Convolution inverses to take out mic character?

[DrNick]

Invertability typically won't be an issue for a mic IR as their is plenty of response at all points on the unit circle. So H*H^-1 is never singular.

The problem is that a mic is typically used in the near-field. There isn't any way to know a priori what the IR of the mic was at the time the IR was acquired. IOW, the IR of a mic varies with it's position relative to the speaker until you get into BOTH the speaker's far field and the mic's far field.

You can find the far field IR of a mic by putting it in the far field of a speaker in very close proximity to a known mic (i.e. something like an Earthworks TC30). The difference between the two IRs is the mic IR.

The mic IRs in the Axe-Fx II assume a nominal position and distance from a typical speaker.

Did you mean to say that H itself it non-singular (since presumably H*H^-1 is the convolution identity hence plenty invertible)?

You raise a good point about the proximity affecting the IR. But I'm not quite sure what you mean by the Axe-Fx II assuming a "nominal" position. Given that the typical usage for a cab is near-field, is this how factory mic IR's are taken?

 

[Smilzo]

Did you mean to say that H itself it non-singular (since presumably H*H^-1 is the convolution identity hence plenty invertible)?

Yes.

You raise a good point about the proximity affecting the IR. But I'm not quite sure what you mean by the Axe-Fx II assuming a "nominal" position. Given that the typical usage for a cab is near-field, is this how factory mic IR's are taken?

Most of cab is near field: the room can be added with reverb and with Cliff's trick (6 ms delay between stereo signal).

 

[DrNick]

Hmm. If we only had a NULL cab. But, how about using a cab with a 57 and a cab with a NULL mic? Tone match the difference to get the inverse 57?


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I implemented this idea, and my early impression is that it actually works quite well!

By way of details, used the null cab that was posted in this thread with an SM57 as my local signal, and the same null cab with no mic ("none" in the settings) as my reference. No AMP block in either case. Then I ran the tone match process just strumming around my guitar to generate each signal.

To evaluate the resulting TMA block, I've been comparing cabs with no mic ("none") to cabs with an SM57 followed by the TMA block. I've only done this in a couple settings (amps and cabs) but the results are quite close.

I gotta say, I knew the Axe-Fx sounded great, but I am pleasantly surprised to learn that it's also a seemingly never-ending source of fun!

 

[FractalAudio]

Did you mean to say that H itself it non-singular (since presumably H*H^-1 is the convolution identity hence plenty invertible)?

The issue of invertability occurs when there are zeros in the response as those lead to infinite response in the inverse. Cabinets often have zeros (or near zero) in the response, especially at high frequencies. Even if it isn't zero, if the response is low enough the inverse has poles that have very high magnitude which can lead to overflow (clipping) in the digital and/or analog domains.

IOW, if H(z) has a response at some z where the magnitude is, say, 60 dB down relative, the inverse will have a magnitude that is 60 dB greater which can easily cause clipping somewhere. Microphone IRs are typically well-behaved and don't vary wildly over the ROI.

As noted you can use the Tone Match block to create an inverse IR.

To create a null IR you can simply put a cable between Ouput 2 and Input 2 and shoot an IR of the cable.

 

[DrNick]

The issue of invertability occurs when there are zeros in the response as those lead to infinite response in the inverse. Cabinets often have zeros (or near zero) in the response, especially at high frequencies. Even if it isn't zero, if the response is low enough the inverse has poles that have very high magnitude which can lead to overflow (clipping) in the digital and/or analog domains.

IOW, if H(z) has a response at some z where the magnitude is, say, 60 dB down relative, the inverse will have a magnitude that is 60 dB greater which can easily cause clipping somewhere. Microphone IRs are typically well-behaved and don't vary wildly over the ROI.

As noted you can use the Tone Match block to create an inverse IR.

To create a null IR you can simply put a cable between Ouput 2 and Input 2 and shoot an IR of the cable.

Ah, I see. I think I had a erroneous mental picture of how this worked internally (I was just guessing...). This makes sense, as does the previous comment about "zeros" causing problems in invertibility. The problematic "zeros," as you say, are zero response and not 0db relative. So, effectively -∞db relative.

Thanks to everyone for your helpful comments on this curiosity of mine!

 

[Rex]

The issue of invertability occurs when there are zeros in the response as those lead to infinite response in the inverse. Cabinets often have zeros (or near zero) in the response, especially at high frequencies. Even if it isn't zero, if the response is low enough the inverse has poles that have very high magnitude which can lead to overflow (clipping) in the digital and/or analog domains.

Would it be practical to take the inverse of a response, shift it to a useful average level, and then process it to cap the response at a predetermined level?