Please note that this post uses the phrase Nyquist theory and not Nyquist theorem. The Theory from a mathematical point of view is probably correct (I am not qualified to say). However, this post aims to show that there could be reasons to question its use in real-world applications. So what is the Nyquist Theory?
The Nyquist theory states that a periodic signal must be sampled at more than twice the highest frequency component of the signal. In practice, because of the finite time available, a sample rate somewhat higher than this is necessary.
In digital audio, 44,100 Hz (alternately represented as 44.1 kHz) is a common sampling frequency. Analog audio is often recorded by sampling it 44,100 times per second, and then these samples are used to reconstruct the audio signal when playing it back. The 44.1 kHz audio sampling rate is widely used due to the compact disc (CD) format, dating back to its use by Sony in 1979.
The CD sampling rate has to be larger than about 40 kHz to fulfill the Nyquist criterion that requires sampling at twice the maximum analog frequency, which is about 20 kHz for audio. Red Label CDs are thus set at 44.1kHz/16-bit. The definition of hi-res audio states that any music file recorded with a sample rate and bit depth higher than this.
High-Resolution Audio is audio that uses a higher sampling rate than red-label CDs and MP3s for the encoding and playback of music. Higher sampling rates mean that more samples per second were taken when the original analog sound was converted into digital.
High-Resolution Audio files have a sampling frequency of at least 96 kHz/24 bit, which is significantly higher than the 44.1 KHz/16-bit sampling frequency of CDs.
Nyquist theory and high-resolution audio
Here are some salient points that relate to the real-world application of the Nyquist theory
The difficulty with the Nyquist-Shannon sampling theorem is that it is based on the notion that the signal to be sampled must be perfectly band limited. This property of the theorem is unfortunate because no real-world signal is truly and perfectly band limited. In fact, if a signal were to be perfectly band-limited—if it were to have absolutely no energy outside of some finite frequency band—then it must extend infinitely in time.
1) Nyquist died in 1976. CD was invented in 1982. It is unlikely that Nyquist foretold all of the technical and engineering issues associated with creating a CD set at 44.1 kHz. In other words, there are good reasons to question the real-world applications of the Nyquist theory
2) There are many sounds that we may not be able to hear – but we may, in theory, feel or register subconsciously e.g. strong subterranean bass. These can be included if we expand the dynamic range recorded.
3) In practice there are aliasing artifacts near the limit of the filter, with less computationally complex filters having worse aliasing. These filters affect sound quality. When you’re designing your anti-alias filter it means that you simply cannot set the cutoff frequency to the Nyquist rate. So, the point of a higher sampling rate used in digital video is to buy enough headroom for simple filters to operate without introducing audible artifacts.
4) The Nyquist Theory states that to get an accurate signal, the sample rate must be at least twice the highest frequency. It fails to say how much more than twice it needs to be. Therefore, the theory provides a useful guide
5) If we do a split A/B listening test using very good equipment between a red-label CD and a very high-resolution recording of the same music (SACD, for example), many people can hear audible differences.
6) Some people have better hearing than others. There is some speculation suggesting that sounds that we can NOT hear consciously could be picked up subconsciously. extremely low and powerful bass can physically move floorboards etc. So limiting sounds to simply what we can hear is inherently not always a good idea as we are denying other senses.
7) 48 kHz is, in principle, a better rate than 44.1 kHz since it is a multiple of the other standard sampling rates, namely 8 and 16 kHz for telephone-quality audio. If you want to capture all of the sounds accurately, a higher sampling rate would obviously be better.
8) The red-label CD rate was good at the time of its creation (1982) – however, technology has improved since then. Fast broadband internet now means audiophiles can download high-resolution audio files easily. So, why would you want an inferior product anyway?
9) DACs have improved massively in recent times. It is now possible to buy resister-ladder DACs that have all the benefits of Analog sound and none of its drawbacks.
10) Streaming has changed the way many people listen to music. There simply isn’t a need for a CD player or a turntable. Digital audio files have opened up new ways to listen to music. I have a Synology DS 220+ NAS drive connected to a Cambridge Audio CXA81 amplifier and Q Acoustics speakers. My NAS stores many albums in FLAC files…
The Nyquist theory is probably correct in terms of pure mathematics. I am not good enough at mathematics to really know. However, in terms of creating recorded digital audio files, it is questionable. It seems to me to make perfect sense to keep as much of the original recording as possible and to also include space for the filters and relevant metadata (titles of tracks, names of artists, dates composed, art covers, etc.).
In other words, high-resolution audio is better than the standard CD. Whether people can hear the difference is another issue. That is very much dependent on other factors such as 1) How good your hi-fi system is and 2) How good your hearing is, etc. CD quality will thus be good enough for many people. For more information on high-resolution audio, please click here.
Listening to High-Resolution Audio allows you to pick up on the subtle details and nuances that you would hear in a recording studio. So, if you’re waiting to get your hands on Adele’s newly released album, “25”, try listening to it in high resolution. It’ll sound like you pulled up a stool next to the British diva, allowing you to hear every note of her soulful, impressive range.