Derivatives? Differentiation and Integration

[dave2010]

Anyone here really well up on how audio signals get processed?

There are different kinds of microphones. Some give a signal which is, I believe, related to pressure, and some work on pressure differences - i.e the time derivative of pressure.

Many hi-fi enthusiasts praise vinyl, but LPs were made using magnetic cutters. The cutters most likely respond to the time derivative of the input signal.

Similarly, many pickups also respond to the time derivative of the mechanical motion producing the movement of the stylus.

The last link in the reproducing chain is usually a loudspeaker or headphone set. Some are electrostatic, but most use coils. Again we see the use of technology which is based on time derivatives.

Each time a derivative of a complex signal is produced, the frequency response of the signal changes. This will tend to emphasise the higher frequencies - just think d/dt (sin w t) = w cos x t etc. There will be integrating and differenting effects in electrical/electronic circuits. It is also possible to do integration and differentiation in the digital domain.

Reversing a single differentiation step is possible by an integration process, though there will be a loss of a constant - which will normally be a DC offset which can be ignored. Multiple differentation steps may result in more significant loss of data, though it's probably still not too bad providing the frequency response characteristics are maintained. I speculate that phase information may be compromised significantly.

My question is "does all this matter in the hi-fi kit that we use today?" How many stages does a signal go through which differentate a complex signal, and is this effectively compensated for by other stages in the process, or is it simply ignored?

It could be that, just as lossy compression methods such as mp3 fool many people into thinking that they are hearing something similar to "real sound", that there is still enough information in a moderately heavily processed signal - for example on a CD or DVD, to fool us that we are listening to a good approximation, even though the waveforms may bear little resemblance to the originals.

If it is an issue, then at least partial solutions can be found by appropriate analogue or digital methods, or hybrid methods which use both.

Has anyone out there thought about this recently?

[DSJR]

If there was that big a difference between the input and output signals, the difference could easily be measured and identified as distortion. Red Book CD is higher resolution than UK FM radio (13 bit PCM and brick walled at 15KHz) by a substantial factor, yet we all loved the excellent radio 3 live concerts at this resolution. The bits between the bits are easily filled in and noise shaping improves the mid no end, so no trouble.

As for the ancient argument regarding the supposed superiority of "analogue," you'd probably find loads of time-smearing and noise smoothing out the nasty bits for all I know and most well-used pro tape decks don't do much over 25Khz anyway, unless they're running at 30IPS and apparently even this has problems as I recall..

[dave2010]

Dave
If there was that big a difference between the input and output signals, the difference could easily be measured and identified as distortion. Fair comments, though slightly side-stepping. What you are saying is that for all practical purposes it is possible to assert that the input and output match (or not).

How easy is it to do what you say on a complete "round trip"? The electrical (or optical/digital) signals are easy to process, but what about input and output transducers?

My original point was that depending on the transducers used, it is likely that at some points in the chain the signal is effectively differentiated wrt time, and unless a compensating integration step is carried out, this must change the signal.

Unfortunately there is also quite strong evidence that we don't actually process audio based solely on the waveform. I once found a web site which had details of an artificial clarinet. I think it was probably just a software tool which could generate sounds similar to a clarinet. The interesting thing was that it was possible to compare several clarinettists and similar sounds done on the artificial system. It was definitely possible to distinguish two of the clarinettists - and maybe even to have a preference. It was not easy to distinguish the artificial "instrument" from one of the real ones. The algorithms used to produce the artificial sounds were reasonably well known. Looking at the waveforms, the two real clarinet waveforms looked similar, though they didn't sound exactly the same, while the generated one looked very different but was hard to distinguish from one of the others.

The logic of this is that while we might think it is necessary to maintain exactness of the measured parameters of the source sound in order to achieve a realistic result, this is strictly not necessary. If we do, then to a high degree we should be able to do so, but it is not necessary. However, similar arguments are put forward for lossy compression, and unfortunately at relatively low bit rates at least, we know it is not high quality, and becomes tiring very quickly. Whether 320 kbps MP3 can be considered inferior to other sources though is perhaps a more open question.

So, perhaps worrying about whether a signal is integrated or differentiated is similarly not something we need to concern ourselves with. However, I was questioning whether much/any consideration is, or has been, given to this issue. I really don't know. It is possible that having circuits which process signals to give a flat resonse is mathematically equivalent to cancelling out any of the intermediate processes - but I don't know this, and it may not be true.

[Themis]

I will follow this subject carefully. Very interesting. :)

[DSJR]

Too much for me at the moment :scratch:

[dave2010]

Dimitri
I will follow this subject carefully. Very interesting. :)I hope we can get someone who knows a bit more to contribute. It's the sort of thing that I know some engineers were following 30-50 years ago, but not sure if anyone follows this these days. I was amazed to read in quite an old book (maybe for the BBC) that engineers used to check on the phasing for microphone placements, using oscilloscopes and relatively sophisticated methods. Does this still happen, or is it all done by trial and error and "experience" these days?

It is possible that some of my original question(s) can be answered easily by someone with a greater knowledge of linear circuit theory - which would at least give a theoretical justification to the end to end process - though might not even then give the whole story as theory and practice don't always coincide.

[Dave Cawley]

The answer is 42 and also yes. The problem on this thread is determining what is the question?

Dave

[Barry]

There are different kinds of microphones. Some give a signal which is, I believe, related to pressure, and some work on pressure differences - i.e the time derivative of pressure.

Most microphones used in recording studios are pressure operated: dynamic (electromagnetic) types such as Shure and Sennheiser; capacitor (condenser) types such as Neumann. Ribbon microphones are velocity operated.


Each time a derivative of a complex signal is produced, the frequency response of the signal changes. This will tend to emphasise the higher frequencies - just think d/dt (sin w.t) = w cos w.t etc.

That's what equalisation is all about. Magnetic cartridges follow Lenz's law, that is, the voltage output is related to the rate of change of magnetic flux: V = -L.dB/dt The RIAA equalisation 'reverses' or equalises the emphasis of high frequencies.

I don't see it as being a problem.

Regards