3. Signal Processing (Continuous to Discrete) · Concept 7 of 11
Transfer Function
It is a single description of what a piece of gear does to a sound, telling you what comes out for whatever goes in.
Flat signal in, shaped signal out: the transfer function is the gear's magnitude-and-phase fingerprint at every frequency.
What it is
A transfer function is one complete description of what a piece of gear does to a signal: output for any input, at every frequency.
Key facts
Transfer Function H = Output / Input, measured across all frequencies (the gear's fingerprint).
It has TWO parts: MAGNITUDE (gain/loss in dB per frequency) and PHASE (timing shift in degrees per frequency).
+6 dB = double the voltage; +3 dB = double the power; +10 dB = roughly twice as loud to the ear.
-3 dB point = half-power point = the standard cut-off (corner) frequency that defines bandwidth.
0 dB on the curve = unity gain = signal passes unchanged (flat = transparent).
Speed of sound in air = 343 m/s at 20 C; 1 ms of delay = 343 mm of path; 360 phase deg = one wavelength late.
Human hearing spans 20 Hz to 20 kHz; transfer functions are plotted on a log frequency axis.
A dual-FFT analyser (Smaart, Open Sound Meter, REW) computes H by comparing reference input to measured output; coherence 0 to 1 tells you which data to trust (near 1 good, below 0.5 ignore).
Cascading gear MULTIPLIES magnitudes (so ADD the dB) and ADDS the phase shifts.
Octave = 2x frequency, decade = 10x; filter slopes quoted in dB/octave (12, 24 dB/oct); an EQ curve on screen IS a transfer function.
How it works
Send a known test signal (pink noise or a sweep) INTO the device or system.
Measure what comes OUT with a calibrated mic or a direct return.
Analyser divides output by input at every frequency: H = Out / In.
Plot MAGNITUDE (dB vs frequency) on top and PHASE (degrees vs frequency) below.
Check COHERENCE: only trust the curve where coherence is high (near 1).
Read it: flat 0 dB line = no change; bumps = boosts; dips = cuts; sloping phase = delay.
Real examples
EQ curve on your console screen: the exact transfer function you are applying to a channel.
Speaker measurement in Smaart: magnitude + phase trace showing how the box colours pink noise.
Room correction: capture the room's transfer function, then apply the inverse EQ to flatten it.
High-pass filter at 100 Hz, 24 dB/oct: a transfer function that is 0 dB above 100 Hz and falls steeply below.
Aligning a sub to a top: matching their phase transfer functions at the crossover so they sum, not cancel.
How it helps in live sound
Run a dual-FFT measurement (Smaart/Open Sound Meter) with a calibrated mic before doors to see the real system curve.
Only EQ where coherence is high; a dip caused by a reflection (low coherence) will NOT fix with EQ.
Time-align subs and tops by matching phase at the crossover; use the 343 m/s rule (1 ms = 343 mm) to set delay.
Aim for a smooth house curve, not a ruler-flat line: gentle tilt down toward the highs sounds natural.
Compare DSP presets by overlaying their transfer functions instead of guessing by ear.
Use a 1/3-octave or smoothed view to set broad EQ; narrow spikes are usually room artefacts, not the speaker.
Everyday analogy
It is a tint sheet for sound: whatever signal hits the gear, the transfer function tells you exactly which frequencies come out brighter, darker, or late.
Watch out
Myth: a dip in the curve always means turn up that EQ band. Truth: if it is a reflection or comb filter (low coherence, non-minimum-phase), boosting just wastes headroom and makes it worse.
Fun fact
A transfer function is so complete that for a well-behaved (minimum-phase) box you can largely undo it by applying the mathematical inverse: that is the basis of room correction and FIR speaker tuning. The catch is reflections and deep notches are non-minimum-phase, so they cannot be fully reversed.
Key takeaways
Transfer function = Output divided by Input, at every frequency. The gear's fingerprint.
Two halves: magnitude (dB, how loud) and phase (degrees, how late).