Wide bandwidth = necessary?

Possibly, I don't know how high you are talking. For example, an analog filter with a low slope is going to have a large knee with an effect on frequencies over about a decade. (so a simple analog RC low pass filter with a 3db point way up there at 40KHz would still audibly attenuate frequencies down to about 8,000 Hz - it would be subtle though)

Almarg...My experience with the digital representation of analog waveforms (precision servos in missile guidance systems) leads me to the conclusion that, in the real world, four times the highest frequency of interest is the minimum requirement for good performance. Audio signals are no doubt even more demanding than servo error signals.

Shadorne...The Low Pass filter in question was pure analog 6 or 12 dB. There were no artifacts in the passbvand of my degraded hearing range.

humans also have a type of wavefront detection mechanism that is independent of our freqency perception. The pre ripple trips this wavefront detector and is perceived as diminishing the detail in the music.

I have long believed that our sense of hearing includes a "waveform steepness" factor quite independent of frequency response.

Those are excellent points (and excellent posts), and I suspect that what is behind this is the Haas Effect, which causes our hearing mechanisms to "latch on" to the leading edge of closely spaced sound arrivals. We evolved that capability to aid localization of the source of sounds that may arrive at our ears via both a direct path and (slightly later) via reflections. See the following:

http://en.wikipedia.org/wiki/Haas_Effect

Also, a few comments re the Nyquist rate and the Sampling Theorem and why sampling at twice the highest frequency that may be present is valid in theory but not in practice.

Counter-intuitive though it may seem (as Viridian indicated, sampling at the minimum Nyquist rate provides only two samples per period of the highest input signal frequency), that sample rate (of twice the highest possible signal frequency) maintains 100% of the information in the original waveform, regardless of the complexity of the waveform (sinusoidal or not), provided that two things are true:

1)No out-of-band spectral components are present (which would alias down to lower frequencies following the sampling process).

2)The sample record is of infinite length. I believe that follows from the fact that any arbitrary waveform (in the time domain) is mathematically equivalent to a summation of sine waves at various frequencies and amplitudes, but determination of that equivalency requires that an entire sample history covering all time is available. The equation defining the Fourier Transform, which mathematically converts between the time domain and the frequency domain, involves an integration from -infinity to +infinity. The relevant distinction between a pure sine wave and a complex musical waveform, which ElDartford referred to, is that for the pure sine wave we essentially know its entire past and future history -- it's always the same.

That's in theory. In practice, we need an anti-aliasing filter in front of the a/d, to filter out-of-band frequencies, and the steeper the filter slope the worse its side-effects will be, everything else being equal. And of course, item 2 can only be satisfied in the real world to some approximation. The idea seems to be that the sample record need only be "long," relative to the changes that occur in the content.

All things considered, it's remarkable that redbook cd (sampling at just about 10% above the Nyquist rate) works as well as it does.

Regards,
-- Al

I found out that I could hear the introduction/removal of a low pass filter at a frequency well above the frequency at which I became stone-deaf to a sine wave (the usual test signal).

That is quite normal from many sharp low pass or brick wall filters which will introduce a ripple on what passes through - you can indeed hear the ripple. Essentially any box function applied to a signal will introduce ripple within the band. There are phase effects to. You don't have to resort to the idea that we can hear ultrasonics (like a bat) to believe that a filter can be audible.

Here is an example of a chebyshev filter

It should be "artificially", not "superficially". Sorry for typo.

Chris

Eldartford: that is an interesting phenomenon. Do you think we humans can appreciate more of the sound if the gear is capable of reproducing frequencies above 20kHz even if the recording itself doesn't contain any frequency above 16kHz? With other words: would the music sound more "natural"? If that is the case, then I have to have this super tweeter also --> it will superficially create naturalness (sounds like contradictio in terminis).

Chris

Viridian...I have long believed that our sense of hearing includes a "waveform steepness" factor quite independent of frequency response. I came up with this idea a couple of decades ago when I found out that I could hear the introduction/removal of a low pass filter at a frequency well above the frequency at which I became stone-deaf to a sine wave (the usual test signal). This would also explain why a supertweeter operating above 20KHz makes an audible difference.

The oft-quoted sampling rate of twice the highest frequency of interest applies to regeneration of a continuous analog sine wave. That ain't music. In practice, even for non-musical signals at least a four to one ratio is desirable.

Chris, I obviously misinterpretted what you intended to discuss in this thread! :-( That makes my long rambling post irrelevant. Please ignore it. Thanks.

The above links work even though they seem to be the same.Don't know why.

Bandwidth is not limited,which John Atkinson illustrates here, http://stereophile.com/features/282/ He closely looks at the very issue of what is captured on vinyl.Doug Rife postulates a theory of why this is important, http://www.mlssa.com/pdf/Upsampling-theory-rev-2.pdf both of these articles are good reading if you are interested and James Boyk's work at the Caltech Institute http://www.cco.caltech.edu/~boyk/spectra/spectra.htm looked at what ultrasonic content is captured by microphones until the signal starts to break-up at around 50Khz.

For those who haven't looked at it, I think that Stefanl's link is an excellent and very in-point medical/scientific paper. It documents a study in which "non-stationary" ultra-sonic sounds increased pleasurable brain activity in the test subjects, but only when sounds within the normal audio spectrum were simultaneously present. "We conclude, therefore, that inaudible high-frequency sounds with a nonstationary structure may cause non-negligible effects on the human brain when coexisting with audible low-frequency sounds."

So it would seem like ultra-sonic frequencies can be "audible," but only as a result of some intermodulation process with lower frequencies, or else, as the paper put it, "participation of nonauditory sensory systems such as somatosensory perception also needs to be considered in further investigations."

Still I can't understand the need for such a response (to 40kHz) while during recording the bandwidth is limited.

I'm not particularly familiar with the roll-off characteristics of professional recording microphones, but I would expect that although their bandwidth may only be specified to 20kHz in many cases, the roll-off would be gentle enough to capture significant content well above that frequency, assuming it is present.

So, if you are want to transport a 16-b word of music @ a 44.1KHz rate - this is what a CD laser mechanism does: every 1/44.1KHz seconds it spits out a 16-b word read off the physical spinning CD - you would have to transport each bit in 1/(16-b * 44.1KHz = 705.6KHz) seconds (so that you are ready to transport the next 16-b word that will arrive 1/44.1KHz seconds later.
So, your USB cable needs to have 705.6KHz bandwidth (& your DAC needs to run at 2*705.6KHz, as per Nyquist's criteria).

Keep in mind that two channels are present. That is the reason for the factor of 2 (which actually will be a little greater than 2 because additional non-data bits are needed to support the communication protocol).

Also, I'm not sure it's clear to everyone that the Nyquist criteria (sampled data systems being able to handle frequencies no higher than 1/2 the sample rate) does not relate to filtering at the output of a dac. Ultra-sonic spectral components that are present at the output of the dac chip itself, due to the 44.1kHz sample rate, will not alias, or "fold-down" to lower frequencies. A brick-wall anti-aliasing filter, which as I mentioned is needed at the input to an a/d, is not needed at the output of a d/a, even a non-oversampling d/a running at 44.1kHz. The spectral components associated with the sampling will be at frequencies of 44.1kHz and its harmonics (88.2, etc.), or at much higher frequencies if oversampling is used. They needn't necessarily even be filtered at all (consistent with Paulfolbrecht's comment), or if they are filtered the roll-off can be gentle.

Re Paul's comment about the desirability of no filtering, btw, I would expect that to be dependent on the specific components (preamp, power amp, speakers) that are being driven by the signal (particularly their bandwidths and their sensitivities to intermodulation distortion at high frequencies).

Regards,
-- Al

Amazing! Thank you for the references. Still I can't understand the need for such a response (to 40kHz) while during recording the bandwidth is limited.

Chris

Well Dazzdax,I can refer you to an old Hi-Fi review (1982) of 5 cartridges by Martin Colloms who was in the lab testing those cartrides square wave responses out to 40Khz for his review,this is in the members section articles at The Vinyl Engine.I at one time hooked up my phono stage to my soundcard and using the old Cool Edit program recorded some Led Zepplin at 96/24 and there was ultrasonic content definitely present out to 40Khz.This was actually to duplicate an experiment by John Atkinson of Stereophile who did an article about the high resolution of vinyl (still in the archives).The Sheffield Direct to Disk series used to advertise how their recordings captured sonic information out to 50Khz.

First of all I would like to thank all of you for the wonderful comments. The reason for this post was to get clarification from you the need for the ability to reproduce frequencies beyond human hearing.
In the past some manufacturers like Pioneer tried to "reconstruct" the signal content above 20kHz by using special filters like the "Legato Link". This was done because the designers believed that the frequencies above the 20kHz (up to 40kHz) were necessary for a natural sound. This is also one of the arguments of the vinyl people. But if the mics are capable only of picking up frequencies up to 20kHz, why the need for gear that can reproduce frequencies above that (if that is already bandlimited in the first place)? In case of vinyl: I truly believe cartridges are capable of reproducing frequencies above 20kHz, but if the vinyl itself contains no frequencies above let's say 16kHz at all, what is the use for such a bandwidth?

Chris

Here is a link to the main "formal" arguement about why wide bandwidth is necessary.For your health!http://jn.physiology.org/cgi/content/full/83/6/3548

After trying them all, I like many people, have concluded that the best format for digital sound is redbook CD played back on a DAC with NO oversampling and NO digital or analog filtering - such as an Audio Note DAC! This bandwidth-limited solution gives digital sound that is truly as close to analog and as lifelike as is possible with any digital technology thus far.

Oversampling introduces non-musical artifacts into the signal. This is a fact. And the problems with filters of all types are well-known.

Hi Al,

The main benefit of higher sample rates, which figures to be a very significant one, is that it allows for a gentler rolloff of the "anti-aliasing filter" that precedes the A/D converter in the RECORDING CHAIN.

Looks like I read your post too quickly & did not note the A/D part. My bad.

Hi folks, there is one paradigm that bothers me a bit: many experts and audiophiles are stating that Red Book technology is outdated because of it's bandwidth limited function. I've read the human ear is capable of perception of frequencies beyond the normal human hearing, up to 40kHz. But this is only with live music! When listening to recorded music there is a restricted bandwidth because many microphones can only pick up frequencies up to 20kHz. So why the need for more and more bandwidth with regard to digital sound reproduction technology? What is not present in the recording can't be heard either, even with very wide bandwidth music reproduction gear

Chris, you are quite confused about the need for bandwidth in the reproduction of digital playback.
Basically, what mankind is trying to do is trying to make digital sound more & more like analog. I believe that this is an implicit acknowledgement of analog reproduction being more suitable for the human ear. However, people want the positives of analog playback (naturalness) without its hassles (tape hiss, crackles & pops, flipping a side every 20-25 minutes, groove wear-out due to repeated use, too many minutes to clean a LP, etc).
In the earlier days of CDs, people were not careful when mastering digital music - they used 16-b of music data, mixed tracks & processed the whole album. As a result, several bits were lost due to additive noise & what one effectively got was 12-13 bits of music. This manifested itself as drastically reduced dynamic range in the music. To the listener it felt like compressed music as the range of lowest music signal to highest music signal was not large enough to portray the essence of the music.
As time went by & the recording industry understood this, they started using 20-b of raw music data as the starting point of their mixing, processing. In this case, even if bits were lost due to additive noise, they were still left with 16-17 music bits. When that was pressed onto CDs, the sound got far more dynamic. It sounded much more like real music.
Several corollary advancements were made such as HDCD, XRCD, XRCD2, XRCD24. These technologies used 20-b & even 24-b as the starting point for the processing.
Then, came 24-b, 96KHz audio in the form of DVD-A.
These days we have hi-rez downloadable music in 24-b, 192KHz.
Then, there is the DSD signal - also called SACD - that is a 1-b signal oversampled at a 2.8+ MHz rate (I think I guessed the sampling rate correct? or did I??)

So, what's happening here? The sampling rate of the digital signal is steadily increasing - from 44.1KHz --> 48KHz --> 96KHz --> 192KHz. This bascially means that there are more samples of the analog signal being taken during the conversion of the analog signal to digital (if old master tapes are being converted) OR, if music is being recorded fresh today, the analog signal coming from the mic is being sampled at 96KHz or 192KHz right off the bat & is being stored on HDD.
If one has more samples of a signal , there is much less variation in the music signal amplitude from one sample to the next - like analog! :-) If you draw an analog waveform (say, a sine wave) you'll notice that the values change smoothly from one value to another - no abrupt changes. If you want to digitize an analog waveform & you take a lot of closely spaced samples, you are trying to emulate an analog waveform in the discrete-time domain.

If one is increasing the sampling rate of the digital signal in an effort to make it sound more analog-ish, then the bandwidth of the electronics processing this signal also has to increase (otherwise, the electronics will not be able to settle to their final voltages before the next clock cycle & this will lead to signal-dependent distortion - a very bad thing).

Also, if you are dealing with higher sampled rate music data when using a USB mode of communication then the data is flowing in a *serial* fashion between computer & DAC (or jitter box). USB - univeral SERIAL bus.
So, if you are want to transport a 16-b word of music @ a 44.1KHz rate - this is what a CD laser mechanism does: every 1/44.1KHz seconds it spits out a 16-b word read off the physical spinning CD - you would have to transport each bit in 1/(16-b * 44.1KHz = 705.6KHz) seconds (so that you are ready to transport the next 16-b word that will arrive 1/44.1KHz seconds later.
So, your USB cable needs to have 705.6KHz bandwidth (& your DAC needs to run at 2*705.6KHz, as per Nyquist's criteria).
When you want to transport a 24-b, 96KHz word using the USB port, your USB cable needs to have 2.304MHz bandwidth.
So, now you can see how the bandwidth of the hardware is increasing to support higher & higher sampling rates.

The music info in redbook CD still remains 16-b but we are trying to make the sound more & more analog-ish (by inc. the sampling rate) & we need hardware to keep up with this higher rate digital signal; hence, the bandwidth of the hardware is also inc. in tandem.

There are DACs today, like the Weiss Minerva, that will natively accept a 24-b, 192KHz signal over FireWire (another high-speed interface invented at Apple) but I believe that the DAC inside is still a 20-b DAC (someone correct me if I'm wrong. Thanx). I do not think that there are many (or any) 24-b *audio* DACs - I believe that it's very hard to achieve the fidelity with so many bits. (I could be wrong). Even if you have a 20-b or 24-b DAC, your cables, preamp, power amp & speakers, noisy AC power, inadequate chassis damping, inadequate rack damping, room acoustics, etc will ulitmately limit your overall dynamic range as heard by you at your listening chair.

Ok, I've rambled way too much! I hope tho' that I could be some help. Thanks.

Your post makes sense *if* you are about to do an A-->D conversion

That's exactly what I was talking about. Please note that I said:

The main benefit of higher sample rates, which figures to be a very significant one, is that it allows for a gentler rolloff of the "anti-aliasing filter" that precedes the A/D converter in the RECORDING CHAIN.

I wasn't talking about DAC's or playback equipment at all.

-- Al

Al,
you got it all wrong, I'm afraid!

The main benefit of higher sample rates, which figures to be a very significant one, is that it allows for a gentler rolloff of the "anti-aliasing filter" that precedes the a/d converter in the recording chain.

The higher sampling rate is meant to benefit the reconstruction filter that follows the DAC.
Remember that the data going into the DAC is digital - a stream of 1s & 0s. What sort of anti-aliasing filtering are you going to do on a stream of 1s & 0s???

Your post makes sense *if* you are about to do an A-->D conversion. Then, yes, you need to band-limit the analog signal.

So the anti-aliasing filter has to pass everything up to 20kHz, with flat frequency response, but attenuate everything at 22.05kHz and above to (hopefully) below what is the threshold of audibility at lower frequencies.

it's the reconstruction filter that needs to pass everything DC-->22.05KHz & *not* the anti-aliasing filter.

I agree with Viridian. The main benefit of higher sample rates, which figures to be a very significant one, is that it allows for a gentler rolloff of the "anti-aliasing filter" that precedes the a/d converter in the recording chain.

The theoretical maximum frequency that a sampled data system can capture is 1/2 of the sample rate, or 44.1 x 1/2 = 22.05 kHz in the case of redbook cd. Anything above that frequency must be prevented by the filter from entering the a/d converter, or it would "fold down" to a much lower (and very audible) spurious frequency when reproduced.

So the anti-aliasing filter has to pass everything up to 20kHz, with flat frequency response, but attenuate everything at 22.05kHz and above to (hopefully) below what is the threshold of audibility at lower frequencies.

A filter with such an extremely sharp rolloff will inevitably introduce both phase distortions and frequency response ripple, within the 20 to 20kHz passband. 96 or 192kHz sampling would drastically reduce the sharpness of the rolloff, and minimize those effects correspondingly.

Regards,
-- Al

I've read the human ear is capable of perception of
frequencies beyond the normal human hearing, up to 40kHz.

Where have you read this? Was it in a reputable science journal or someone who
just bought a supertweeter?

The ear drum is filter - I don't think anything much above 20 Khz gets through.