This time you could compare the summer hole with a bass hole, which can result from unbalanced conditions of a given stereo arrangement. Examples would be an L-shaped room, an unbalanced setup (one speaker in the corner, the other speaker in the middle of the wall) or unbalanced furniture.
The starting point is a given system in an L-shaped room. The test convolution shows the unsmoothed result of the correction
So far so good, so far ok.
But if we now add the impulse responses we get a sum frequency response
which shows a clear dip in the marked area. I'm not just talking about the narrowband hole, but also about the drop in the range 35 Hz to 70 Hz. Just where you need the bass for warmth it is missing. Although both channels are ok in themselves.
What can be done now? One approach, perhaps often used unconsciously, is to change the target curve with a bass boost, e.g. with a bass hump at 60 Hz. This means, however, that you put more energy into the LS, the membranes have to work harder.
Another approach is presented here:
The minimum in the marked range is at 49.796 Hz, displayed on the right of the frequency response chart.
Now a sine with this frequency is generated with Generate - Tone Generator and the two impulse responses are each convolved with the sine.
The time diagram then shows
If you zoom into the stationary area in the center (=steady state), you can see that the oscillations are in opposite phase. The sound components cancel out each other.
The whole thing happens already during the transient stage, you can see that the right channel is delayed somehow. Although both channels start at the same time.
The cause is to be found in the L-shaped room, the bass spreads out non-symmetrically. And this results in other reflection states.
Now you can create an allpass filter at 49.796 Hz by Generate - IIR filter, as a further parameter the quality is to be indicated. Here you have to play a little bit. In our case Q=4 is chosen. Independently of the Q (which in principle influences the group delay) a phase curve results which starts at 0°, then shifts the phase at the selected frequency with -180° or -Pi and then runs in phase again in the upper frequency range. The Q defines only the steepness of the curve.
Now the other channel is to be convolved with the allpass filter, here the left channel. The right channel already has the delay.
The result is then cut back to the original length from start position 0 using CutNWindow.
Now we get a new sum frequency response (brown), shown in comparison to the previous sum (blue).
As you can see, just shifting the frequency range around 50 Hz over phase/time produces a clear improvement. And this without additional energy expenditure!
Finally the task remains to fold the corresponding correction filters with the allpass filter (generated per sample rate) and to cut them back to the correct length.
The result is worthwhile, at the listening position the bass is now present as it should be. The additional delay is not really noticeable (as you can see, the room plays it own role, too).
PS some more remarks:
- since every configuration is different, you really have to try, so apply a little playfulness. There are also narrow holes where it is not worth use this approach. In our example, trying to fill the hole at 64.6 Hz is counterproductive.
- Theoretically you could reverse the allpass and then fold the right channel with it. The sum frequency response is then also ok. However, this creates a clear preringing and that is not really desired.
