Topic: Do CD's reproduce lower frequencies much better than higher freque (Read 12720 times)
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Do CD's reproduce lower frequencies much better than higher freque

At the beginning of a sample period, the capacitor is at zero. It's being fed by the input signal. As the amplitude of an input signal rises, so does the voltage across the capacitor. However, when the signal starts falling down, the capacitor remains at the maximum signal level.

Sounds more like a filter circuit and peak detect functionality (not that the two go together).  I've always thought sample-and-hold referred to the DAC side of the system (stair-step output) whereas a potential corollary on the ADC side might be a circuit which integrates over some time period instead of instantaneous sampling (can be done with an op-amp and capacitor, but not capacitor alone).  Regardless, isn't this all to try to turn the <Fs/2 requirement into <=Fs/2?  So that instead of being able to capture 22.049999999999kHz we can actually read 22.05kHz with Fs=44.1kHz?  Seems like a very complicated scheme to achieve an infinitesimal gain in bandwidth.

I think the simple answer is don't try to introduce weird non-linear systems (integrators or peak detect or...) after an appropriate anti-aliasing filter.  Just anti-alias and then get as close to instantaneous sampling as possible.  Then the theories will apply fairly well.

P.S.  If you want to use an integrator rather than instantaneous sampling of the audio signal, that's what delta-sigma is all about.

http://en.wikipedia.org/wiki/Delta-sigma_modulation

Do CD's reproduce lower frequencies much better than higher freque

But, if you (analogue) sample-and-hold during the sample period, you would always acquire maximum value.

Quote
In electronics, a sample and hold circuit is used to interface real-world signals, by changing analogue signals to a subsequent system such as an analog-to-digital converter. The purpose of this circuit is to hold the analogue value steady for a short time while the converter or other following system performs some operation that takes a little time.

In most circuits, a capacitor is used to store the analogue voltage, and an electronic switch or gate is used to alternately connect and disconnect the capacitor from the analogue input. The rate at which this switch is operated is the sampling rate of the system.

Perhaps you want to correct that on Wikipedia?

Do CD's reproduce lower frequencies much better than higher freque

I have no practical knowledge of what filters are used in this application, but I would be curious if you could tell me.  Filter type, order, cutoff frequency, phase effect...  It seems that we would want somewhere around a 96dB (round to 80dB for optimism and simplicity) cut by the Nyquist frequency (22.05kHz) while still retaining a pass-band to about 20kHz.  That leaves a ten percent frequency change to achieve the cut that a fourth order filter creates over 2 decades.

Without challenging the apparent fact that this can be achieved reasonably well, do you know how it's done?  Or, what trade offs are accepted to make it happen?

Hmm..  Is the signal attenuation simply accepted as stored on the CD, but undone by the recovery filter ? (I think that's the term for the DAC's filter that corresponds to the antialiasing filter)

Well, now, there is another tutorial at www.aes.org/sections/pnw/ppt.html titled "filter tutorial" or something of that sort.

Excuse me for not compressing a fast survey in a 3 hour talk into an article here.

Depending on how the 40 Hz sampling synchronizes with the 20 Hz sine wave, you could get anything from full amplitude (sampled at positive and negative maxima) to zero amplitude (sampled at every zero crossing).

Not if sample-and-hold is used in the ADC, instead of theoretical instant sampling...

Regards,
Goran Tomas

This is nothing more than a kind of filter.

As the amplitude of an input signal rises, so does the voltage across the capacitor. However, when the signal starts falling down, the capacitor remains at the maximum signal level. At the end of the sampling period, the capacitor would have the maximum value of the signal during the whole sampling period.

That's not what a sample-and-hold does.  Some average over the "open" period (which would be what I refer to as a "filter" above) and some take a snapshot. None of them take "maximum", which, if you think about it, would be creating something much like the opposite of center-clipping, would be a nonlinear system, and would create gobs of distortion at high frequencies.

n.b. the "averaging" kind are actually more rare than the "grab and hold" kind, but are used in some modem systems, etc.

In any case, the only way to get all the way to fs/2 is to have an infinite-length filter.
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J. D. (jj) Johnston

Do CD's reproduce lower frequencies much better than higher freque

Woodinville posted a link, but it had an extra l which broke it, so I thought I'd be helpful.
You need a couple of hours spare to read that ppt properly, but it's very good.

Cheers,
David.

Do CD's reproduce lower frequencies much better than higher freque

Woodinville posted a link, but it had an extra l which broke it, so I thought I'd be helpful.
You need a couple of hours spare to read that ppt properly, but it's very good.

Cheers,
David.

Whoops, sorry, I posted from a s l o w connection at a hotel at CES. Thanks for posting both the correction and the actual ppt files.
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J. D. (jj) Johnston

Do CD's reproduce lower frequencies much better than higher freque

At the beginning of a sample period, the capacitor is at zero. It's being fed by the input signal. As the amplitude of an input signal rises, so does the voltage across the capacitor. However, when the signal starts falling down, the capacitor remains at the maximum signal level.

Sounds more like a filter circuit and peak detect functionality (not that the two go together).  I've always thought sample-and-hold referred to the DAC side of the system (stair-step output) whereas a potential corollary on the ADC side might be a circuit which integrates over some time period instead of instantaneous sampling (can be done with an op-amp and capacitor, but not capacitor alone).  Regardless, isn't this all to try to turn the <Fs/2 requirement into <=Fs/2?  So that instead of being able to capture 22.049999999999kHz we can actually read 22.05kHz with Fs=44.1kHz?  Seems like a very complicated scheme to achieve an infinitesimal gain in bandwidth.

I think the simple answer is don't try to introduce weird non-linear systems (integrators or peak detect or...) after an appropriate anti-aliasing filter.  Just anti-alias and then get as close to instantaneous sampling as possible.  Then the theories will apply fairly well.

P.S.  If you want to use an integrator rather than instantaneous sampling of the audio signal, that's what delta-sigma is all about.

http://en.wikipedia.org/wiki/Delta-sigma_modulation

I'm new here -- I hope I didn't quote too much text. I just had to comment on critical sampling and sample-hold. I define "critical sampling" as input frequencies that are lower than 1/2 the sample rate by an infinitesimal amount.

Critical sampling and sample-hold are separate issues. If you sample at exactly 2x the input frequency, you will get DC -- a zero beat. If your sampler happens to be synchronized with zero crossings, you will get zero. If it is synchronized with peaks, you'll get a constant peak value, and so on, for everything in between. A sample-hold won't change that. It merely delays the effective sample position, and changes what DC voltage you get from your zero beat. Sample-hold does have first-order filtering side effects, but that in no way changes the sampling criteria.

You can think of the reconstruction filter as a curve fit program. If the data is DC, then the only curve that fits is a straight line (also DC). The instant that the input frequency drops below the sample rate by even the tiniest amount, you start getting a beat frequency with the sample rate, and the reconstruction filter function will fit that curve with a sine wave exactly representing the input signal. If the input is a complex waveform, the reconstruction filter can curve fit those frequencies as well, as long as they too remain less than fs/2. Aliasing occurs because a frequency above fs/2 will create a beat note that is indistinguishable from a beat note below fs/2 by the same amount. The filter can only produce valid solutions for signals below fs/2.

Now, the ability of the reconstruction filter to exactly curve fit critically sampled signals is related to the performance of the filter itself. Only a brick wall filter can actually do that. All real filters, even digital FIR filters, have a finite transition band, although they can be really steep. Practical digital FIR filters (e.g., as used in CD players) can be practically ideal, with extremely flat frequency response in the passband, with attenuation in the stopband well below 1/2 LSB. Since the digital filters are always oversampling filters, the design parameters for the analog reconstruction filters can also be made arbitrarily easy to achieve, again with a practically flat passband, and excellent stopband performance. And both of the filters can be completely phase-linear. Digital FIR filters are intrinsically phase linear.

In short, properly designed sampled data systems can be made arbitrarily "perfect" in the literal sense, and there will be no difference between the "quality" of any low or high frequencies within the filter passband.

Do CD's reproduce lower frequencies much better than higher freque

If you sample at exactly 2x the input frequency, you will get DC -- a zero beat. If your sampler happens to be synchronized with zero crossings, you will get zero. If it is synchronized with peaks, you'll get a constant peak value, and so on, for everything in between. A sample-hold won't change that. It merely delays the effective sample position, and changes what DC voltage you get from your zero beat. Sample-hold does have first-order filtering side effects, but that in no way changes the sampling criteria.
If you instantaneously sample at 2x the input frequency, with sample instants synchronised to the waveform peaks, you won't get "DC" - you'll get the positive and negative waveform peaks falling on alternate samples.

You'll never get a simple DC shift - either you'll get zero when the sampling instants are synchronised to the zero crossings, or a positive / negative waveform when they fall elsewhere. The exact amplitude depends on the synchronisation, which is why it's basically useless, and sampling only works properly for less than fs/2.

"a zero beat" - i.e. a simple DC shift related to the signal>sample synchronisation - happens when the input frequency is equal to the sampling frequency.

Obviously we use a filter to reject everything at and and fs/2 to prevent these problems. (I know you know that, but I state it anyway just in case someone reads this and gets the mistaken idea these are fundamental flaws!).

Cheers,
David.