Hi John,
Sorry in advance for the lengthy post.
An MSO user recently noted that correlation between MSO sub response predictions (computed from superposition of filtered individual sub data) and final REW measurements of all subs together was somewhat off below about 25 Hz and good above that for his project. His hypothesis was that it might be due to having an IR window that was not wide enough in the REW measurements prior to export. He showed that a measured SPL response changed below 25 Hz when widening the IR window from its default 500 msec to about 1.7 sec.
At first I thought that such a change couldn't affect the correlation between predicted response and final measurement at all. I thought it might only affect the predicted combined sub responses in an absolute sense, and that the final measurement of all subs together would also be affected in the absolute sense in the exact same way, resulting in no net error in correlation of predicted and final measurements. This thought was further reinforced by a statement he made that when staying within REW itself, the SPL response of the A+B sum computed from individual sub measurements by trace arithmetic matched perfectly with the two subs measured together.
But then it occurred to me that if each sub measurement exported from REW were affected in a different way by the windowing (something analogous to applying a different, unknown filter to each measurement), the integrity of the superposition would be compromised and prediction/measurement correlation errors could occur. This only raised another question though. If this hypothesis were true, why would it work perfectly within REW itself and not in MSO? After thinking about it some more, it seems likely that REW is first computing the sum, then windowing the result, while MSO is computing (in the frequency domain) the sum of already-windowed results. I guess the windowing is not a linear operation, so the order of summation and windowing matters. Does this explanation sound reasonable?
If this is a reasonable explanation, it points to a potential remedy of widening the window before exporting (or preferably specifying a wider window for all measurements prior to performing them). While investigating this, I ran into a couple of things that confused me. The first project I checked was allowing a very wide window (5461 msec), making it easy to determine the narrowest window width above which the data at the lowest frequencies no longer changed. But then I tried a newer project, and it was limiting the maximum window width to 1731 msec. So I took a look at the measurement info for each one.
Here's the newer one that's allowing a maximum of 1731 msec
Everything seems consistent. It's downsampled to 3000 Hz with 8192 samples, giving a frequency resolution of 0.366 Hz and a total impulse length of 2.73 sec.
The older measurement shown below is puzzling me though. It's the one that allows the wider window due to the longer impulse length.
It has an impulse length of 32768 samples, or 4 times the length of the previous one, despite (or maybe because of?) its original sweep being 256k, rather than the longer 1M of the previous one. Yet the frequency resolution is the same 0.366 Hz, despite the total number of samples being 4x that of the earlier measurement. I'm certainly no DSP expert, so what might be obvious to someone who is, is baffling me.
I'd like to specify in the MSO documentation a way to ensure a longer impulse length than 2.73 sec in REW. This would allow the user to clearly find the window width above which no further changes in the data around 10 Hz occur. The full 10.92 sec of the second measurement appears to not be needed, but it would be nice to have a 5.46 sec impulse length or similar. A typical exported data set would contain data for frequencies no higher than 400 Hz.
So this finally gets to my question. Is there a method or set of REW measurement parameters I can specify to be used that guarantees that the user will end up with an impulse length of 5.46 sec or thereabouts after downsampling, along with what appears to be the standard of a final frequency resolution of 0.366 Hz? If so, what should these parameters be?
Sorry in advance for the lengthy post.
An MSO user recently noted that correlation between MSO sub response predictions (computed from superposition of filtered individual sub data) and final REW measurements of all subs together was somewhat off below about 25 Hz and good above that for his project. His hypothesis was that it might be due to having an IR window that was not wide enough in the REW measurements prior to export. He showed that a measured SPL response changed below 25 Hz when widening the IR window from its default 500 msec to about 1.7 sec.
At first I thought that such a change couldn't affect the correlation between predicted response and final measurement at all. I thought it might only affect the predicted combined sub responses in an absolute sense, and that the final measurement of all subs together would also be affected in the absolute sense in the exact same way, resulting in no net error in correlation of predicted and final measurements. This thought was further reinforced by a statement he made that when staying within REW itself, the SPL response of the A+B sum computed from individual sub measurements by trace arithmetic matched perfectly with the two subs measured together.
But then it occurred to me that if each sub measurement exported from REW were affected in a different way by the windowing (something analogous to applying a different, unknown filter to each measurement), the integrity of the superposition would be compromised and prediction/measurement correlation errors could occur. This only raised another question though. If this hypothesis were true, why would it work perfectly within REW itself and not in MSO? After thinking about it some more, it seems likely that REW is first computing the sum, then windowing the result, while MSO is computing (in the frequency domain) the sum of already-windowed results. I guess the windowing is not a linear operation, so the order of summation and windowing matters. Does this explanation sound reasonable?
If this is a reasonable explanation, it points to a potential remedy of widening the window before exporting (or preferably specifying a wider window for all measurements prior to performing them). While investigating this, I ran into a couple of things that confused me. The first project I checked was allowing a very wide window (5461 msec), making it easy to determine the narrowest window width above which the data at the lowest frequencies no longer changed. But then I tried a newer project, and it was limiting the maximum window width to 1731 msec. So I took a look at the measurement info for each one.
Here's the newer one that's allowing a maximum of 1731 msec
Everything seems consistent. It's downsampled to 3000 Hz with 8192 samples, giving a frequency resolution of 0.366 Hz and a total impulse length of 2.73 sec.
The older measurement shown below is puzzling me though. It's the one that allows the wider window due to the longer impulse length.
It has an impulse length of 32768 samples, or 4 times the length of the previous one, despite (or maybe because of?) its original sweep being 256k, rather than the longer 1M of the previous one. Yet the frequency resolution is the same 0.366 Hz, despite the total number of samples being 4x that of the earlier measurement. I'm certainly no DSP expert, so what might be obvious to someone who is, is baffling me.
I'd like to specify in the MSO documentation a way to ensure a longer impulse length than 2.73 sec in REW. This would allow the user to clearly find the window width above which no further changes in the data around 10 Hz occur. The full 10.92 sec of the second measurement appears to not be needed, but it would be nice to have a 5.46 sec impulse length or similar. A typical exported data set would contain data for frequencies no higher than 400 Hz.
So this finally gets to my question. Is there a method or set of REW measurement parameters I can specify to be used that guarantees that the user will end up with an impulse length of 5.46 sec or thereabouts after downsampling, along with what appears to be the standard of a final frequency resolution of 0.366 Hz? If so, what should these parameters be?
