3. Signal Processing (Continuous to Discrete) · Concept 8 of 11
Impulse Response
It is the recording of how something reacts to one tiny instant click, which captures its whole sonic character.
One spike goes in, the decaying tail that comes back is the system's full fingerprint, and convolving any dry signal with that IR drops it into the same space.
What it is
A recording of how a space or device responds to one instant click, capturing its entire sonic character in a single file.
Key facts
Impulse Response (IR) = the output you get when you feed in one perfect spike (a Dirac delta: infinitely short, infinitely tall, area = 1).
Speed of sound in air = 343 m/s at 20 degC. Sound travels ~34 cm per millisecond.
Convolution theorem: convolving any signal with an IR applies that system's full response (time-domain convolution = frequency-domain multiplication).
A Linear Time-Invariant (LTI) system is FULLY described by its IR. Know the IR and you can predict the output for ANY input.
RT60 = time for the reverb tail to drop 60 dB (a 1,000,000:1 power drop). Small room ~0.3 to 0.6 s, concert hall ~1.8 to 2.2 s, cathedral 4 to 8 s.
+6 dB = double the sound pressure (voltage). +3 dB = double the power. -3 dB = half power (the standard 'half-power' point).
IR length in samples = duration (s) x sample rate. A 2 s reverb at 48 kHz = 96,000 taps; stereo doubles it.
Standard rates: 44.1 kHz (CD), 48 kHz (pro/video), 96 kHz. Nyquist limit = half the rate (48 kHz captures up to 24 kHz).
Cab/IR sims are tiny: a guitar cab IR is often 200 to 1024 samples (~5 to 20 ms). Reverb IRs run 1 to 10+ seconds.
Capture via a balloon pop/starter pistol (broadband impulse) or a log sine sweep (20 Hz to 20 kHz) deconvolved into the IR; bit depth 24-bit (144 dB range) or 32-bit float.
How it works
Send ONE short broadband spike into the system: clap, balloon pop, or starter pistol.
Record what comes back at the mic: the direct hit, then early reflections, then the decaying tail.
That whole captured tail IS the impulse response, the system's fingerprint.
To apply it, convolve your dry signal with the IR (multiply spectra, then inverse-transform).
Load the IR file into a convolution reverb or cab sim and the dry sound inherits the captured space/amp.
Real examples
Convolution reverb: load 'Sydney Opera House IR' and your dry vocal sounds like it was sung on that stage.
Guitar cab sim: a 1024-sample IR of a mic'd 4x12 makes a silent amp-sim DI sound like a real speaker in a room.
Acoustic measurement: pop a balloon, capture the IR, read RT60 to spec a room's reverb time.
Hardware emulation: an IR of a vintage spring reverb or plate recreates that exact gear in software.
How it helps in live sound
Use IR-based cab sims (e.g. NAM/cab-sim blocks, Two Notes) for silent guitar/bass stages, send a real-amp tone straight to FOH.
Keep cab IRs short (under ~20 ms) so they add zero perceptible latency to the in-ear monitor mix.
Run a sine-sweep IR capture of the room to measure RT60 before tuning the PA and setting delay times.
Load a tasteful hall/plate convolution IR on vocals, but watch CPU: long stereo IRs are heavy on the live rig.
Match IR sample rate to your console/interface rate (48 kHz live standard) so the cab/reverb sounds correct.
Trim or gate long IR tails in fast venues so reverb doesn't smear into a muddy low-mid build-up.
Everyday analogy
It's like clapping once in an empty church and the echo that comes back is a complete sonic fingerprint of that church, bottled so you can drop any sound into it later.
Watch out
Myth: an IR is just an EQ curve. Truth: it captures the FULL time-and-frequency behaviour (reflections, decay, phase), not just tone, which is why a 2 s reverb IR sounds nothing like a static EQ.
Fun fact
A single broadband click contains every frequency at once, so one clap tests the entire 20 Hz to 20 kHz audio band simultaneously, which is exactly why it can fingerprint a whole hall in one shot.
Key takeaways
One spike in = the system's complete fingerprint out.
An LTI system is fully defined by its impulse response.
Convolving a dry signal with an IR transplants that space or amp onto it.
RT60 (the 60 dB decay time) is the headline number an IR encodes.
Tiny file, huge effect: a sub-1 KB cab IR can transform a tone.