Applying Nyquist theorem to digital vs. analog audio quality

I had a recent conversation with a friend about analog vs. digital recordings. He shared his opinion that music recorded by analog techniques is of superior sound quality to music recorded by digital techniques. His reasoning was that whenever music is turned into digital, not all of the information is captured, and thus, some of the music is lost.

I was not too sure about his statements as I recently took a DSP course and learned a bit about the Nyquist-Shannon theorem. As human hearing is typically in the range of 20 Hz to 20 kHz, I was under the impression that the common sampling rate of 44.1 kHz should be enough to capture all information that is needed to reproduce the sounds that we can hear. Therefore, I thought that differences between music reproduced from digital and analog should unnoticeable to human ears.

Who is correct? If anyone, could shed some light on this and clear up any misunderstandings, I would greatly appreciate it. Thank you very much.

By the way, I am new to Stack Exchange, and I have already tried to find similar questions but to no avail. Hopefully, this is not a repost.

my judgement is a little more polemic than Fat's or hot's judgement.

given the resolution of present-day ADCs and DACs, I believe that there is no reason that the best analog recording can compare to a digital recording in faithfully capturing the original sound.

ADCs and DACs nowadays have 24-bit words with an honest 20 or 21 bits. that is, the dynamic range of the audio (which is the sum of the dB of headroom plus dB of S/N) in a digital recording is about 125 dB. i just do not think you can get close to this with even the highest-quality analog recording gear.

regarding frequency response, the analog recording can get better and better with higher tape speed. like 15 inches per second. the counterpart for digital recordings is sample rate.

in my opinion, a recording good 24-bit converters running at 96 kHz, played back through really good and linear amplifiers and speakers can be indistinguishable to a blindfolded listener than the original. having a bandwidth up to nearly 48 kHz and an honest 125 dB dynamic range is pretty goddamn close to a wire. i don't think an analog recording environment recording the same source and played back through the same amplifier and speakers is within even 20 dB of that.

and when you compare equal transparency and cost, there is no way that analog can compete with digital. if you want something pretty clean and reasonably cheap, you cannot get both with analog recording.

that said, i sorta understand what people mean regarding that "warm analog sound" and, because i do not believe in magic, that warm analog sound is a mathematical phenomenon. might have something to do with vacuum tube characteristics. if we understood the math well enough, we should be able to emulate that warm analog sound within the DSP chain. we're getting closer and closer.

• Most people who complain about digital audio do actually refer to compressed audio phenomenon. And somewhat they are right, a naive attempt at "saving bitrate" inadequately will result in an unpleasant audio, defeating the main reason for listening; its pleasure. Yet analog is a headache whose cure is avoding as much as possible. Nevertheless the mics and speakers are affecting the audio "feeling" more than anything else, and they are currently analog that we cannot avoid yet... :) – Fat32 Jun 25 '17 at 12:29
• that's true, Fat. lossy compressed audio is, decidedly, not as clean as 24-bit, 96 kHz PCM. – robert bristow-johnson Jun 25 '17 at 18:41

The Nyquist-Shannon reconstruction theorem applies to perfectly bandlimited signals and perfectly flat reconstruction filters. Unfortunately, neither exists in the real world. Nor do digital system that use an infinite number of bits per sample to avoid quantization noise.

The headroom allowed by using higher sample rates than 44.1k may allow a closer approximation (for the bandlimit and reconstruction filter response) to the required perfection. So does using more bits than 16 to reduce quantization noise.

But analog recording is also not perfect, as noiseless analog recording media and head amplifiers do not exist (because of the existence of atoms and non-zero K temperatures).

So there can be a trade-off. Choose your preferred sounding reproduction artifacts(s).

• boy, hot, i dunno if i wanna jump into this with $\approx \tfrac{1}{3}$ the rep you have. but there are some things you're saying that lead to misconception. maybe i'll write my own answer, but like Fat says, "there is no short answer." – robert bristow-johnson Jun 25 '17 at 5:46

There is no short answer. When properly implemented the digital audio should preserve the inital available quality of the captured audio in addition to providing incomparable persistency of the recorded data. Digital information is mathematically represented, whereas analog is physically. This's the reason why digital is preferred over analog formats. Capturing, storage, transmission and playback are the most important issues related with audio, and digital audio provides most convenient solutions. Nevertheless analog has advantages too, such as early simplicity or being low power.