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Re: Waveform horror! Is a 44.1 kHz sampling rate sufficient?

I used Audacity to generate a 19 kHz tone, planning on burning it to a

> CD and playing it in my car stereo for... um... well, let's not get > into that. I then zoomed in on the waveform to take a peek, prior to > burning the waveform. What horror! > >
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> > The waveform is severely distorted. I could see where the points > mathematically > would be correct, but given the sparse sampling points, the speaker > would not be instructed to swing rail-to-rail at, say, between 15.0000 > and 15.0005 seconds. > > A FFT gives a spread of frequencies centered around the 19 kHz, but, > yuck! > > I tried various other frequencies: 9 kHz gives a pretty distorted > waveform as well. > > What are the implications as far as accurate sound reproduction at a > 44.1 kHz > sampling frequency, as used by CDs?

As long as your CD player runs the discrete sample values through a proper low-pass "reconstruction filter" before they're sent out its analog output, you end up with a nice, smooth waveform which looks just the way you'd want it.

First-generation CD players tended to use a "brick wall" reconstruction filter implemented in the analog domain (e.g. several stages of op amp low-pass filter). Newer ones tend to use one or another "oversampling" design, which do the first part of the filtering digitally (reconstructing numerous intermediate points between the incoming samples via a digital sinc filter) and then use a single-stage low-pass analog filter.

Now, if you were to ignore the essential requirement for a reconstruction filter during playback - if you were to just take each of these sample points, convert them to an analog voltage when it arrived, and then "hold" this analog value until the next point arrived - you would indeed end up with a rather nasty-looking waveform. It would be "stair-stepped". In the frequency domain, it would have a string signal component at 19 kHz, and numerous "aliases" of this signal at higher frequencies.

The reconstruction filter eliminates the aliases, and leaves you with just the 19 kHz signal you want.

The issue you've encountered is one of the subtler ones in CD and sampled-audio design. It's very counterintuitive to many that you actually *can* accurately sample and reconstruct a signal, using just a bit more than two points per sine... but it actually does work out that way, both mathematically and in practice (when properly implemented).

--
Dave Platt                                    AE6EO
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Dave Platt
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Did some CD player manufacturer actually use some passive LC (or active RC+op-amp) brick wall filters at 20 kHz ?

At least the early Philips player designs used 4x oversampled 14 bit DACs simply because they could not produce cheap 1x 16 bit DACs.

The LC brick wall filtering was more of an issue with the early PCM adapter ADC/DACs for ordinary VCRs.

Paul

Reply to
Paul Keinanen

So I understand. Typically RC+opamp, I believe, although it's possible that some LC types might have been used. My recollection is that they weren't all that "brick wall" - not enough stages - and did allow some of the first-image signal through. This may have contributed to the reputation for shrill, unmusical treble that some early-generation CD players had.

Trimming them to be flat and accurate must have been a royal pain!

16-bit converters running at 4x seem to have been popular in the next generation or two after that... I recall some fairly high-end players which used Burr-Brown DACs in this class. 
--
Dave Platt                                    AE6EO
Friends of Jade Warrior home page:  http://www.radagast.org/jade-warrior
  I do _not_ wish to receive unsolicited commercial email, and I will
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Reply to
Dave Platt

"Paul Keinanen"

** Early Sony models used 16 bit DACs with no over-sampling followed by Murata ceramic filters with a 100 dB octave slope above their 20kHz turnover frequency.

Most other brand's models had significant supersonic noise in the output making accurate measurement of the THD and s/n ratios a hassle.

..... Phil

Reply to
Phil Allison

Why on earth would anyone use sharp low pass filters at reproduction ? After all the amplifier chain, loudspeakers and the human hearing will effectively filter out any ultrasonic components ?

Did somebody actually think that a typical audio amplifier was so bad that feeding some ultrasonic components would cause bad intermodulation distortion ?

Are you sure that the "unmusical treble" was not simply caused by the

1x 16 bit or 4x 14 bit DAC nonlinearity ? Those DACs were quite bad, not even monotonous.

On the recording side, it is essential to cut out any ultrasound components (e.g. cymbals), before passing it over to the ADC, in order to avoid aliases.

Paul

Reply to
Paul Keinanen

Because that's what the process requires, mathematically.

And (I suspect) because the measured distortion+noise performance of a system without such a filter would look rather horrid, especially when fed a signal with a lot of treble content (where the first image would appear at frequencies not a lot higher than the fundamental).

The amplifiers... probably not.

The speakers (tweeters in particular)... quite possibly.

Consider a CD-rate (44.1 kSample/second, 22.05 kHz cutoff) system which is reproducing a signal which has some 20 kHz content. The first image of this signal component would be at 24 kHz. If you don't filter out the image, and if your tweeter (or your ear!) isn't quite linear, these two signals could result in an IMD component at 4 kHz, which could sound distinctly odd.

There were probably several things contributing to this impression... DAC nonlinearity being one (as you say) and non-flat frequency response being another.

Yup, that's where the worst problems would be.

Burr-Brown has an interesting app note dating back to 1991

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which discusses this issue. This paper suggests that in a 4x oversampling system (where much of the low-pass filtering is performed digitally), good performance requires the use of a sixth-order low-pass filter for the ADC, and a third-order filter for the DAC.

A non-oversampling (1x) filter would require higher-order analog filters for equivalent performance.

--
Dave Platt                                    AE6EO
Friends of Jade Warrior home page:  http://www.radagast.org/jade-warrior
  I do _not_ wish to receive unsolicited commercial email, and I will
     boycott any company which has the gall to send me such ads!
Reply to
Dave Platt

The Nyquist Thoerem states: If a function x(t) *contains no frequencies higher than B hertz*, it is completely determined by giving its ordinates at a series of points spaced 1/(2B) seconds apart.

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-- Les Cargill

Reply to
Les Cargill

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