DSP Toolbox

Modelling Strategies — Circuit, Capture & Learned Models

The previous page showed the problem: a real device may depend on level, frequency, history and internal state. So how do we build a useful model without measuring every possible combination?

REAL DEVICE ↓ choose what information matters ↓ MODEL ↓ predict NEW behaviour

Different modelling methods make different assumptions. None is automatically “best”. The question is: what behaviour do we need to reproduce, how much do we know about the real system, and how much computation can we afford?

1. Three broad routes

CIRCUIT MODEL

Model the mechanism

Represent components, nonlinearities, feedback and stored state. Instead of memorising outputs, recreate a simplified version of the process that produces them.

COMPONENTS + NONLINEARITY + STORE / STATE → OUTPUT

CAPTURE / PROFILING

Probe the real box

Send known signals through the device, compare input with output, then infer a compact model that reproduces important behaviour.

TEST SIGNAL → REAL DEVICE → MEASURE → INFER MODEL

LEARNED MODEL

Learn the relationship

Give a model many examples of input and output over time and train it to predict the device response on audio it has not seen before.

x[n], history → learned F(...) → y[n]

2. Same target — different assumptions

Use the controls below to make our fictional device more difficult. Then compare which modelling strategy is likely to cope best.

STATIC NONLINEARITY55%

DYNAMIC MEMORY / STATE45%

FREQUENCY DEPENDENCE40%

AVAILABLE TRAINING / MEASUREMENT DATA50%

Circuit model—

Capture model—

Learned model—

Dominant difficulty—

These scores are pedagogical only. They illustrate trade-offs, not benchmark real products or algorithms.

3. Circuit modelling — build the machine in maths

If we understand the physical mechanism, we can write equations for the parts that matter:

INPUT ↓ NONLINEAR DEVICE ↓ FILTER / FEEDBACK ↓ STATE ↺

A capacitor does not literally contain a digital delay. But in software we can represent its changing condition with stored numbers. The model recreates useful behaviour rather than reproducing every atom in the hardware.

Strength

Can generalise naturally when the structure is right. Parameters may correspond to meaningful physical quantities.

Cost

Requires good understanding of the circuit and numerical care. Complex devices can become computationally expensive.

Mechanism first: “I know roughly why the device behaves this way, so I will model that mechanism.”

4. Capture / profiling — ask the device directly

KNOWN
PROBE

→

REAL
AMPLIFIER / PREAMP

→

RECORDED
OUTPUT

→

COMPARE
& INFER

Profiling-style systems can use carefully chosen test signals to reveal how a device responds. The model does not necessarily need a complete schematic — it learns useful behaviour from measurements.

Important: a proprietary profiling product is not simply “an IR”. Exact commercial algorithms are generally not public, so we should describe the broad system-identification principle rather than pretend to know their implementation.

5. Learned / neural modelling — examples become the specification

input sequence: x[n−k] ... x[n−2] x[n−1] x[n] ↓ LEARNED MODEL ↓ output prediction: y[n]

The model is trained on real input/output pairs. If the architecture has temporal memory, it can learn behaviour that depends on what happened before the current sample.

Static learned model

Current output depends mainly on current input.

y[n] = F(x[n])

Temporal learned model

Current output can depend on a sequence or internal hidden state.

y[n] = F(x[n], history / state)

The key test is generalisation: does the model behave sensibly on guitar, drums, speech or transients that were not part of the exact training examples?

6. What each approach is really storing

Approach	What is stored?	Where does “knowledge” live?
IR	Samples / filter coefficients	A fixed linear response
Operating-point capture	Several measured responses	Measured states + interpolation rule
Circuit model	Equations, parameters, dynamic state	Structure of the simulated mechanism
Learned model	Trained weights + runtime state	Patterns inferred from examples

7. The toolbox never disappeared

Even sophisticated models still reduce to combinations of familiar operations.

+ ADD × MULTIPLY z⁻¹ STORE / STATE MEASURE COMPARE FUNCTION ... arranged into a much larger system

A “complex model” is not magic. It is a large organised patch of mathematical operations whose parameters have been designed, measured or learned.

8. Another family of distortion

So far, nonlinearity has mostly meant changing the input→output function. Later we can return to a different digital family: quantisation and bit crushing.

WAVESHAPING: continuous input values → nonlinear function BIT CRUSHING: continuous-ish sample amplitudes → fewer allowed amplitude levels

That becomes a clean callback to sampling, bit depth, quantisation error and dither.