John Atkinson: Yes, MQA IS Elegant...

[Fokus]

1 hour ago, Shadders said:

Can you explain why it does have out of band energy ?.

 

Your function is the multiplication of a sine and a rectangle function. The spectrum of the

result is the convolution of the part spectra. The spectrum of the rectangle function, while

falling with frequency, still extends to infinity.

 

Something to ponder: the ringing imparted by a low-pass filter is not something added to the

signal. Rather, it is the result of something being taken away from the signal.

 

 

[mansr]

1 minute ago, Fokus said:

Something to ponder: the ringing imparted by a low-pass filter is not something added to the

signal. Rather, it is the result of something being taken away from the signal.

Exactly. It's obvious if you think about it, but probably unintuitive to the average person.

[adamdea]

5 hours ago, John_Atkinson said:

 

Fig.12 at https://www.stereophile.com/content/zen-art-ad-conversion-page-2

 

John Atkinson

Editor, Stereophile

 

Sorry - but that seems to me to be the "impulse response" of a dac fed *something*. The something seems to be a non band limited impulse fed to a QA at 96khz and then sample rate converted to 44.1. Why are you calling this a perfectly legal band limited impulse" ?-it simply seems to be a conflation of the impulse responses of the decimation filter fed an illegal impulse and then whatever the dac does with it . Surely the ringing is the result of feeding a non band-limited impulse (whose frequency response is at figure 5 - it seems very clearly not to be band limited)  into a sample rate converter which presumably applies a brick wall 44.1khz filter? You have not isolated that ringing (ie the ringing  implicit in the 44.1khz data) from any ringing caused by the dac.  

In any event the prior question (which i think I asked above, but perhaps forgot) is why the original "impulse" (whose frequency response is at figure 5) is supposed to represent a musical transient. 

You say "With a musical transient, ie, when there is silence then data". Is a musical transient *silence* followed by data- where does that happen (even supposing that the rest of the orchestra stops playing before the transient), in space? 

It would be useful to see all of this demonstrated with a real musical transient

[Shadders]

1 hour ago, Fokus said:

Your function is the multiplication of a sine and a rectangle function. The spectrum of the

result is the convolution of the part spectra. The spectrum of the rectangle function, while

falling with frequency, still extends to infinity.

Hi,

Apologies for the delay in responding, it is a bank holiday here in the UK - so it is eat, drink and be merry.

 

OK - so, in my slightly inebriated state, are you are stating that at the sin(phi)=0 (start of the sine wave in the example) that there is a discontinuity ?

 

Or, that the function applied to the filter which you state is the multiplication of the sine which is continuous (-infinity to +infinity) is gated by the rectangular function, and this gating function of the rectangular pulse causes the ringing ?

 

Sorry, may not be making sense - too much drink for merriment.

 

Regards,

Shadders.

[Shadders]

2 hours ago, mansr said:

Exactly. It's obvious if you think about it, but probably unintuitive to the average person.

Hi,

OK - i am assuming that you completely agree with the statements from Fokus. Is this correct ???.

 

I need to investigate the rectangular function a bit more. hic.

 

Regards,

Shadders.

[mansr]

1 minute ago, Shadders said:

OK - so, in my slightly inebriated state, are you are stating that at the sin(phi)=0 (start of the sine wave in the example) that there is a discontinuity ?

 

Or, that the function applied to the filter which you state is the multiplication of the sine which is continuous (-infinity to +infinity) is gated by the rectangular function, and this gating function of the rectangular pulse causes the ringing ?

Those statements are equivalent.

[Shadders]

Just now, mansr said:

Those statements are equivalent.

Hi,

OK - will await for the response from Fokus.

 

Sorry for labouring the point, i am only average engineer - if an engineer at all.

 

Regards,

Shadders.

[mansr]

I suppose this is as good a time as any to unveil my new website. Here's something I wrote up about filter ringing:

https://troll-audio.com/articles/filter-ringing/

 

 

[John_Atkinson]

5 hours ago, adamdea said:

Sorry - but that seems to me to be the "impulse response" of a dac fed *something*.

 

Fig.12 in my article plots the sample values in the digital domain. No DAC involved.

 

Quote

The something seems to be a non band limited impulse fed to a QA at 96khz and then sample rate converted to 44.1.

 

To create those digital-domain data, I digitized at 96kHz a unidirectional, shaped analog pulse with an approximate bandwidth of 60kHz with the Ayre QA9 A/D converter with its "Listen" antialiasing filter. I then sample-rate-converted those data to 44.1kHz. This is described in the article.

 

Quote

Why are you calling this a perfectly legal band limited impulse" ?

 

Because there is no spectral content above the new Nyquist frequency of 22.05kHz, due to the SRC's high-order low-pass filter. (Actually, spectral content above 22.05kHz analyzed in the digital domain after resampling to 96kHz, lies at approximately -127dB ref. the peak pulse level.) It is thus a "legal" 44.1kHz signal.

 

John Atkinson

Editor, Stereophile

 

[adamdea]

38 minutes ago, John_Atkinson said:

 

Fig.12 in my article plots the sample values in the digital domain. No DAC involved.

 

 

To create those digital-domain data, I digitized at 96kHz a unidirectional, shaped analog pulse with an approximate bandwidth of 60kHz with the Ayre QA9 A/D converter with its "Listen" antialiasing filter. I then sample-rate-converted those data to 44.1kHz. This is described in the 

 

Apologies about the dac - but the confusion arose from

your original quote which I still can’t understand. But the ringing in figure 12 is just the src faced with an illegal impulse it seems 

[Hugo9000]

1 hour ago, mansr said:

I suppose this is as good a time as any to unveil my new website. Here's something I wrote up about filter ringing:

https://troll-audio.com/articles/filter-ringing/

 

 

I love the clean look of your site, and the clarity and precision of your writing.  I look forward to further articles beyond these first three, thanks very much for sharing!

[Fokus]

6 hours ago, John_Atkinson said:

Because there is no spectral content above the new Nyquist frequency of 22.05kHz, due to the SRC's high-order low-pass filter.

 

But if the SRC is half-band then there is content exactly at 22.05k (and aliased content below that), and that makes the signal illegal in the sense that it will trigger the ringing of any later reconstruction filter.

 

Now if you had commanded the SRC to stop at 22.04k all would be well, but most SRCs do not support this.

 

This is Bias Peak Pro 6.03:

 

 

This is iZotope:

 

 

The difference, and its implications, is significant.

 

[Archimago]

10 hours ago, mansr said:

I suppose this is as good a time as any to unveil my new website. Here's something I wrote up about filter ringing:

https://troll-audio.com/articles/filter-ringing/

 

 

 

Very nice Mans! Love the logo/avatar .

[Fokus]

14 hours ago, Shadders said:

 it is a bank holiday here in the UK - so it is eat, drink and be merry.

 

Any Sunday will do for that. In our case a Roter Veltliner with salmon and green asparagi.

 

14 hours ago, Shadders said:

 are you are stating that at the sin(phi)=0 (start of the sine wave in the example) that there is a discontinuity ?

 

is the multiplication of the sine which is continuous (-infinity to +infinity) is gated by the rectangular function, and this gating function of the rectangular pulse causes the ringing ?

 

There certainly is a discontinuity. Switching something on or off in our ideal mathematical world implies a discontinuity. Your particular test signal is simple enough to be separated into its component functions, namely an eternal sine, a rectangle (keying the sine on and off), and a step (keeping the signal at high after the sine went off). For all of these functions we have closed-form Fourier transforms, two of which stretch to infinity. This allows us to see/know quickly that the gated sine also stretches to infinity in the frequency domain.

 

 

[Shadders]

2 hours ago, Fokus said:

There certainly is a discontinuity. Switching something on or off in our ideal mathematical world implies a discontinuity. Your particular test signal is simple enough to be separated into its component functions, namely an eternal sine, a rectangle (keying the sine on and off), and a step (keeping the signal at high after the sine went off). For all of these functions we have closed-form Fourier transforms, two of which stretch to infinity. This allows us to see/know quickly that the gated sine also stretches to infinity in the frequency domain.

Hi,

I can see how you can for the gated sine state that it is a rectangular function multiplied by the eternal sine.

 

This issue i have with your response is that you state it is "implied". The filter has no knowledge of what the signal is.

 

As such, are you stating that when the sine wave starts that there is definitely a discontinuity, or no discontinuity ?

 

Please do not use the word implied, there either is or there isn't. The filter has to respond to the incoming data, not an "implied" signal.

 

Regards,

Shadders.

[Jud]

6 hours ago, Fokus said:

 

But if the SRC is half-band then there is content exactly at 22.05k (and aliased content below that), and that makes the signal illegal in the sense that it will trigger the ringing of any later reconstruction filter.

 

Now if you had commanded the SRC to stop at 22.04k all would be well, but most SRCs do not support this.

 

This is Bias Peak Pro 6.03:

 

 

This is iZotope:

 

 

The difference, and its implications, is significant.

 

 

There are quite a lot of SRCs shown at http://src.infinitewave.ca/ that don't behave as well as iZotope in this regard.

[Jud]

13 hours ago, mansr said:

I suppose this is as good a time as any to unveil my new website. Here's something I wrote up about filter ringing:

https://troll-audio.com/articles/filter-ringing/

 

 

 

Neither of my phone browsers will connect. Certificate problem.

[Shadders]

2 hours ago, Fokus said:

and a step (keeping the signal at high after the sine went off)

Hi,

Regarding your statement above. Let us assume that your "implied" signal theory is correct.

 

For the sine to stop, the rectangular pulse has a negative going discontinuity at (pi/2).

 

For the step to start, the step has a positive going discontinuity at (pi/2).

 

The two discontinuities cancel out at (pi/2).

 

Therefore, how can there be a discontinuity at (pi/2) causing the ringing ?

 

Regards,

Shadders.

[mansr]

20 minutes ago, Shadders said:

I can see how you can for the gated sine state that it is a rectangular function multiplied by the eternal sine.

 

This issue i have with your response is that you state it is "implied". The filter has no knowledge of what the signal is.

 

As such, are you stating that when the sine wave starts that there is definitely a discontinuity, or no discontinuity ?

 

Please do not use the word implied, there either is or there isn't. The filter has to respond to the incoming data, not an "implied" signal.

The transition from zeros to sine wave can be described as a multiplication of a continuous sine with a step function. Time domain multiplication corresponds to convolution in the frequency domain. The Fourier transform of a sine is an impulse, and that of the step function extends to infinity (or Nyquist for a discrete-time system). It follows that the Fourier transform of the product also extends to infinity (or Nyquist).

[mansr]

23 minutes ago, Jud said:

Neither of my phone browsers will connect. Certificate problem.

Strange. It's using Cloudflare certificates. What browsers do you use?

[mansr]

13 minutes ago, Shadders said:

Regarding your statement above. Let us assume that your "implied" signal theory is correct.

 

For the sine to stop, the rectangular pulse has a negative going discontinuity at (pi/2).

 

For the step to start, the step has a positive going discontinuity at (pi/2).

 

The two discontinuities cancel out at (pi/2).

 

Therefore, how can there be a discontinuity at (pi/2) causing the ringing ?

There's still a corner, or a discontinuity in the first derivative, where the sine wave switches to a straight line. That also has unbounded bandwidth.

[gdpr]

8 minutes ago, mansr said:

Strange. It's using Cloudflare certificates. What browsers do you use?

It is not working on my mobile either : Chrome on Samsung phone - certification issue.

It works perfect on Windows PC chrome browser.

 

Dirk

 

[mansr]

Just now, ddetaey said:

It is not working on my mobile either : Chrome on Samsung phone - certification issue.

Can either of you please provide a screenshot of the full error message?

[gdpr]

Sorry, cannot do as it is now working !

Dirk

[Shadders]

1 minute ago, mansr said:

There's still a corner, or a discontinuity in the first derivative, where the sine wave switches to a straight line. That also has unbounded bandwidth.

Hi,

No, there is no discontinuity, neither in the sine waveform starting, nor the sine wave levelling to value 1 (constant).

 

For the sine wave starting, approaching from the negative axis, the value is zero. Approaching from the positive axis, the value tends to zero. NO discontinuity.

 

For the sine wave levelling to 1. Approach from the negative direction, the value tends to wards 1. Approach from the positive direction the value is 1. NO discontinuity.

 

You state that there is a discontinuity in the first derivative. Approach from the negative direction, the first derivative value tends to zero (cos(pi/2) = 0). Approach from the positive direction the derivative is zero. NO discontinuity.

 

Regards,

Shadders.