Speaker(s) Recommendation for Vinyl

I was not questioning Nyqyist. What I was questioning was spending £500-800 on a turntable to connect it to a relatively cheap pair of speakers that will have equally cheap ADC/DAC stages along with fairly powerful radio transmitters. Seems like a waste of money if you want good quality vinyl audio, where I would stand by my ‘non-answer’. (We’ll gloss over the fact that most vinyl pressings these days are cut from digital masters)

If you just enjoy the process of buying vinyl, and using it, then fine, but I’d go Era 300’s over Five’s as they have much more modern innards so won’t get dropped by Sonos so quickly in the future. 

Unless you’ve dug the master disk cutter out of the 1970’s scrap heap, the cutter will digitize the input while cutting the pressing master.

That’s exactly my point. You have to decide the frequency limit beyond which you give up trying to capture anything - any content above that frequency is just thrown away. That’s what Nyquist demonstrated as a quantifiable effect.

The result is that what you get out of the other end can never be an exact copy - it will only be an accurate copy within the limits you place on your sample frequency.

Of course to most people the stuff that you throw away isn’t important, because they simply can’t hear it - though some people argue that they can still perceive it in one way or another.

And I have to admit that I agree with Ian_S - what is “best” in terms of speakers depends on the quality of the rest of your system. It doesn’t make sense to say that a £160,000 pair of Focal Grande Utopia EM Evos is the best solution if the rest of the system budget is £2000. In that respect, the OP’s question was a non-question.

I say it because it is true.

https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem

Strictly speaking, the theorem only applies to a class of mathematical functions having a Fourier transform that is zero outside of a finite region of frequencies. Intuitively we expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result depends on the density (or sample rate) of the original samples. The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity for the class of functions that are band-limited to a given bandwidth, such that no actual information is lost in the sampling process. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions. The theorem also leads to a formula for perfectly reconstructing the original continuous-time function from the samples.

Actually, that wasn’t your point.  At first you argued that “Everything between your sample points is thrown away. That is inevitable”, and we must “make guesses about the missing information”.  Then, when @buzz explained there are no gaps between sample points within a limited frequency range, you moved the goalposts to say everything above the range is thrown away, not everything between the sample points.. 

The filter can be constructive by removing distortion products from upstream processing that will have inband consequences later.  Tomlinson Holman is a narrow band advocate. Wide band advocates vociferously disagree with this approach.

I would argue that when sampled for all frequencies audible to any human ear which ever existed, what you have is indeed an exact copy.  No test of human hearing has ever proved differently. 

DAC/ADC chips are commodity items, you don’t have to spend more than a few pennies for 100% accuracy.  The math behind them is over 100 years old.  

It seems there aren’t many people in this thread that understand the basics of how digital encoding of audio actually happens. The gaps between sample points are gaps in time. It’s not possible to have “no gaps between sample points” - that would require an infinite sampling rate.

What actually happens is that you take a sample of the amplitude of the signal once for each tick of the sampling frequency “clock” - for CD audio you take one sample every 1/44100th of a second. What happens between each of those sample points? You don’t know because you only take a measurement at each tick of the clock. But you don’t care, as long as you don’t want to include any information with a frequency greater than half your sample rate. That’s what Nyquist documented.

What happens to the frequencies that are higher than that? That information is gone. You can’t get it back at the other end of an ADC - DAC conversion. It is simply not present.

Hence the copy is not an exact copy.

Even an analog process cannot result in an exact copy because the process adds noise and distortion and will probably not have an exactly uniform frequency response — assuming that the process bandwidth is as least as wide as the source. Even though a number of people consider an analog copy to be “perfect”, it’s always a little disheartening to compare copy 100, in a chain, with the original.

The real issue is: How well will the resulting copy fulfill its intended purpose?