Sanity check: using y(t)=IFFT(1/Z(f)) as an admittance kernel from loudspeaker impedance

[K.E]

Hello everyone,

I am looking for a technical DSP / loudspeaker-measurement sanity check on one specific physical chain.

This is not a product pitch, and I am not asking for endorsement. I am trying to verify whether the following representation is physically and mathematically reasonable before building anything larger on top of it.

The chain is:

Z(f) → Y(f)=1/Z(f) → y(t)=IFFT(Y(f))<br>
where Z(f) is a complex loudspeaker electrical impedance model, Y(f) is admittance, and y(t) is then used as a convolution kernel on a voltage signal:

i(t) = fftconvolve(v(t), y(t))<br>
The intended interpretation is:

given an applied voltage v(t), the output i(t) is the current that would flow through the equivalent loudspeaker impedance.

So this is not treating impedance as an audio EQ curve.

Current test case​

I am using an Eminence DV-77 8 Ω as a reference driver.

The impedance model is a lumped-element TS-parameter model:

• motional branch from published fs, Re, Qms, Qes
• HF voice-coil behaviour modelled as a semi-inductive lossy term:

Z_L = K · (jω)^n<br>
with n = 0.6.

The FFT setup is:

• sample rate: 48 kHz
• FFT size: 16384
• linear FFT grid, not log-spaced
• complex Hermitian-symmetric spectrum
• no magnitude-only IFFT shortcut
• outer 5% cosine taper on the one-sided spectrum
• final kernel truncated to 2048 samples with a short Hann tail

Internal checks so far​

The implementation currently passes these checks:

• Y(0) ≈ 1/Re
• Z(f) peak occurs near fs
• Y(f) notch occurs near fs
• for the DV-77, modelled peak |Z| ≈ 171.9 Ω at about 70.3 Hz, matching the analytic TS prediction:

Re · (1 + Qms/Qes) ≈ 172 Ω<br>

• sweep recovery: applying the kernel to a log sweep and estimating |I(f)/V(f)| recovers |Y(f)| within roughly 0.3–0.4 dB RMS over the main checked range
• FFT/IFFT round-trip residual is at numerical floor
• Re(Z(f)) ≥ 0 over the frequency range

Important caveats​

The chain has not yet been validated against a measured impedance curve from a physical speaker. So far, the main “reality” check is the analytic TS-derived impedance peak for one driver.

Also, the n = 0.6 lossy inductance model is not strictly causal in the IFFT sense. The full IFFT shows around 1.6–2% wrap-around / tail energy. I have kept this as a warning rather than hiding it, because it may be a real modelling issue rather than an implementation bug.

This is also not:

• an amplifier model
• a tube output stage model
• an output transformer model
• an acoustic cabinet simulator
• a nonlinear / thermal model
• a real-time implementation

It is only a static, linear, small-signal admittance reference.

Questions​

I would appreciate any critique on these specific points:

1. Is y(t)=IFFT(1/Z(f)) the right primitive if the input is voltage and the desired output is current?
2. Would you instead use another representation for this kind of problem, such as direct ODE/network integration, ABCD matrices, state-space, or minimum-phase reconstruction?
3. Is n = 0.6 a defensible default for lossy voice-coil inductance in guitar/loudspeaker modelling, or is there a better standard starting point?
4. If you were validating this against one physical speaker on a bench, what measurement would you run first to falsify the approach quickly?
5. Are there obvious pitfalls here around causality, sampling, phase, or voltage/current interpretation that I am likely missing?

I am especially interested in criticism of the physical framing, not in whether the broader project is useful or novel.

A short pointer to one broken assumption would be more useful than a broad review.

Thank you.