"Andreas Huennebeck" <acmh@gmx.de> wrote in message
news:4ddj7cF19dbi5U1@individual.net...
> Thomas Magma wrote:
>
>> Thinking in the time domain, as you lower the sample rate you increase the
>> digitization (Your sampled sine wave will start to look like a square
>> wave).
>
> And this is exactly the point where you stumble: It does not matter at all
> how the digitized signal looks like! It will be perfectly reconstructed by
> the reconstruction filter behind the DAC.
So wave editors (e.g. CoolEdit, now Adobe Audition) use a high-order
interpolation filter when displaying the digital waveform. The actual sample
points are usually dots or squares and they are connected with a smooth curve
representing what a good reconstruction filter would do. In that way, the
stumbling block mentioned above is hopefully removed. (In my old version of
CoolEdit, it looks like about a 40th order FIR. So while it is good, it is not
perfect. Using a 48kHz sample rate, it does a great job drawing a 20kHz sine
wave, but a 23 kHz sine has noticeable ripple)
Reply by Andreas Huennebeck●May 22, 20062006-05-22
Thomas Magma wrote:
> Thinking in the time domain, as you lower the sample rate you increase the
> digitization (Your sampled sine wave will start to look like a square
> wave).
And this is exactly the point where you stumble: It does not matter at all
how the digitized signal looks like! It will be perfectly reconstructed by
the reconstruction filter behind the DAC.
One good reason for high oversampling is in DSOs because then you
really want to look at the digitized signal itsself.
> Clocking that data through a DAC at the same rate will produce
> strong harmonics (3rd 5th 7th etc). You can't regenerate the original sine
> wave out of a DAC no matter what digital reconstruction filtering you use
> if the playback rate is too slow.
Wrong. As long as the signal is sampled according to Nyquist and Shannon,
it is reconstructed exactly to its (bandlimited) original.
> The output of a DAC will always start
> digitizing and producing harmonics as you lower the sample/playback rate,
> unless you have exceeded the full power bandwidth of the DAC or have
> analog filtering after the DAC.
You must understand that the output of the DAC does not represent the
reconstructed signal. The reconstructed signal appears at the output of
the analog reconstruction filter behind the DAC. The chain of AD/DA
starts with the input of the antialiasing filter before the ADC and ends
at the output of the reconstruction filter behind the DAC.
bye
Andreas
--
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Reply by Andreas Huennebeck●May 22, 20062006-05-22
Thomas Magma wrote:
>> Then you are not playing back the same signal that was originally
>> recorded. What conclusions can you draw from such a circumstance?
>>
>
> Ask the engineers at Creative. They resample at 48 kHz during playback
> regardless of the input sample rate.
> "Thomas Magma" <somewhere@overtherainbow.com> wrote in message
> news:E0obg.175306$P01.14809@pd7tw3no...
>
>>
>>Thinking in the time domain, as you lower the sample rate you increase the
>>digitization (Your sampled sine wave will start to look like a square wave).
>>Clocking that data through a DAC at the same rate will produce strong
>>harmonics (3rd 5th 7th etc). You can't regenerate the original sine wave out
>>of a DAC no matter what digital reconstruction filtering you use if the
>>playback rate is too slow. The output of a DAC will always start digitizing
>>and producing harmonics as you lower the sample/playback rate, unless you have
>>exceeded the full power bandwidth of the DAC or have analog filtering after
>>the DAC.
>
>
> A perfect analog reconstruction filter, i.e. brickwall at 100 Hz _would_
> perfectly reconstruct the original sine wave with no "harmonics" as you call
> them or aliases.
Not really. The real (cosine) component can be reconstructed, but the
imaginary (sine) component will always be unknown. It will take a very
long time to learn the imaginary component if the sampled frequency is
only very slightly less than 100 Hz.
> Such a filter can't be built, hence it is useful to oversample
> by some amount and/or use digital resampling filters to help.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Jerry Avins●May 20, 20062006-05-20
Jon Harris wrote:
> "Jerry Avins" <jya@ieee.org> wrote in message
> news:GIadnYKqYo00hfPZRVn-uw@rcn.net...
>
>>Thomas Magma wrote:
>>
>>
>>>>Thinking in the time domain, as you lower the sample rate you increase the
>>>>digitization (Your sampled sine wave will start to look like a square
>>>>wave). Clocking that data through a DAC at the same rate will produce
>>>>strong harmonics (3rd 5th 7th etc). You can't regenerate the original sine
>>>>wave out of a DAC no matter what digital reconstruction filtering you use
>>>>if the playback rate is too slow. The output of a DAC will always start
>>>>digitizing and producing harmonics as you lower the sample/playback rate,
>>>>unless you have exceeded the full power bandwidth of the DAC or have
>>>>analog filtering after the DAC.
>>>>
>>>>Thomas
>>>>
>>>
>>>
>>>Just to debate a little with myself (slow day). A soundcards playback and
>>>recording rates are typically independent of each other. Playback being much
>>>higher. So reconstruction filtering is possible. If the playback rate
>>>equaled the recording rate you would notice the effects I was trying to
>>>explain.
>>
>>Wrong again. How do you change the playback rate without changing the
>>playback duration?
>
>
> Thomas is correct in this case. Most modern sound cards generate audio at a
> fixed sample rate (typically 48kHz, IIRC) regardless of the source material.
> They use digital resampling to convert whatever the input audio source is to
> 48kHz. This is necessary to allow for playing back (mixing) multiple sounds
> files with different sample rates at the same time. You may think that is a
> strange thing to do, but every time you listen to streaming audio and hear your
> computer's beep sound, that is most likely happening. This also simplifies the
> DAC and output filter design, since the sample rate is fixed.
Thomas is wrong to claim that the same signal recorded at one rate is
played back at another. The playback signal is derived from the recorded
signal, but is not the same as the recorded signal. His consistent
failure to make distinctions -- confounding sampling with digitizing and
aliasing with harmonic distortion are two more examples -- throws his
intuition off track. The answer to my question, "How do you change the
playback rate without changing the playback duration?" is "Change the
sample rate." It's not the same signal if it has a different sample
rate. What's more, there's been some filtering in the process.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Oli Filth●May 20, 20062006-05-20
Thomas Magma said the following on 19/05/2006 23:44:
> Jerry Avins wrote:
>> The reconstruction filter removes aliases, not harmonics. If the signal
>> was properly sampled (Nyquist and all that) there are no harmonics.
>> Quantization noise, once assimilated into the signal (there are ways
>> when capturing the signal to minimize it) can't later be removed.
>
> Any distortion of a sine wave will cause harmonics.
It's only worth considering quantisation as harmonic distortion when the
sine wave amplitude, A, is comparable to that of the quantisation
interval, Q. If A is more than about an order of magnitude greater than
Q, then the quantisation noise is essentially uncorrelated with the
input signal, and approximates spectrally white noise, not harmonic noise.
> Lower sample rates cause
> quantization noise which is a form of distortion.
Sampling does not cause quantisation noise. Quantising causes
quantisation noise. Sampling and quantising aren't the same thing...
> Then resampling at a
> higher rate increases bandwidth, allowing you to see those harmonics. A low
> pass at the original fs/2 helps remove these.
In the case of harmonic distortion, the interpolation filter isn't going
to be of any help. Imagine your sample rate was 2 kHz, and your sine
wave was 100 Hz. fs/2 is 1 kHz, which will allow through the first 10
harmonics of the sine wave. The higher-order harmonics will already
have aliased back into the passband, so you won't be removing these either.
--
Oli
Reply by Jon Harris●May 20, 20062006-05-20
"Jerry Avins" <jya@ieee.org> wrote in message
news:GIadnYKqYo00hfPZRVn-uw@rcn.net...
> Thomas Magma wrote:
>
>>>Thinking in the time domain, as you lower the sample rate you increase the
>>>digitization (Your sampled sine wave will start to look like a square
>>>wave). Clocking that data through a DAC at the same rate will produce
>>>strong harmonics (3rd 5th 7th etc). You can't regenerate the original sine
>>>wave out of a DAC no matter what digital reconstruction filtering you use
>>>if the playback rate is too slow. The output of a DAC will always start
>>>digitizing and producing harmonics as you lower the sample/playback rate,
>>>unless you have exceeded the full power bandwidth of the DAC or have
>>>analog filtering after the DAC.
>>>
>>>Thomas
>>>
>>
>>
>> Just to debate a little with myself (slow day). A soundcards playback and
>> recording rates are typically independent of each other. Playback being much
>> higher. So reconstruction filtering is possible. If the playback rate
>> equaled the recording rate you would notice the effects I was trying to
>> explain.
>
> Wrong again. How do you change the playback rate without changing the
> playback duration?
Thomas is correct in this case. Most modern sound cards generate audio at a
fixed sample rate (typically 48kHz, IIRC) regardless of the source material.
They use digital resampling to convert whatever the input audio source is to
48kHz. This is necessary to allow for playing back (mixing) multiple sounds
files with different sample rates at the same time. You may think that is a
strange thing to do, but every time you listen to streaming audio and hear your
computer's beep sound, that is most likely happening. This also simplifies the
DAC and output filter design, since the sample rate is fixed.
Reply by Jon Harris●May 20, 20062006-05-20
"Thomas Magma" <somewhere@overtherainbow.com> wrote in message
news:E0obg.175306$P01.14809@pd7tw3no...
>
>
> Thinking in the time domain, as you lower the sample rate you increase the
> digitization (Your sampled sine wave will start to look like a square wave).
> Clocking that data through a DAC at the same rate will produce strong
> harmonics (3rd 5th 7th etc). You can't regenerate the original sine wave out
> of a DAC no matter what digital reconstruction filtering you use if the
> playback rate is too slow. The output of a DAC will always start digitizing
> and producing harmonics as you lower the sample/playback rate, unless you have
> exceeded the full power bandwidth of the DAC or have analog filtering after
> the DAC.
A perfect analog reconstruction filter, i.e. brickwall at 100 Hz _would_
perfectly reconstruct the original sine wave with no "harmonics" as you call
them or aliases. Such a filter can't be built, hence it is useful to oversample
by some amount and/or use digital resampling filters to help.
Reply by Ron N.●May 20, 20062006-05-20
banton wrote:
> >For digitized audio signal, intuitively higher oversampling ratio, the
> >digitized signal is closer to original signal, therefore, higher
> >fidelity.
>
> As longer as you don't have frequency components that are
> above samplerate/2 (nyquist frequency), you cannot get "closer"
> to the original signal. You can perfectly reconstruct your signal
> (at least in theory).
The key is the "in theory". One rarely wants to wait an
infinite time for the output of the pre-digitizing anti-alias
audio filter, so the input will not be perfectly bandlimited.
And there is an implementation cost with respect to how
close to Nyquist rate a reconstruction filter can get for
a given accuracy.
In addition, for a given word size, a higher sample rate
can reduce the total quantizing noise by proper use of
dithering, which will get you "closer" to the original
signal if any processing takes place where rounding of
the result is required.
IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M