3. Signal Processing (Continuous to Discrete) · Concept 5 of 11
Convolution
It is a way of stamping the character of one sound or space onto another sound.
Convolution slides the room's impulse response across every sample of your signal, then sums the overlapping decaying copies into the wet output.
What it is
Convolution stamps the full echo fingerprint of one sound or space onto another sound, point by point.
Key facts
Convolution = sliding multiply-and-add of two signals; output sample y[n] = sum over k of x[k] x h[n-k]
x = your dry signal (vocal), h = the impulse response (IR), the captured 'fingerprint' of a room, cab, or amp
An Impulse Response (IR) is the recording of how a space/device reacts to one instant click (an impulse)
Output length = length(x) + length(h) - 1 samples; a 3 s IR adds ~3 s of tail to your sound
Convolution in time = simple multiplication in the frequency domain (the Convolution Theorem)
Speed of sound in air = 343 m/s at 20 degrees C; 1 ms of delay = 34.3 cm of path difference
Reverb time RT60 = time for the tail to drop 60 dB; cathedral IR can be 3 to 8 s, small room ~0.4 s
+6 dB = double the amplitude (voltage); +10 dB = roughly double perceived loudness
-3 dB = half the power (half-power point); -6 dB = half the amplitude
Direct fast convolution cost grows as N x M; FFT-based 'partitioned convolution' cuts this so it runs live with low latency
How it works
Capture an Impulse Response: pop a balloon, fire a starter pistol, or play a sine sweep in the target space and record it
That IR holds every reflection, decay and tone of the space in one file
Feed your dry signal and the IR into a convolution engine
Engine slides the whole IR across every sample of your signal, scaling and summing each copy
All those overlapping, decaying copies pile up into the wet output
Result: your dry sound now wears that room, cab, or device as a costume
Real examples
Convolution reverb: drop in an IR of Sydney Opera House and your dry vocal sounds like it was sung on that stage
Guitar cab/IR loader: swap a real 4x12 speaker cab capture onto a DI'd amp signal with no mic or cab in the room
Speaker/system tuning: load a measured IR to correct a PA's response
Headphone/room correction plugins apply an IR to flatten dodgy frequency response
Sampling a stairwell or car park with a balloon pop, then wearing that exact space later
How it helps in live sound
Use convolution reverb on vocals and snare for a real-venue tail; pick an IR with RT60 ~1 to 2 s for music, shorter for speech clarity
Watch CPU/latency: long IRs (5 s+) are heavy; use a low-latency partitioned-convolution plugin live, not an offline one
Load guitar cab IRs (e.g. from a Two Notes / OwnHammer pack) instead of mic'ing a cab on a loud stage
Capture your own room IR with a balloon pop or sine sweep, then reuse that space on later mixes
High-pass the reverb return ~120 to 200 Hz so the convolved tail doesn't mud up the low end
Keep one dry send 100% dry; blend wet to taste so intelligibility survives in a live mix
Everyday analogy
It is like pressing a rubber stamp (the room's echo) onto every single dot of your sound, so the whole signal soaks up the same inky pattern.
Watch out
Myth: convolution reverb is just a fancy preset. Truth: it replays a real measured impulse response, so it is only as good (and as long/heavy) as the actual IR you load.
Fun fact
A single balloon pop or starter-pistol crack is enough to capture an entire concert hall's reverb forever, because that bang is a near-perfect 'impulse' the room answers with its full echo signature.
Key takeaways
Convolution = multiply-and-add slide of your signal against an impulse response
The IR is the captured 'fingerprint' of a room, speaker cab, or amp
It is how convolution reverbs and cab/amp sims let you wear a real space as a costume
Output gains the IR's full tail: length(x)+length(h)-1, so a 3 s IR adds ~3 s of decay