Formular — Scripting DSP Device with Spectrum Analyser

Concept

An educational device where students write DSP code and see the frequency/harmonic response in a connected spectrum analyser. Inspired by Plugin Doctor's static response analysis.

Built on top of the Werkstatt — same Processor class contract, same parameter system, same worklet integration. Formular adds an onboard analyser that runs measurement signals through the user's code and visualises the results.

Analysis Techniques

For Linear Systems (filters, EQs)

Impulse Response → FFT

Send a Dirac impulse (single sample at 1.0, rest zeros) through the user's code
Capture the output (impulse response)
FFT the IR: magnitude → frequency response, phase → phase response
One-shot, perfectly static, mathematically exact
This works because a Dirac impulse has equal energy at all frequencies

For Nonlinear Systems (distortion, compression, waveshaping)

Impulse method breaks down because the output depends on signal level.

1. Logarithmic Swept Sine (Farina method, 2000)

Generate a log sweep from 20 Hz to Nyquist over N seconds
Pass through the system, capture output
Deconvolve: inverse-FFT of Output(f) / Input(f)
Log sweep's special property: harmonic distortion products arrive at different times in the IR, separating cleanly
Result: linear frequency response AND individual harmonic distortion orders (2nd, 3rd, 4th...) from a single measurement
This is what Plugin Doctor primarily uses

2. Single-Tone Harmonic Analysis (THD)

Send a pure sine at frequency f
FFT the output
Measure energy at f, 2f, 3f, 4f...
Shows the harmonic series the nonlinearity generates
Very visual for students — they can see how waveshaping creates overtones

3. Two-Tone Intermodulation (IMD)

Send two sines at f1 and f2
Look for new frequencies at f1±f2, 2f1±f2, etc. in the output
Demonstrates how nonlinearities create frequencies that weren't in the input

4. Level-Dependent Frequency Response

Run impulse or sweep at multiple input levels, overlay curves
Shows how behaviour changes with level (e.g. compressor flattening)

Proposed Device Architecture

Code editor: student writes DSP code (init + process functions) — inherited from Werkstatt
Mode 1 — Impulse: Dirac → FFT → frequency + phase response (filters)
Mode 2 — Single tone: adjustable frequency sine → FFT → harmonic spectrum (distortion)
Mode 3 — Swept sine: log chirp → deconvolution → linear IR + harmonic separation (advanced)
Spectrum display: magnitude in dB vs frequency (log scale)

Mode 1 and 2 cover 90% of educational value. Mode 3 (Farina) is the advanced showpiece.

Open Questions

Does the analyser run in the worklet (offline, feeding test signals through the user's Processor) or on the main thread?
How does the analyser interact with live audio? Does it pause live processing to run measurements, or run a separate Processor instance?
FFT implementation: use an existing library or implement a basic radix-2 FFT?
Display: Canvas 2D or WebGL for the spectrum plot?

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