What an Impulse Response Is, and What It Isn't

I like impulse responses. I use them, I build tools around them, and for most recording situations they are the right answer. So this is not an article about why IRs are bad.

It is an article about what an IR actually is, because the way people talk about them has wandered a long way from the file itself. "It's a Vintage 30 in a 4×12." "It's that exact cab." "It's the real thing, just quieter." None of those is quite true, and the gap between what an IR is and what people think it is explains most of the frustration I hear about them.

So let me do it properly: what the file contains, why it sounds so convincing, and then the myths, one by one, with what is actually missing.

The Short Version

• An impulse response is a linear, time-invariant snapshot of one signal path: the speaker, the cabinet, the mic, its position, the preamp and whatever room was captured, measured at one level, at one moment.
• It is extremely good at what it holds. Frequency response, phase, the mic's character and the exact spot on the cone are all in there, and it plays back identically every single time.
• It cannot hold anything that changes with level. Feed an IR twice the signal and you get exactly twice the output, same shape. A real speaker, a real transformer and a real amp pushing a real speaker all change shape as you turn up.
• Whether the amp–speaker interaction is in the file depends entirely on how it was captured. The usual capture advice is a clean, flat solid-state power amp, which leaves the speaker's impedance curve almost completely out of the sound.
• A longer or higher sample-rate IR does not hold more of the real thing. Length buys low-end detail and room. Sample rate buys nothing a guitar speaker produces. Neither adds level-dependent behaviour.
• Real gear never treats the same signal quite the same way twice. An IR always does. That difference is small, and it is not nothing.

What an Impulse Response Actually Is

One tap, heard in full

The idea is old and simple. If you hit a system with a perfect, infinitely short click and record what comes out, that recording tells you how the system responds to every frequency at once: how loud each one comes out and how late. That recording is the impulse response.

In practice nobody captures a guitar cab with a click, because a click cannot carry enough energy to rise above everything else in the room. The standard method is a sine sweep: a tone that glides from the bottom of the audio band to the top over several seconds, played through a power amp into the cab, recorded with a mic, and then mathematically unwound (deconvolved) back into the click response the sweep stands in for.

Then an IR loader does the reverse. It convolves your guitar signal with that file: every sample of your playing triggers a scaled copy of the cab's click response, and all those copies are added together. What comes out is your guitar, heard through that exact capture.

Linear and time-invariant, in one line

That whole trick only works for a system that obeys two rules. The first is superposition:

$$h * (a x_1 + b x_2) = a\,(h * x_1) + b\,(h * x_2)$$

In words: the response to two signals added together is the two responses added together, and doubling the input doubles the output without changing its shape. The second rule is time invariance: the system answers the same input the same way whether you play it now or in ten minutes.

An IR is not a system that happens to obey those rules. It is those rules. Anything in the original rig that didn't obey them has nowhere to live in the file.

Why it works as well as it does

Credit where it is due, because it is a lot of credit.

• A close-miked guitar cab is dominated by its frequency response, and that response is anything but flat. The peaks and dips a speaker, a cabinet and a mic put on a guitar signal are enormous next to the moves you would make with an EQ, and every one of them is linear. The IR holds all of it.
• Phase is in there too, not just level. That is why two IRs blended together comb-filter exactly the way two real mics on one cab do.
• The mic is in there. Its own frequency response, its proximity effect at that distance, its angle, the exact spot on the cone. Move a mic an inch across a real speaker and the top end changes more than most tone controls would. An IR freezes one of those spots perfectly.
• It is repeatable. Same sound tonight, tomorrow and in two years when the client wants a recall. No real cab, mic and room can promise that.

For a lot of recording, that is most of what matters, and it is why IRs took over.

What Everyone Gets Wrong

"An IR is the speaker"

It is the linear part of one speaker, as one mic heard it, at one level.

That qualifier matters more than it sounds. At low level a guitar speaker is very close to linear. Drive it hard and it isn't: the cone can no longer move in strict proportion to the signal, and the speaker starts adding harmonics of its own and rounding off the biggest peaks. That behaviour is part of why a cranked cab sounds like a cranked cab.

An IR doesn't hold it, and not by accident. The swept-sine method most capture tools use was designed to separate the two. Any harmonic distortion the speaker produced during the sweep lands in a separate stretch of the result, ahead of the linear response, and gets trimmed off as the file is prepared. The method keeps the linear response and throws the rest away on purpose.

Two more things the file can't be:

• It is one point in space. A speaker cone gets strongly directional as the wavelength shrinks towards the cone's own size, around 1.4 kHz for a 12-inch speaker. On-axis and a foot to the side are different tones. The IR is exactly one of them.
• It is usually one speaker out of four. A close mic on a 4×12 hears the driver in front of it. The other three, which never measure quite alike even when they carry the same label, are a big part of what you hear standing in the room.

"An IR includes the amp–speaker interaction"

Only if it was captured through a real valve power amp into the real cab, and even then only at that one setting.

A speaker's impedance swings enormously across the band, and an amp with a real output impedance prints that curve onto the sound. I went through the arithmetic in why reactive loads sound different from real cabinets: the same cab gets about 4.4 dB of low-end bump from a zero-feedback valve amp and under 1 dB from a heavily fed-back one.

In that article I described an IR as captured through a real power amp, because that is the case where the double-count trap bites. Plenty of IRs are not captured that way. The usual advice for capturing a cab is a clean solid-state power amp with plenty of headroom, precisely so the amp adds nothing of its own. The consequence is further down, in Running the Numbers, but the short version is that the speaker's impedance curve all but disappears from the result.

The same thing happens on the playback side. Record your valve amp through a resistive load box, or play through a clean solid-state power amp, or go straight from a modeller into an interface, and the speaker's impedance never pushed back on anything. Whatever IR you put after that, the conversation between amp and speaker simply did not take place.

"An IR includes the output transformer"

An IR includes whatever was upstream of the mic when it was captured, and nothing else.

A cab IR shot with a flat solid-state power amp contains no output transformer at all. There wasn't one in the path.

An IR captured through a real valve amp does contain the transformer, but only its linear side, at that one level: its bandwidth, its roll-off at the extremes. What makes an output transformer interesting is the part that changes with level. As I explained in output transformers and impedance matching, the transformer is what couples the power tubes to the speaker, and it has limits. It needs more of its core to pass a low note than a high one at the same voltage, so when it runs out of room it does so from the bass up. A big low note compresses and blooms into harmonics while the top of the same chord sails past. That is level-dependent by definition, and the capture method trims it away with the rest of the distortion.

So if your signal chain has no real output transformer in it (a preamp-only amp sim, a modeller without a power stage, a solid-state power amp), and your IR was captured with a flat amp, that part of the amp is simply absent from your sound.

"Turn it up and the IR behaves like a louder rig"

This is the one that surprises people most, and it follows directly from the equation above.

Double the signal going into an IR and you get exactly double the output: 6 dB louder, identical shape. Push your amp sim harder and the amp sim changes character, but the cab after it does not care how hard you hit it. Hit it with +20 dB and you get +20 dB.

A real rig answers volume completely differently. The speaker adds its own harmonics and rounds off its peaks. The transformer gives way from the bass up. The amp and speaker push against each other harder. Each of those changes the shape of the sound, not only its size, which is why a real cab sounds different at rehearsal volume than at bedroom volume even with your ears taken out of the equation. (Your ears change with level too; that part is in why everything sounds better louder, and it applies to IRs and real cabs equally.)

The level is baked into the capture itself, too. People who shoot IRs professionally talk about spending real time finding the right volume for a given speaker, because too quiet and too loud produce audibly different files. The file you load is that one level, forever.

"A longer, higher-resolution IR holds more of the real thing"

Length and sample rate both change something. Neither one adds level-dependent behaviour or life. There is nowhere in a linear file for that to go.

What they actually do is in Running the Numbers below. The short answer: length buys low-end detail and room reflections, and past a point, nothing but room. Sample rate above 48 kHz buys content above 24 kHz, from a speaker that has run out of output long before that.

"Real gear sounds the same take after take"

It doesn't. Real gear never treats the same signal quite the same way twice. It answers to how hard it is driven and to what was played a moment ago. Play the same riff twice through a real amp into a real cab and the two takes are not identical files.

An IR is. Feed it the same samples and you get the same samples out, bit for bit, every time. That is a genuine strength for recall and a genuine difference from the real thing, and both are true at once.

"A close-miked IR is how the cab sounds"

A close-miked IR is how the cab sounds to a mic an inch from the grille. Nobody listens from there.

Standing in front of a real cab you hear the off-axis sound, the other speakers, the floor and the walls, all arriving at slightly different times. You also feel it. At real volume a cab moves enough air to push on your body and on your guitar, and the guitar answers back: strings and body pick up the sound from the speaker, which changes sustain and how a note blooms. That loop runs through the room, not the signal path, and no file can hold it. Headphones and studio monitors can't recreate it either, which is a playback limit, not an IR limit, but it is part of why the same IR can feel so different from the same cab.

Running the Numbers

The divider, with a clean capture amp

Take the same example cab as the reactive-loads article: 8 Ω through the mids, 40 Ω at resonance. The voltage that reaches the speaker is set by the divider between the amp's output impedance and the speaker:

$$V_{\text{load}} = V_{\text{source}} \cdot \frac{Z_{\text{load}}}{Z_{\text{out}} + Z_{\text{load}}}$$

A zero-feedback valve amp with $Z_{\text{out}}$ around 8 Ω gave a 4.4 dB bump at resonance. Now a clean solid-state power amp, which typically has an output impedance down around 0.1 Ω, a damping factor near 80:

$$\text{mid: } \frac{8}{0.1+8} = 0.9877 \qquad \text{resonance: } \frac{40}{0.1+40} = 0.9975$$ $$20 \cdot \log_{10}\!\left(\frac{0.9975}{0.9877}\right) \approx 0.09\ \text{dB}$$

Less than a tenth of a decibel. The amp holds the voltage on the speaker almost perfectly steady no matter what the speaker's impedance does. That is exactly why it is recommended for capture: it keeps the amp out of the IR. It also keeps the speaker's impedance curve out of the IR. A cab IR shot this way is the speaker's acoustic response, and nearly none of its electrical argument with the amp.

That is not a defect in the IR. It is a choice, and it is the right one for a file you want to reuse behind many different amps. You just have to know that the interaction has to come from somewhere else, or it isn't there.

What length and sample rate actually buy

Length. A close-miked cab's response is short. Some well-known IR makers deliberately trim their files to a few tens of milliseconds, to leave the room out and keep latency down. For scale: a 2048-sample IR at 48 kHz is 42.7 ms. Sound covers about 34 cm per millisecond, so a reflection off a wall two metres away arrives roughly 12 ms after the direct sound, well inside that window.

Length does matter at the bottom end. An IR can't describe detail finer than about one divided by its own length, so a 42.7 ms file resolves the spectrum in steps of roughly 23 Hz, coarse enough to smear the shape of a cab resonance around 100 Hz. Longer files hold that more faithfully. Beyond that, extra length is room tail and silence. A file that is mostly padding costs CPU on every sample and gives nothing back.

Sample rate. A 48 kHz file already holds everything up to 24 kHz. A Celestion Vintage 30, one of the brightest common guitar speakers, has a published frequency range of 70 Hz to 5 kHz. A 96 kHz IR adds the band from 24 kHz to 48 kHz, where the speaker has nothing left to give and your ears couldn't hear it if it did. Quite a few high-rate IRs turn out to have nothing in them above the limit of a lower rate at all: they were captured lower and upsampled.

Neither number moves the IR one step closer to behaving like a speaker at volume. That is a different kind of information, and a linear file has no slot for it.

What This Means on the Bench

When an IR is exactly the right tool

• Recording quietly. A good IR behind a good amp or amp sim beats a real cab miked badly in a bad room, every time.
• Consistency and recall. Same tone every night, every session, every recall.
• Mixing choices after the fact. Swap cabs, swap mics, blend two positions, long after the player has gone home.
• Cabs you don't own. A well-captured IR of a great cab in a great room is access you otherwise wouldn't have.

Match the IR to the way it was captured

This is where most of the practical trouble comes from, and it is all the same mistake: counting something twice, or counting it zero times.

• Find out how the IR was captured. Good IR makers say what power amp they used and whether a file is cab-only or a full amp-and-cab capture. If they don't, the flat-amp cab-only capture is the safe assumption.
• If the IR was shot through a real valve amp into the cab, the interaction at that setting is already in the file. Don't add a strongly voiced reactive load or an amp sim's speaker-impedance feature on top. That is the double-count from the reactive-loads article, and it's where the honk comes from.
• If the IR was shot with a flat solid-state amp, it has no interaction and no transformer in it. Those have to come from upstream: a real valve amp into a reactive load, or an amp sim that models the power stage and the speaker load. If neither is true, they're missing.
• If your amp sim already includes a cab, turn one of the two off. Stacking two cabinets is the fastest way to a boxy, honky tone and I still hear it constantly.

Capture through the real thing when you can

If you own the amp and the cab, the most honest IR you can make of your own rig is the one shot through your valve amp into your cab at the volume you actually play. It still won't answer level changes, but at least the interaction and the transformer's linear colour are the real ones, set where you use them.

And if you can record the real cab, record the real cab. An IR is a brilliant substitute. It is still a substitute.

Why ReactIR exists

Everything in the myths section is the reason I built ReactIR. I didn't want to replace IRs; they are too good at what they do. I wanted to keep the IR and give back what the file itself can't hold: the parts of an amp and a speaker that answer to how you play. Your IR is a photograph. ReactIR brings it to life.

Try It Yourself

The interaction, drawn. Feedback Lab shows how much of a speaker's impedance curve reaches the speaker for a given amp. Load the Vox AC30 preset, then a Hiwatt, and compare the response at the speaker. The difference between those two is the part of the sound a flat-amp cab IR never had in it.

The level test, on a real rig. Reamp the same DI part through your real amp and miked cab twice, once at low volume and once loud, without moving the mic. Level-match the two recordings, flip the polarity of one and sum them. Whatever doesn't cancel is the part of your rig that changes shape with level. Now do the same through an IR: the two versions cancel completely, because to an IR, loud is just bigger.

Even two real takes at the same volume won't cancel completely. Real gear never treats the same signal quite the same way twice. But the loud-and-quiet pair will leave far more behind, and listening to what's left is the fastest way I know to hear what an IR is not.

Sources

• The swept-sine capture method and the separation of the linear response from harmonic distortion: A. Farina, "Simultaneous Measurement of Impulse Response and Distortion with a Swept-Sine Technique," AES 108th Convention, 2000.
• The recommendation of a clean solid-state power amp with plenty of headroom for cab capture: TONE3000, "How to Capture an Impulse Response (IR) of a Speaker Cabinet."
• Capture volume changing the result, a flat solid-state amplifier chain, and IRs trimmed to roughly 20 to 41 ms with no room captured: Colin Cartmell interviewed in Sound On Sound, "Making Great Guitar Cab IRs."
• Celestion Vintage 30 frequency range of 70 Hz to 5 kHz: Celestion's published specification.
• Superposition, time invariance and convolution are standard linear systems theory. The divider figures reuse the round numbers from the reactive-loads article (8 Ω mid-band, 40 Ω at resonance) with an assumed 0.1 Ω solid-state output impedance; real amps vary, the order of magnitude does not.
• Directivity and IR length figures are arithmetic: 343 m/s for the speed of sound, a 25 cm effective cone diameter, and 2048 samples at 48 kHz.

Know what's in the file. It's Slightly Technical — but it makes all the difference.