Stereophile Series on MQA Technology

[The Computer Audiophile]

5 minutes ago, mansr said:

That's all true, but it doesn't contradict what I said.

In signal processing, a filter is a complex multiplication in the frequency domain. This is equivalent, through the Fourier transform, to a convolution in the time domain. This is true for both continuous-time and discrete-time systems. Conversely, any convolution can be regarded as a filter operation.

 

A sampled signal is a sequence of (regularly spaced) impulses. Interpolation fills in the gaps with additional impulses or a continuous function. The simplest interpolation is a zero-order hold, meaning the value of each impulse is simply repeated (held) until the next impulse arrives. This is equivalent to convolution with a rectangle function. Linear interpolation, where the impulses are joined by straight lines, is convolution with a triangle function. Any interpolation scheme you care to define can be expressed as a convolution. Since a convolution is a filter, it follows that interpolation is also a filter.

 

If you don't like this, so be it. Mathematics doesn't care.

Just as my wife and I discussed at the breakfast table this morning ?

[Kal Rubinson]

13 minutes ago, The Computer Audiophile said:

Just as my wife and I discussed at the breakfast table this morning ?

We had bagels with a schmear, too.

[firedog]

8 minutes ago, Kal Rubinson said:

We had bagels with a schmear, too.

Actually, I did too. But I cheated and used a nice gooey French style cheese. Those multicultural influences....

[Brinkman Ship]

56 minutes ago, Kal Rubinson said:

We had bagels with a schmear, too.

Russ & Daughters?

[mav52]

1 hour ago, Kal Rubinson said:

We had bagels with a schmear, too.

 

We had lots of scallion cream cheese. schmear.  ?

[crenca]

Going back to 

 

https://www.computeraudiophile.com/forums/topic/37821-stereophile-series-on-mqa-technology/?page=28&tab=comments#comment-837226

 

 

I am curious as to what @Galileo365 point is besides perhaps a confusion or imprecision of the terms "filter" and "interpolation" as applied to Audio (as if this is surprising).  Is he asserting that MQA, or more specifically an MQA DAC and/or software (such as Tidal & Roon "unfolding") is processing PCM (and remember as Bob S famously says MQA "is just PCM") is a fundamentally different way, doing the math differently?  Nothing in the reverse engineering would indicate that, on the contrary, so...what's the point again?

 

So Bob S is a marketing genius (at least in Audiophooldom circus) and gets his lacky's (e.g. Jim Austin) to throw out terms like "B- Spline" and the like and suddenly MQA has credence?!?

 

Here is a prediction on par with the Sun coming up tomorrow morning:  Bob S and his lacky's in the trade publications will continue to obfuscate and suggest that we don't really understand MQA...

 

[mav52]

9 minutes ago, crenca said:

Going back to 

 

https://www.computeraudiophile.com/forums/topic/37821-stereophile-series-on-mqa-technology/?page=28&tab=comments#comment-837226

 

 

I am curious as to what @Galileo365 point is besides perhaps a confusion or imprecision of the terms "filter" and "interpolation" as applied to Audio (as if this is surprising).  Is he asserting that MQA, or more specifically an MQA DAC and/or software (such as Tidal & Roon "unfolding") is processing PCM (and remember as Bob S famously says MQA "is just PCM") is a fundamentally different way, doing the math differently?  Nothing in the reverse engineering would indicate that, on the contrary, so...what's the point again?

 

So Bob S is a marketing genius (at least in Audiophooldom circus) and gets his lacky's (e.g. Jim Austin) to throw out terms like "B- Spline" and the like and suddenly MQA has credence?!?

 

Here is a prediction on par with the Sun coming up tomorrow morning:  Bob S and his lacky's in the trade publications will continue to obfuscate and suggest that we don't really understand MQA...

 

 

Kinda like a shady car salesmen, 

 

 

 

[Kal Rubinson]

40 minutes ago, mav52 said:

 

We had lots of scallion cream cheese. schmear.  ?

I like a more discrete bagel.   Once you chop up the scallions and embed them in the cream cheese, it becomes impossible to completely resolve the flavors.  My preference is a coherent layering with slices of raw onion and belly lox.

[rickca]

It's curious that a thread titled Stereophile Series on MQA Technology turns into a bunch of posts about schmear.  Another meaning of the word schmear is a corrupt or underhanded inducement; a bribe.

 

 

[Allan F]

14 minutes ago, Kal Rubinson said:

I like a more discrete bagel.   Once you chop up the scallions and embed them in the cream cheese, it becomes impossible to completely resolve the flavors.  My preference is a coherent layering with slices of raw onion and belly lox.

 

Right! And don't forget the capers.

[mav52]

17 minutes ago, Kal Rubinson said:

I like a more discrete bagel.   Once you chop up the scallions and embed them in the cream cheese, it becomes impossible to completely resolve the flavors.  My preference is a coherent layering with slices of raw onion and belly lox.

 

We also like fresh avocado , with chopped pistachios and a drizzle of honey

 

And fresh smoked salmon with greek yogurt

 

cream cheese with fresh strawberry, raspberry/blueberry's

 

And avocado egg salad with  lemon and fresh herbs

[mav52]

Just now, mav52 said:

 

We also like fresh avocado , with chopped pistachios and a drizzle of honey

 

And fresh smoked salmon with greek yogurt

 

cream cheese with fresh strawberry, raspberry/blueberry's

 

And avocado egg salad with  lemon and fresh herbs

 

And now i'm hungry

[Fokus]

9 hours ago, PeterSt said:

If someone name Bob Stuart somewhere tells that there's B-spline interpolation "involved" he can be correct.

 

December 2014: BS in search of the minimal AA and AI filter.

 

"Reconstruction can be regarded as the dual of sampling
and approached in a similar way. Thus, it is not
recommended to present the samples as unfiltered Dirac
spikes to subsequent equipment. Even convolving each
spike with a rectangle of width one sample period (which
is equivalent to a zero-order hold) still generates
theoretically infinite slew rates at the transitions.

 

It thus seems that convolution with a triangle function is
the least that is needed to produce a signal that can be
handled satisfactorily. This is equivalent to linear
interpolation between sample values.

If sampling and reconstruction each use a triangular
kernel, then simplistically8 the total impulse response is
a 3rd-order B-spline, of total width four sampling periods.
That is a total width of 42 μs at a sample rate of 96 kHz
and a time from 10% of peak to the peak of 13.2 μs.

Unfortunately, that is not the end of the story, for we also
have to correct a frequency response droop from the 3rdorder
B-spline which, for 96-kHz sampling, amounts to
2.5dB at 20 kHz (or 3 dB if sampling at 88.2 kHz).
To meet a criterion such as 0.1dB for the maximum
acceptable 20-kHz droop we have generally used a
maximally-flat minimum-phase 3rd-order FIR digital
flattening-filter immediately prior to the triangle
convolution in the reconstruction.

The flattening filter increases the total length of the endto-
end impulse response by three sample periods, giving
a total length of seven sample periods. Inevitably, the
impulse response is then no longer a single pulse, there
being a negative downswing, a positive, and another
negative following, as shown in Figure 12 below."

 

It just shows how they initially dreamed up their weak filters.

That splines were used is pretty irrelevant. It could have been

anything, including second-order bagels.

 

[Kal Rubinson]

1 hour ago, Brinkman Ship said:

Russ & Daughters?

Sables UES

[Brinkman Ship]

45 minutes ago, Kal Rubinson said:

Sables UES

Oh yes, so good.

[mansr]

1 hour ago, Fokus said:

December 2014: BS in search of the minimal AA and AI filter.

 

"Reconstruction can be regarded as the dual of sampling
and approached in a similar way. Thus, it is not
recommended to present the samples as unfiltered Dirac
spikes to subsequent equipment. Even convolving each
spike with a rectangle of width one sample period (which
is equivalent to a zero-order hold) still generates
theoretically infinite slew rates at the transitions.

 

It thus seems that convolution with a triangle function is
the least that is needed to produce a signal that can be
handled satisfactorily. This is equivalent to linear
interpolation between sample values.

If sampling and reconstruction each use a triangular
kernel, then simplistically8 the total impulse response is
a 3rd-order B-spline, of total width four sampling periods.
That is a total width of 42 μs at a sample rate of 96 kHz
and a time from 10% of peak to the peak of 13.2 μs.

Unfortunately, that is not the end of the story, for we also
have to correct a frequency response droop from the 3rdorder
B-spline which, for 96-kHz sampling, amounts to
2.5dB at 20 kHz (or 3 dB if sampling at 88.2 kHz).
To meet a criterion such as 0.1dB for the maximum
acceptable 20-kHz droop we have generally used a
maximally-flat minimum-phase 3rd-order FIR digital
flattening-filter immediately prior to the triangle
convolution in the reconstruction.

The flattening filter increases the total length of the endto-
end impulse response by three sample periods, giving
a total length of seven sample periods. Inevitably, the
impulse response is then no longer a single pulse, there
being a negative downswing, a positive, and another
negative following, as shown in Figure 12 below."

 

It just shows how they initially dreamed up their weak filters.

That splines were used is pretty irrelevant. It could have been

anything, including second-order bagels.

Note that there is no attempt to explain why this approach is a good idea in the first place.

[Galileo365]

4 hours ago, mansr said:

In signal processing, a filter is a complex multiplication in the frequency domain. This is equivalent, through the Fourier transform, to a convolution in the time domain. This is true for both continuous-time and discrete-time systems. Conversely, any convolution can be regarded as a filter operation.

 

Yes, I know; although, the mathematics behind that presume a “perfect” brick-wall filter, as one example, which is something that at least currently cannot be built. Plus, Fourier transforms work well at expressing attributes of the frequency domain but not so much the time domain, convolution notwithstanding. So using this particular point to say that interpolation and filtering equivocate particularly in reference to “temporal smearing” has no mathematical support and little basis in reality.

[Ralf11]

11 hours ago, firedog said:

Correction: on a bagel, the correct term is "schmear". Let's not insult bagels by associating them with MQA.

 

a schmear is a foodstuff that does not contain any brains AFAIK

 

a smear uses the temporal lobes

 

and it is too late to prevent the Assault on Bagels (AoB) - Noah's did that that decades ago, hence the term Dough-ah's

[Ralf11]

5 hours ago, mansr said:

In signal processing, a filter is a complex multiplication in the frequency domain.

 

a multiplication of scalars using complex numbers, right?

 

or does this mean a matrix multiplication?

 

[Ralf11]

5 hours ago, The Computer Audiophile said:

Just as my wife and I discussed at the breakfast table this morning ?

 

describe your bagels

[mansr]

19 minutes ago, Galileo365 said:

Yes, I know; although, the mathematics behind that presume a “perfect” brick-wall filter, as one example, which is something that at least currently cannot be built. Plus, Fourier transforms work well at expressing attributes of the frequency domain but not so much the time domain, convolution notwithstanding. So using this particular point to say that interpolation and filtering equivocate particularly in reference to “temporal smearing” has no mathematical support and little basis in reality.

I suggest you spend a few more years studying these topics before trying to argue about them.

[mansr]

15 minutes ago, Ralf11 said:

a multiplication of scalars using complex numbers, right?

 

or does this mean a matrix multiplication?

Multiplication of complex numbers, one for each frequency.

[Galileo365]

26 minutes ago, mansr said:

I suggest you spend a few more years studying these topics before trying to argue about them.

I suggest that you stop assuming I haven’t already done so and consider the possibility that you are in error.

[mansr]

12 minutes ago, Galileo365 said:

I suggest that you stop assuming I haven’t already done so and consider the possibility that you are in error.

I said you should study some more. By definition, you can't have done this. I don't know what your background is, but your understanding of these matters is clearly confused. If you want to convince me otherwise, you'll have to do better than quoting dictionary definitions.

[NOMBEDES]

3 hours ago, Fokus said:

 

December 2014: BS in search of the minimal AA and AI filter.

 

"Reconstruction can be regarded as the dual of sampling
and approached in a similar way. Thus, it is not
recommended to present the samples as unfiltered Dirac
spikes to subsequent equipment. Even convolving each
spike with a rectangle of width one sample period (which
is equivalent to a zero-order hold) still generates
theoretically infinite slew rates at the transitions.

 

It thus seems that convolution with a triangle function is
the least that is needed to produce a signal that can be
handled satisfactorily. This is equivalent to linear
interpolation between sample values.

If sampling and reconstruction each use a triangular
kernel, then simplistically8 the total impulse response is
a 3rd-order B-spline, of total width four sampling periods.
That is a total width of 42 μs at a sample rate of 96 kHz
and a time from 10% of peak to the peak of 13.2 μs.

Unfortunately, that is not the end of the story, for we also
have to correct a frequency response droop from the 3rdorder
B-spline which, for 96-kHz sampling, amounts to
2.5dB at 20 kHz (or 3 dB if sampling at 88.2 kHz).
To meet a criterion such as 0.1dB for the maximum
acceptable 20-kHz droop we have generally used a
maximally-flat minimum-phase 3rd-order FIR digital
flattening-filter immediately prior to the triangle
convolution in the reconstruction.

The flattening filter increases the total length of the endto-
end impulse response by three sample periods, giving
a total length of seven sample periods. Inevitably, the
impulse response is then no longer a single pulse, there
being a negative downswing, a positive, and another
negative following, as shown in Figure 12 below."

 

It just shows how they initially dreamed up their weak filters.

That splines were used is pretty irrelevant. It could have been

anything, including second-order bagels.

 

 

 

Does anyone think this is just too much processing and filtering and sundry BS?   Flattening filter?  weak filters?

3rd order B spline?

 

I just want to rock and roll.

 

God help us.   When I win the big lotto, I will get rid of all my equipment and invite people over for live music. 

 

The End.