Pio2001
Senior Member
Discussion splitted from https://www.audiosciencereview.com/forum/index.php?threads/genelec-8341a-sam™-studio-monitor-review.11652/page-22#post-336991
Here is food for thought.
Let's play with Rephase and Foobar2000's convolver. We can design any amplitude or phase correction that we want, and see the effects on audio signals.
First, here are two amplitude corrections, in green and red.
You can see that they are the exact opposite of each other. If I apply the red correction, then the green correction, I should go back to the original frequency response.
BUT... you can see the associated blue and pink curves that show the phase responses of these two corrections. They are flat. These corrections are not minimal phase, but linear phase. They are thus going to introduce pre-ringing. What will happen ? Let's apply them to a 57 Hz truncated sine.
On top, the original.
The middle part shows the result after the application of the red curve to the original (corrected in volume). A lot of pre and post ringing appear.
Think about it for a second : we changed only amplitude, not phase. Nonetheless, the signal was completely smeared in the time domain. Energy appears before and after the original signal. This debunks a strong misconception : that amplitude deals with volume only, and phase with time only. Wrong ! A change in the amplitude response alone has strong effects in the time domain !
The bottom shows the middle signal, further altered with the application of the green correction.
We can see that, as expected, it returns to its original shape.
But what's counter-intuitive is that the operation cancelled all the pre and post ringing !
Now, let's do the same thing with phase corrections alone. Here are two all-pass filters, with a perfectly flat amplitude response, but with random phase response. Again, the two filters are the exact opposite of each other.
Let's apply them to our original truncated sine :
Again, a lot of pre and post ringing are introduced. And again, both are completely cancelled by the application of the inverse correction.
Well, nearly completely, we can see a small imperfection at the end of the signal.
This is an answer to your question : pre and post ringing are not cumulative. They are reversible.
Of course, cancelling them completely requires an extreme accuracy in the correction. the slightest approximation, and all the ringing reappears. We can see that even in the digital domain, with 16 bits wave files, the process is not perfect.
In the acoustic domain, if we take room modes as an example, the best we can do is decreasing the ringing without cancelling it completely, and only at very low frequencies. Typically under 100 Hz.
Sure, minimal phase IIR filters are causal, so without any pre-ringing. But as soon as you touch the phase..
So, the million-dollar question seems to be how do you correct phase without introducing any pre-ringing visible in step response?
Here is food for thought.
Let's play with Rephase and Foobar2000's convolver. We can design any amplitude or phase correction that we want, and see the effects on audio signals.
First, here are two amplitude corrections, in green and red.
You can see that they are the exact opposite of each other. If I apply the red correction, then the green correction, I should go back to the original frequency response.
BUT... you can see the associated blue and pink curves that show the phase responses of these two corrections. They are flat. These corrections are not minimal phase, but linear phase. They are thus going to introduce pre-ringing. What will happen ? Let's apply them to a 57 Hz truncated sine.
On top, the original.
The middle part shows the result after the application of the red curve to the original (corrected in volume). A lot of pre and post ringing appear.
Think about it for a second : we changed only amplitude, not phase. Nonetheless, the signal was completely smeared in the time domain. Energy appears before and after the original signal. This debunks a strong misconception : that amplitude deals with volume only, and phase with time only. Wrong ! A change in the amplitude response alone has strong effects in the time domain !
The bottom shows the middle signal, further altered with the application of the green correction.
We can see that, as expected, it returns to its original shape.
But what's counter-intuitive is that the operation cancelled all the pre and post ringing !
Now, let's do the same thing with phase corrections alone. Here are two all-pass filters, with a perfectly flat amplitude response, but with random phase response. Again, the two filters are the exact opposite of each other.
Let's apply them to our original truncated sine :
Again, a lot of pre and post ringing are introduced. And again, both are completely cancelled by the application of the inverse correction.
Well, nearly completely, we can see a small imperfection at the end of the signal.
This is an answer to your question : pre and post ringing are not cumulative. They are reversible.
Of course, cancelling them completely requires an extreme accuracy in the correction. the slightest approximation, and all the ringing reappears. We can see that even in the digital domain, with 16 bits wave files, the process is not perfect.
In the acoustic domain, if we take room modes as an example, the best we can do is decreasing the ringing without cancelling it completely, and only at very low frequencies. Typically under 100 Hz.