post #16 of 16

Reviving an old thread here!

 

There is definitely more to be squeezed from the 16 bit /44.1k format, at least in theory.  Just not economically.

 

The Nyquist/Shannon theory has often been quoted as a justification for the 44.1kHz sampling frequency being sufficient to cover the audible frequency spectrum.  And it is, I have no issues with that.  However, very few audiophiles actually understand this theory.  The original CD architects certainly seem not to have understood, or decided to ignore some aspects.

 

Where this theory has been misappropriated is in the way all CD players and D/A converters reconstruct the digital samples into an analog signal.  Beyond the core statement re. the sampling frequency, the Nyquist/Shannon theory implicitly places very strict conditions on both sampling and reconstruction algorithms, and CD players violate most of them.

 

  • First, during mastering, the minimum sampling frequency required is not double the highest frequency you want to reconstruct, but double the highest frequency present in the source.  This means that (ideally) prior to sampling, the source material needs to be very sharply bandpass-filtered between 0 to 22.05kHz.  Such ideal filters do not exist.  But let's skip over that one for now.
  • Second, the CD player sample-and-hold type reconstruction mechanism is flawed (oversampled or not).  If you want to convince yourself, sample a 20kHz sine at 44.1kHz sampling frequency (e.g. in Excel), and observe the beautiful type of amplitude modulation that results.  CD players will play this back as is.  Not good.  Nothing to do with Nyquist/Shannon being at fault though.
  • One practical (but unaffordable) implementation satisfying Nyquist/Shannon would be reconstruction in the frequency domain rather than the time domain.  This would consist of first appending an (ideally infinite, but practically large number) of zero samples prior to and after the digital samples (the reason this seemingly pointless exercise is required is beyond scope here, but has a mathematical foundation).  Then a Fourier transform (FFT in practice) would be required to transform the digital samples from the time domain to a representation in the frequency domain.  In the frequency domain anything greater then 44.1kHz (or 22.05kHz, I would have to check the math) would need to be filtered out (which is easy, unlike sharp bandpass filtering in the time domain).  Finally you would need as many ideal analog zero-distortion zero-noise harmonic oscillators of definable fixed frequency as there are digital samples in your original signal, each of which would be multiplied by the Fourier transform amplitude at the corresponding frequency, and all would need to be electronically added.  That is about 160 Million oscillators to cover a typical CD (did I mention this would be expensive?).  This whole process is still a much simplified description, and covers about a book's worth of mathematics by the way.

 

Other than the unavailability of zero distortion zero noise super-stable harmonic oscillators, the above could be built, we have the technology.  But it would be expensive. VERY expensive. Plus, you would load the CD, wait for it to be read (completely), THEN wait for about a couple of weeks or so whilst the CD player calculates its Fourier transforms. THEN you would hear the music.

 

So, as I said, neither economical nor practical.  However, in theory a CD player could be built that finally proves 44.1kHz is a sufficient sampling frequency.  The current (and past) crop of CD players and D/A converters fail in that respect though.

 

The much more practical solution is to realise you will be using a suboptimal D/A conversion methodology, and therefore use a higher sampling frequency.  And this is why e.g. SACD (in theory) sounds better than RBCD.  44.1kHz is enough, but the currently practical D/A convertors are not up to the job of properly extracting the information contained in the digital samples.  Now whether or not people would actually hear the difference is a different story (can you tell an amplitude modulated 20kHz from a clean one?).  This could explain some audiophiles' early complaints about the harshness of the "digital sound" though.


Edited by 2leftears - 2/24/14 at 10:43am