DSP Toolbox · Page 42
Capture Lab — How Do We Copy a Real Device?
Imagine a real analogue mic preamp on the bench. Feed it known signals, record what comes back, then ask: how much must we measure before software can predict what the box will do?
KNOWN INPUT → REAL DEVICE → MEASURE OUTPUT → BUILD MODEL → TEST WITH NEW INPUT
This uses a fictional preamp whose hidden mathematics we know. That lets us see exactly what incomplete models miss.
1. Is one fixed response enough?
If the device were linear, changing input level would simply scale the output. Normalised transfer behaviour would coincide. Here it changes as the device is driven.
Highlight level
If response changes with operating level, one ordinary LTI impulse response cannot describe the whole device.
2. Capture several operating points
Now use the idea of measuring several levels and interpolating between neighbouring captures.
Captured points
Hidden “real” device
Interpolated model
Below—
Above—
Between—
Error—
3. Now break it with history
The level model knows how hard the signal is now. But what if the real box retains a slowly changing state after being driven hard?
Test
Model
BlueReal device
PurpleModel
AmberState
Error—
Level-only: no knowledge of what happened a moment ago.
4. Too many variables to capture?
10 LEVELS = 10 points
10 LEVELS × 10 FREQUENCIES = 100 points
× 10 PREVIOUS STATES = 1,000 points
× 10 MORE DYNAMIC CONDITIONS = 10,000 points
Rather than store every possible situation, we want a model that learns or describes the relationship well enough to predict unmeasured situations.
5. Different modelling strategies
| Approach | Idea |
|---|---|
| Ordinary IR | One fixed linear time-invariant response |
| Operating points | Measure conditions and interpolate |
| Circuit / dynamical model | Model nonlinear mechanisms + evolving state |
| System identification / learned model | Infer a predictive model from known input/output behaviour |
IR CAPTURE:
“What is this linear system's response?”
SYSTEM IDENTIFICATION:
“What model best predicts this system's behaviour?”
The real test is new audio. Can the model predict behaviour it was never explicitly measured with? That is generalisation.