CD v.s LP - When comming from the same MASTER

Twl...You make sense. Mostly.
The Nyquist criteria calls for sampling to be at twice the highest frequency of interest: if this is true the analog waveform is represented without error. BUT...Nyquist was talking about sine waves. Music is not a sine wave. That's why the CD sampling frequency of 44.1 KHz is not adequite. In my experience (non audio) sampling at about four times the highest frequency of interest was useful. (Higher a waste of time).

Analog recordings TRY to reproduce the signal in a continuous manner, but HF filtering gets in the way. A LP can be "read out" with an optical microscope instead of a phono pickup. A few exceptional recordings have groove modulations up to 22 KHz. If the wiggles are not in the vinyl you can't say that the audio system responds.

The Nyquist criteria calls for sampling to be at twice the highest frequency of interest: if this is true the analog waveform is represented without error. BUT...Nyquist was talking about sine waves. Music is not a sine wave.

That's not quite true. The Nyquist Theorem states:

To represent in the digital domain a signal containing frequency components up to FHz it is necessary to sample it at LEAST at 2F samples per second.

It is true that sampling at less than 1/2 the highest frequency gives rise to aliasing, creating components in the output after DAC that were not there to begin with. Obviously undesirable. But Nyquist used the phrase "at least" - sampling could be higher.

In theory, the waveform does not really matter. Music is a periodic waveform and the Fourier Theorem states that:

Any periodic waveform can be represented as a sum of harmonically related sine waves, each with a particular amplitude and phase ...

The mathematics is solid. Problems arise in the implementation.

Regards,

Apologies - I should not have used the word "periodic" when referring to music in the above. It's slightly misleading.

Regards,

There is an example that caused me to form an opinion and that was The Beatles Anthology series.The awful early recordings on Anthology 1 clearly sound better on the Vinyl version than on the CD version,where they sound especially harsh and strangled.Both the LP and CD were produced from the same digital master which they do with Beatles releases these days.In Stereophile Archives online in the "Think" pieces,John Atkinson has analysed and discussed what is on Analogue and Digital recordings.("What's Going On Up There")-extremely informative.L.P's are better.

Metralla....To represent a time-domain waveform by Fourier coefficients, the waveform must be periodic, and remain of fixed spectral content (at least during the time interval of the FFT). Music isn't like that. There are momentary wavefronts with steepness equal to that of a sine wave at well over the 20 KHz upper frequency of human hearing.