lowpass tap count

You argue for symmetry very well. But what do you mean by "oversampe"? 
Interpolation or something? Hardly, I can sample at rate higher than the 
standard bitrate or it is a good idea to undersample the part subject 
for low-filtering.

On 10/27/2011 12:49 PM, valtih1978 wrote:
> You argue for symmetry very well. But what do you mean by "oversampe"?
> Interpolation or something? Hardly, I can sample at rate higher than the
> standard bitrate or it is a good idea to undersample the part subject
> for low-filtering.

These remarks apply to baseband signals. They can be generalized for 
passband signals, but I don't attempt that refinement here.

The absolute minimum sapling rate -- asymptotically approachable but not 
actually achievable -- is twice the the highest frequency component in 
the sampled signal. Any rate higher than that is oversampling. Unless 
you are prepared to deal with daunting difficulties, you should 
oversample by at least 125%. 150% will make life easier yet. I have 
never succeeded in making a robust closed-loop servo that oversampled 
less than a factor of four with respect to the frequencies of interest, 
and ten is not uncommon. Servos are a special case. Large oversampling 
factors allow one to dispense with an anti-alias filter, thereby 
reducing loop delay. Given that the actual frequencies in a servo loop 
may be much higher than the interesting ones, that 4X might actually 
represent undersampling. It is never possible to accurately reproduce an 
undersampled signal.

Jerry
-- 
Engineering is the art of making what you want from things you can get.

Jerry Avins <jya@ieee.org> wrote:

(snip)
> These remarks apply to baseband signals. They can be generalized for 
> passband signals, but I don't attempt that refinement here.

> The absolute minimum sapling rate -- asymptotically approachable but not 
> actually achievable -- is twice the the highest frequency component in 
> the sampled signal. Any rate higher than that is oversampling. 

Hmmm.  I usual consider oversampling somewhat higher than that,
but then it is rare to have a signal with a sharp enough cutoff
to make that distinction.

With 20Hz to 20kHz audio, and the CD 44.1kHz sampling rate,
one must have a filter sharp enough that one can sample at 44.1kHz.
I would, then, not consider 44.2kHz oversampling.  

> Unless you are prepared to deal with daunting difficulties, you 
> should oversample by at least 125%. 150% will make life easier yet. 

Do you mean 125% more than, or 125% of the minimum?

> I have never succeeded in making a robust closed-loop servo 
> that oversampled less than a factor of four with respect to 
> the frequencies of interest, and ten is not uncommon. 
> Servos are a special case. Large oversampling 
> factors allow one to dispense with an anti-alias filter, thereby 
> reducing loop delay. Given that the actual frequencies in a servo loop 
> may be much higher than the interesting ones, that 4X might actually 
> represent undersampling. It is never possible to accurately 
> reproduce an undersampled signal.

But how low does the signal have to get?  If it is below noise
is that good enough?  That is what I always wonder.

I understand that digital cameras have an optical low (spatial
frequency) pass filter in front of the sensor.  How sharp can one
build such a filter?  Even more, when doing scan rate conversion,
one should filter, both vertically and horizontally, to get all
aliased frequencies out, but that is rarely easy.

-- glen

On 10/27/2011 6:37 PM, glen herrmannsfeldt wrote:
> Jerry Avins<jya@ieee.org>  wrote:
>
> (snip)
>> These remarks apply to baseband signals. They can be generalized for
>> passband signals, but I don't attempt that refinement here.
>
>> The absolute minimum sapling rate -- asymptotically approachable but not
>> actually achievable -- is twice the the highest frequency component in
>> the sampled signal. Any rate higher than that is oversampling.
>
> Hmmm.  I usual consider oversampling somewhat higher than that,
> but then it is rare to have a signal with a sharp enough cutoff
> to make that distinction.

If we agree that oversampling is sampling faster than necessary, we need 
to decide what is necessary. I prefer sharp boundaries in definitions.

> With 20Hz to 20kHz audio, and the CD 44.1kHz sampling rate,
> one must have a filter sharp enough that one can sample at 44.1kHz.
> I would, then, not consider 44.2kHz oversampling.

By the definitions I opined, any rate higher than 40 KHz is 
oversampling, and 44.1 is only 1.1025 oversampled. I can imagine super 
filters at the recording end, but the reconstruction filters in all 
those players can't be that good.  I'd bet on some aliasing and an upper 
frequency a bit below 20 KHz.

>> Unless you are prepared to deal with daunting difficulties, you
>> should oversample by at least 125%. 150% will make life easier yet.
>
> Do you mean 125% more than, or 125% of the minimum?

fs >= 2*fmax

>> I have never succeeded in making a robust closed-loop servo
>> that oversampled less than a factor of four with respect to
>> the frequencies of interest, and ten is not uncommon.
>> Servos are a special case. Large oversampling
>> factors allow one to dispense with an anti-alias filter, thereby
>> reducing loop delay. Given that the actual frequencies in a servo loop
>> may be much higher than the interesting ones, that 4X might actually
>> represent undersampling. It is never possible to accurately
>> reproduce an undersampled signal.
>
> But how low does the signal have to get?  If it is below noise
> is that good enough?  That is what I always wonder.

Which signal? Anyway, low enough not to matter. In a servo, not large 
enough to interfere with reasonable operation.

> I understand that digital cameras have an optical low (spatial
> frequency) pass filter in front of the sensor.  How sharp can one
> build such a filter?  Even more, when doing scan rate conversion,
> one should filter, both vertically and horizontally, to get all
> aliased frequencies out, but that is rarely easy.

We put up with spacial aliasing to a remarkable degree.

Jerry
-- 
Engineering is the art of making what you want from things you can get.

Jerry Avins <jya@ieee.org> wrote:

(snip)
>>> The absolute minimum sapling rate -- asymptotically approachable but not
>>> actually achievable -- is twice the the highest frequency component in
>>> the sampled signal. Any rate higher than that is oversampling.

(then I wrote)
>> Hmmm.  I usual consider oversampling somewhat higher than that,
>> but then it is rare to have a signal with a sharp enough cutoff
>> to make that distinction.

> If we agree that oversampling is sampling faster than necessary, 
> we need to decide what is necessary. I prefer sharp boundaries 
> in definitions.

I suppose so, but analog filters aren't usually that sharp.

>> With 20Hz to 20kHz audio, and the CD 44.1kHz sampling rate,
>> one must have a filter sharp enough that one can sample at 44.1kHz.
>> I would, then, not consider 44.2kHz oversampling.

> By the definitions I opined, any rate higher than 40 KHz is 
> oversampling, and 44.1 is only 1.1025 oversampled. I can imagine super 
> filters at the recording end, but the reconstruction filters in all 
> those players can't be that good.  I'd bet on some aliasing and an 
> upper frequency a bit below 20 KHz.

Well, now I think everyone uses fancy digital oversampling filters,
but in the early days of CDs it was all analog filters as far as
I know.  

(snip)
>> But how low does the signal have to get?  If it is below noise
>> is that good enough?  That is what I always wonder.

> Which signal? 

The aliasable signal that gets through the filter.

> Anyway, low enough not to matter. In a servo, not large 
> enough to interfere with reasonable operation.

But for audio you have to do better.  

>> I understand that digital cameras have an optical low (spatial
>> frequency) pass filter in front of the sensor.  How sharp can one
>> build such a filter?  Even more, when doing scan rate conversion,
>> one should filter, both vertically and horizontally, to get all
>> aliased frequencies out, but that is rarely easy.

> We put up with spacial aliasing to a remarkable degree.

For moving pictures, I suppose so.  The picture changes fast
enough that by the time you notice, it has moved on.  In the NTSC
days, with high frequencies going into the color subcarrier they
were much more noticable.

But for still pictures, which you can look at very carefully, 
aliasing generates Moire patterns and can be somewhat more visible.

For cheap cameras maybe the lens resolution is low enough that
you don't have much aliasing, but for expensive cameras it 
shouldn't be so hard.

-- glen

On 10/26/2011 10:26 PM, glen herrmannsfeldt wrote:
> Fred Marshall<fmarshallxremove_the_x@acm.org>  wrote:
>
> (snip)
>> It seems that you've not discussed a fundamental parameter of filter design:
>
>> The length of a filter is very much dependent on the width of the
>> narrowest *transition region*.  It doesn't matter if it's lowpass,
>> highpass, etc.
>
>> The length of the filter is roughly the reciprocal of the width of the
>> narrowest transition region.
>
>> So a lowpass (or a highpass) filter with first edge at 0.3fs and next
>> edge at 0.4fs will have a transition band of 0.1fs and a length around
>> 10/fs.
>> A filter with first edge at .35fs and next edge at .36fs will have a
>> transition band of 0.01fs and a length around 100/fs.
>
>> Maybe there's a factor of 2 in there but this is pretty close.
>
>> And, that's about all there is to say about it except for minute details.
>
> And note that for filters with very low or very high transition
> frequency that the transition will generally be narrow, especially
> for the high end.
>
> -- glen

glen,

Why "especially for the high end"?

Fred

Fred Marshall <fmarshallxremove_the_x@acm.org> wrote:

(snip, I wrote)
>> And note that for filters with very low or very high transition
>> frequency that the transition will generally be narrow, especially
>> for the high end.

> glen,

> Why "especially for the high end"?

(snip)

Well, if you have a low-pass filter at 0.1fs, it could have a 
long tail, but if it is at 0.45fs it can't have a long tail.

That was the reason for the comment.

Now, someone will note that you could have high-pass filters
the other way around, and I suppose so.

The high-pass 0.1fs filter has to be sharp, and a high-pass 0.45fs
doesn't, but what do you use a high-pass 0.45fs filter with a 
long tail for?  But if you want one, I suppose it is fine.

-- glen

On 10/28/2011 11:16 AM, glen herrmannsfeldt wrote:
> Fred Marshall<fmarshallxremove_the_x@acm.org>  wrote:
>
> (snip, I wrote)
>>> And note that for filters with very low or very high transition
>>> frequency that the transition will generally be narrow, especially
>>> for the high end.
>
>> glen,
>
>> Why "especially for the high end"?
>
> (snip)
>
> Well, if you have a low-pass filter at 0.1fs, it could have a
> long tail, but if it is at 0.45fs it can't have a long tail.
>
> That was the reason for the comment.
>
> Now, someone will note that you could have high-pass filters
> the other way around, and I suppose so.
>
> The high-pass 0.1fs filter has to be sharp, and a high-pass 0.45fs
> doesn't, but what do you use a high-pass 0.45fs filter with a
> long tail for?  But if you want one, I suppose it is fine.
>
> -- glen

I was hoping that's all it was.  I'd say that you're constraining the 
transition band widths with these spec's.  So the rule for transition 
band relation to length remains, eh?

Fred

Seems off topic to me.  The issue here is really the sampling rate *in 
frequency* and has not much of anything to do with the temporal sampling 
rate.

The higher the sampling rate in frequency, the sharper the transition 
bands can be.  And that folds right back to the *length* of the temporal 
function .. in this case the filter .. for a given temporal sampling rate.

Now, increase the temporal sampling rate and you get:
- the same transition band width for the same temporal length (more 
samples in time but higher fs to divide samples over).
- wider transition band width for the same number of temporal samples 
because the samples cover less time.  And, the frequency samples cover 
more frequency so less control over transition band width.

Of course, it's fine to go off on a tangent.   :-)

Fred