage size (i.e. a bigger file size) with I assume mostly empty or padded data since the extra bits are not needed for such a small sample rate.

No. You assume that bit rate and bit depth are related when they're not. A 24-bit file will have 24 bits of information per sample, no padding.

That said, it seems like in audio forums, many people anecdotally swear that 24 bit encoding even with a 44.1 kHz sample rate has a larger dynamic range over 16 bit. I get that good mastering (dithering etc) has probably the most impact, but I'm curious if this holds up from a 1s and 0s point of view.

Basically, you gain 6 dB of dynamic range for every bit you add. 16 bit = 96 dB, which is already far more than you can appreciate in even a high-end listening room with thick concrete walls to block any outside sound: the noise floor will be at the limit of your hearing, and the loudest sound that can be encoded is well into 'hearing loss if you're exposed for more than 15 minutes' territory. Going to 24 bits gives more dynamic range, but you can't use that in just about any situation.

Answer 2

The theory around sampling contains quite a bit of mathematics. Leaving that aside, let us look att the practical aspects of your questions.

In practice, today, there are only two effects of sample rate and bit depth when talking about the delivery format of audio. It can be different in the preparation stage, say when mixing.

Sample rate limits the highest frequency the recording can contain. It is in practice slighly less then half the sample rate. 44.1kHz sample rate limits to around 20kHz. 96kHz to perhaps 45 kHz. In practice, with quality equipment, your ears cannot hear any difference going above 44.1 kHz.

Bit depth in practice only defines what is known as the maximum S/N ratio. This is, simplifed, the difference between the strongest signal you can have and the noise floor of the signal. Simplified (the math is quite interesting, but I will leave that out of here), 16 bit gives about about 96dB and 24 bits about 144 dB. Your ears will hear this as the noise in quiet passages. The effect of dithering as you mentioned is to make the noise less disturbing to your ears. Now, even 96dB is an extreme large range, and you will need extremely good circumstances to be able to hear the difference as compared to 24 bits.

As such, at sample rates greater than 44.1 kHz, is it fair to say that 16 bit cannot handle that amount of data being encoded?

There simply is no connection. Sample rate and bit depth are totally unrelated.

If the same master source is mixed down to 44.1 kHz, what benefit is there to using 24 bit rate encoding over 16 bit?

First, bit rate is actually sample rate x bit depth. Bit rate is more often used in destructive compression of sounds, say in mp3 files.

The answer here is that it most probably is a very, very slight benefit. For most users no difference. The difference is a decrease in noise floor, but most of the time you cannot really hear the noise anyway.