# How do impulse response guitar amp simulators work?

I am wondering how impulse response guitar amp simulators/modelers work. I thought it was a matter of convolving a signal of recorded impulse response in time-space with a guitar sample.

I tried to do this with Matlab using conv function. I loaded an example impulse response and recording of a guitar sample and the result was just a badly distorted sound.

I read that using normal convolution will not work and the response of the amp is dynamic and differs based on the input signal amplitude.

I have found this question: Dynamic convolution vs Volterra series, but I do not quite understand how I would apply this to my case and if this even is the right direction.

I am EE student and know a bit about DSP, but we only dealt with basic signal convolutions so I am quite lost on what to try, but I am really curious on how all this works.

• Badly distorted how? Can you edit your post with a graph of the impulse response? Did you try doing the procedure with an identity impulse response, i.e. a 1 followed by a bunch of zeros? Did you try it with an impulse response with gain, or some simple filters (a low-pass filter would be good -- maybe 1 millisecond worth of ones, followed by zeros)? – TimWescott Nov 12 '19 at 20:28
• i think you're conflating guitar simulator (these are hex-pickup pedals that Line6 and others have made that make your guitar sound like a variety of different acoustic guitars) with guitar amp distortion which is much more complicated than just an impulse response. – robert bristow-johnson Nov 12 '19 at 21:06
• i wonder if someone has a got link to a general description of Volterra series? – robert bristow-johnson Nov 12 '19 at 23:53
• @robertbristow-johnson if "diagonal Volterra series" a.k.a. "Hammerstein model" is enough for you, have a look at Angelo Farina, Alberto Bellini and Enrico Armelloni "Non-Linear Convolution: A New Approach For The Auralization Of Distorting Systems", Proceedings of the 110th AES Convention, 2001 and the presentation of the same name. – Olli Niemitalo Nov 13 '19 at 8:05
• Olli Niemitalo, thank you for the links, there is indeed some useful info there. – Klemen Nov 13 '19 at 14:28

When talking about modeling, there are two things that usually get modeled: 1. the guitar amp, and 2. the speaker cabinet. Only the latter is modeled by an impulse response, which means that the cabinet is simply represented by an LTI system and implemented by convolution. This is of course an approximation but it works fairly well. You can find a lot of such measured impulse responses on the internet.

As for the guitar amps, there is no such thing as an "impulse response guitar amp simulator". As mentioned in the comments and in Marcus Müller's answer, guitar amps are much too complicated to be modeled by a simple impulse response. They are non-linear and dynamical, and the corresponding digital models are quite complex. There's a good reason why the big players in amp modeling (Kemper, Fractal Audio Systems, Line6) do not publish their modeling algorithms.

There are two basic approaches to modeling of nonlinear analog circuits: 1. black-box models, which only try to emulate a measured input-output relationship using a set of test signals, and 2. white-box models, which try to simulate the actual analog circuit in all details. You can read a good summary of the basics in A Review of Digital Techniques for Modeling Vacuum-Tube Guitar Amplifiers.

• The crucial thing is that a guitar amp can fairly well described as a composition of the “amp” part, which is highly nonlinear but has a pretty simple time/frequency response (and can thus be modelled as essentially a generic nonlinear dynamical system / ODE without computation cost going over the roof), and the “cabinet” part, which is relatively linear (and can thus be modelled efficiently with FFT-backed convolution) even though the time/frequency response is pretty complex. That really is the basis of “impulse response guitar modelling”, though as you say Kemper etc. use a bit more detail. – leftaroundabout Nov 13 '19 at 5:35
• For more recent work with recurrent neural networks, see: Wright A, Damskägg E-P & Välimäki V, "Real-time black-box modelling with recurrent neural networks", in Proceedings of DAFx2019. – Olli Niemitalo Nov 13 '19 at 8:10

If you're an EE student, you will have encountered the term LTI System (or you certainly will soon enough!): A system that, no matter the absolute time, outputs, given the same input, the same output; if you scale the input by a factor, the output is scaled by the same factor. Linear, time-invariant, so to speak.

LTI systems can be applied to time-domain signals by convolving their impulse response with the signal.

Guitar effects are not LTI, in general. Instead, they are typically at least nonlinear.

Thus, they can't be completely described by a single impulse response, and hence, you can't recreate the effect just by convolving the signal with anything.

Instead, you need a more universal description. For time-independent systems, a (potentially infinite) Volterra series is one of these possible descriptions.

• EQ is an "effect" and is, once the faders stop moving, LTI. but most cool sounding effects have some kinda time-variance and may also have a non-linear element. – robert bristow-johnson Nov 12 '19 at 23:50

If you’re looking for modeling the amplifier itself, convolution will not provide a complete model for the internal processes. However, convolution is the basis for a number of cab modeling products. I have a line 6 helix that I use frequently. A dry guitar doesn’t sound great. A dry guitar through an amp model sounds bad. A dry guitar through an amp and cab model sounds much better. The model seems to be that an amplifier creates a lot of distortion and high frequency content that is unpleasing. The speaker and cab filter out the high frequencies so that it sounds less bad. A speaker and cab are (mostly) an LTI system and can be modeled via an impulse response. Additionally, they can be modeled using physical models, that seem to be loosely based on reverb algorithms. I’ll also add that I don’t consider any models that I’ve heard to be complete in the sense that it doesn’t sound like the actual prototype amplifier. This will continue to be technology that is refined for years to come.