Hi,
Sorry for the long reply. Just clarifying what I plotted here :
https://www.avnirvana.com/attachments/image-png.32780/
I will try to explain better the experiment, and explain what the plotted amplitudes represents.
The experiment is as follow:
I have a sound source in a room, in particular a line-array composed of multiple speakers in a 3-way actively filtered system. The line-array that I used is the one on the left in this picture :
https://drive.google.com/file/d/1xXHpzuGyJQS6AJz5u2fq9SqjgM2A8l38/view?usp=sharing. The speakers in the center, reproducing the bass, was also active. A drawing of the listening setup can be found here :
The system measurement in .mdat format is available here :
https://drive.google.com/file/d/1l7YUyRizLNra0XT1aSaz4kJN3FTIUCTn/view?usp=sharing
And the average amplitude response was looking like this at different positions around the center of my SOFA :
I can't tell for sure the system response at listening position, but it was quite flat because I used the setup and the sound was really good at that time (however, I applied a target curve to increase by abount 8-12dB the basses below 120hz
).
So, because the sound was good, I was trying to see how it would be replicated with my headphones. I used these modded headphones:
https://drive.google.com/drive/folders/1IxrfG6SA8HqXYztnUiUc7RoqRb9KBIe2?usp=sharing
The in-ear response of the modded headphones are approximately looking like this:
When wearing the headphones, my audio system was sounding really good, as if I had no headphones on my head. So I assumed that the headphones was quite 'acoustically transparant" and had, at least, a negligible effect on the perceived quality of my system response, as perceived by me.
I started from the postulate that if the perceived sound was good, using the headphones to achieve a perfect cancellation of sine waves emitted by the line-array on the left, I would be able to know exactly the signal to be sent to my headphones to perfectly reproduce the sound reaching my eardrums when wearing the headphones. That is, I would be able to estimate the impulse response composed of the (System Response * Binary Room Impulse Response * Headphones Compensation Response).
So, I wrote a software to be able to vary, using a gamepad, independantly the amplitude or the delay of the signal sent to the left speaker or the right speaker of my headphones, because achieving sine-wave cancellation requires only to adjust amplitude and phase of the sound emitted from my headphones speakers.
We can reasonably assume that the response of my system was quite linear, the headphones amplitude response was not linear at all but the curve was really smooth.
So I was expecting to get, as a result, a smooth amplitude, and nearly the same amplitude response for the left and right ear signals.
To illustrate with a simpler example, consider the case where the line-array and the headphones would both have a perfectly flat amplitude. If it is required to send a signal at -10dB at a frequency of, let's say 100hz, on the left headphone speaker, that means that my left headphone speaker is able to reproduce the sine wave emitted by my line-array at 100hz as perceived on my left ear with an input of -10dB. If, at 120hz, the left headphone speaker requires an input of -6dB, that means that the signal as perceived by my left ear is stronger by 4dB than at 100hz (because I assumed the headphone response is perfectly flat...). Hence, the amplitudes sent to my headphones is roughly the amplitude response of the BRIR for my left ear for the current setup (position in the room, head direction, distance from the speaker etc.), up to
- some arbitrary gain,
- the error introduced by my line-array,
- the error introduced by my headphones,
- and an error that I estimate negligible (about 0.1dB) that corresponds to the error of setting the amplitude of the headphones speakers to achieve the perfect sine-wave cancellation,
The screenshots I took for each sine wave cancellation are available here:
https://drive.google.com/drive/folders/1w46cdWmKvKU0OdqrOkRHxiUhOpJ-P4yu?usp=sharing
Each screenshot contains the sine wave frequency used in the REW sine wave generator, and the settings obtained through trial & error using my program and the gamepad to adjust the amplitude and delay sent to the L+R headphones speakers in order to achieve perfect perceived sine wave cancellation.
Repeating the process with a lot of sine waves (really, really long and cumbersome), I generated two text files, one for each ear, containing the (frequency, amplitude) values:
Left ear :
https://drive.google.com/file/d/1NbR3_x2312VmAbzjty4KdSOHJI0tTaAu/view?usp=sharing
Right ear :
https://drive.google.com/file/d/1USnkObFmgf7kcK2_ajx5OFBy7E1S3lDB/view?usp=sharing
And plotted on REW, the raw curves are what I plotted previously. Here is a better plot:
(
red = left headphone speaker,
green = right headphone speaker)
I cannot explain the differences for L and R ears at frequencies around 130-180hz, where the wave length is assumed to be around 2.3meters, except if there were stationary waves in my room (there was very little, but there was still some...).