To measure a loudspeaker in an ordinary room, you cut its impulse response off before the first reflection arrives — that cut is gating, and it buys reflection-free data at the price of bass detail. This page is an interactive walkthrough of what that price really is: why zero-padding is mandatory, why truncation (not FFT bin width) sets the resolution, how windows smear the spectrum, how to tell whether a gate is long enough, and what to show when it isn’t.
The red 1/T markers and gate edges are draggable directly on the plots — grab one and pull.
Two objects to keep apart throughout this page: the device’s frequency response — the true response of the DUT, what you want — and the DFT of the gated record — what you actually compute, and what every curve on this page plots. The two coincide only when the gate contains all significant IR energy (multiplication by 1 changes nothing). Otherwise the computed curve is the device’s response convolved with the window’s kernel — a smoothed copy, inaccurate at every frequency, not just the low ones.
All signals below are synthetic impulse responses sampled at 48 kHz. Spectra are computed by direct DTFT evaluation — mathematically identical to a zero-padded FFT at arbitrary resolution. Magnitudes are in dB, arbitrary reference, identical within each demo.
Every result on this page follows from one fact: a signal cannot be simultaneously narrow in time and narrow in frequency. Below is a Gaussian pulse — the unique shape that reaches the tightest possible joint concentration in time and frequency. Drag the slider to squeeze it in time and watch it stretch in frequency. The product of the two widths stays locked to one number. That is a law of mathematics (the uncertainty principle), not a limitation of microphones, rooms or FFTs.
Squeeze the pulse in time by a factor of 2 and its spectrum stretches by a factor of 2 — the product σt·σf is invariant (for a Gaussian it is exactly 1/2π, the minimum any signal can reach).
A rectangular gate of length T obeys the same rule in its own terms: its spectrum’s main lobe is ≈ 1/T wide. That is the seesaw behind every demo that follows. You can choose time resolution or frequency resolution. You cannot have both.
Every impulse response on this page — and every real loudspeaker’s — is a sum of damped sinusoids. Why? Every resonance in the system (woofer in its box, port, cabinet panel, breakup modes) behaves like a bell: hit it with the impulse and it rings — oscillating at its own frequency while losing energy. The natural ringing of one resonance is exactly
with three parameters: the frequency f₀ it rings at, the decay time τ (how long the ringing lasts), and the amplitude a (how strongly the impulse excited it). Mathematically these are the system’s poles: the impulse response of any linear system is the sum of one damped sinusoid per pole.
That is also how they are obtained from a measurement (Demo 6): you look at a decaying tail, count its oscillation period → f₀, measure how fast its envelope falls → τ, read its initial height → a. Try it yourself:
Top: the ringing, with its decaying envelope drawn dashed. One oscillation takes 1/f₀; the envelope falls by a factor e every τ.
Bottom: the same signal viewed in frequency — one peak at f₀. Drag τ up and watch the peak get narrower and taller: a long-lasting ringing is a frequency detail of width ≈ 1/(πτ) = f₀/Q, where Q = πf₀τ. This is the seesaw of Demo 0 in its purest form — and the reason a long-τ resonance demands a long gate: you must record the ringing until it is gone, or the gate smears this narrow peak into a wide bump (Demo 3).
Below is the two-way speaker from Demo 1 plus a slow bass resonance like Demo 2’s port. Switch modes on and off and watch the impulse response and the frequency response assemble themselves:
The bold curve is the coherent sum — note it is not the outline of the thin component curves: damped sinusoids interfere, adding and canceling between peaks. The individual thin curves show what each mode contributes alone.
Two things to try: (1) switch the bass resonance off and on — a single long-τ mode is what forces the long gate for the whole measurement; (2) switch everything off except one fast mode and compare with Demo 1 — that is the whole lesson in miniature: short in time ⇒ smooth in frequency.
The parameters of these exact modes are what a pole-fitting routine would report when analyzing a measured tail in Demo 6.
This IR (a little “2-way speaker”) decays below ≈ −60 dB within 5 ms, so a 5 ms gate throws
away nothing significant — the true response genuinely continues with zeros. With no padding, a 5 ms
record yields FFT bins spaced 1/T = 200 Hz apart (shown as dots). Increase the padding:
Grey curve: the same 5 ms of data evaluated at very high resolution. Every dot — at any padding factor — lands exactly on it. Padding computes true, exact values between the original bins, not an approximation and not new information.
The 5 ms record had already fully determined the response at every frequency — including far below the 200 Hz bin spacing. How accurate that response is relative to the real speaker depends only on how much the window altered the IR — completely unrelated to FFT resolution. Here the window altered nothing (the IR had decayed to zero inside the gate), so the spectrum of the gated data is the device’s response — the happy special case; Demo 3 is what happens when the gate throws data away.
This speaker has a long bass/port tail (decay time ≈ 11 ms around 68 Hz) and a floor reflection arriving at 14 ms. The gate must stop before the reflection — but does the IR decay enough by then? Move the gate and watch what happens to the low frequencies. Thin grey curves are fixed reference gates (2 / 4 / 8 / 12 ms) for comparison.
How to read it: the dashed line marks 1/T — not an FFT bin
spacing. The FFT resolution for the gate length implies nothing here (everything is computed at
arbitrarily fine resolution); 1/T is a property of the gate itself, the width of the smoothing
kernel it applies. Below it the spectrum of the gated data
cannot show features narrower than 1/T — and if the curve still moves there when you lengthen
the gate, the missing tail mattered.
That is the whole test: increase T; when the zero-padded FR stops changing (before the reflection), the gate was long enough. While it still moves, watch how it moves: the curve keeps “focusing”, converging from an initially blurred shape toward something sharper — the signature of an IR that has not finished decaying inside the gate.
Slide past 14 ms to see what a reflection does: a comb filter appears — the response is no longer free-field at all. The decay of the IR itself can also be “read” in the lower plot, but judging that by eye takes experience; the FR convergence test is objective. Tip: you can also grab the gate itself — drag the orange gate-end marker in the IR plot, or the red 1/T line above.
This system contains a tunable high-Q resonance — by default at 1 kHz with a 20 ms decay (Q ≈ 63), a feature only ~15 Hz wide in the true response. Longer τ means higher Q, a longer decay and a narrower feature — exactly the kind of detail a short gate destroys.
The resonance rings as a·e−t/τ·cos 2πf₀t: τ is the e-folding decay time and
the kick a is fixed whatever τ you pick — so a longer τ simply rings longer, and its spectral
peak grows narrower and taller (height ∝ τ, i.e. gain ∝ Q), exactly as in Part A. About its
strength: this IR is the direct sound (relative strength 1.2) plus four fast background modes
(0.90 / 0.55 / 0.35 / 0.15), and the resonance is excited at a = 0.08 — roughly eleven times
weaker than the strongest background mode. A weak, slow detail sitting on a much stronger, fast
background: precisely the situation gating has to deal with.
A gate shorter than the decay multiplies the IR, sample by sample, by the window — and by the convolution theorem, multiplying in time is exactly the same as convolving the true spectrum with the window’s spectrum in frequency. That convolution kernel’s main lobe is roughly 1/T wide — exactly how wide depends on the window shape (hard truncation ≈ 1/T, faded gate ≈ 2/T; Demo 5 measures each one). Fine details get smeared to that width:
The lower plot is the “smearing kernel” — magnitude of the window’s own spectrum
(linear frequency axis): a sinc-like main lobe with first zero at 1/T, and −13 dB
sidelobes for the rectangular gate. Convolution with it is exactly what gating does to the true
spectrum. The brackets at its top compare the two widths that decide everything: the kernel’s width
(red, ≈ 1/T) against the resonance’s own width (green, 1/(πτ)) — when the red bracket swallows the
green one, the feature is gone.
Note what kind of operation this is: a smoothing of fixed width in Hz (≈ 1/T) — unlike the octave-based smoothing of ordinary FR plots — applied equally across the whole range. It lowers the Q of resonances and can erase any detail finer than the kernel outright. So once the IR is truncated, no point of the curve is the accurate true response anymore — not even at the exact multiples of 1/T (200, 400, 600 Hz…); the gate altered the entire curve, everywhere. The converse is just as true: if the gate cuts off only a little of the tail, the smoothing inflicted is only mild.
Grow the gate well past the resonance’s decay time (the slider now goes to 200 ms) and watch the smeared bump sharpen back into the true narrow resonance. The FFT bin width is irrelevant throughout - all spectra are computed at arbitrarily fine (zero-padded) resolution; the only error is the truncation. A half-Hann fade pushes the sidelobes down (less leakage) but widens the main lobe to ≈ 2/T — more smearing, less ringing.
And note: if the gate fully contains everything significant in the IR, multiplication by 1 changes nothing — that is the definition of the correct gate length; there is no other general rule. The red 1/T line above (and the kernel’s first zero below) is draggable.
Back to the slowly-decaying speaker of Demo 2. The reflection at 14 ms caps the usable gate. The family of responses obtained as the gate grows from 1 ms toward that limit is shown in grey; the orange band is their point-by-point min/max — how much the answer still moves. The bold green curve is the longest available gate (the honest best estimate), the dashed white curve is the true anechoic response:
Left of the dashed line (1/T of the longest gate) the band is wide:
those frequencies are not resolved by the available impulse data — different amounts of the
still-decaying tail produce legitimately different answers there.
Drawing a thin curve (or a fake “dotted extrapolation”) below 1/T pretends to know what is going on; drawing nothing hides the best estimate we actually have. The band shows both at once: the green curve is the window-smoothed truth the data supports, and the band width is the remaining uncertainty.
Notice how the band collapses wherever the response has converged — “short in time means smooth in frequency”, so convergence arrives first at high frequencies — while at low frequencies the family of curves is still heading toward the dashed true response. The band shows how far the answer can still move; shrinking it needs a longer gate — or a different method. The red 1/Tmax line is draggable.
Every gate shape faces the same trade: a narrow smoothing kernel (fine resolution, little smearing) versus little ringing (no sidelobes smeared beside sharp features). No window beats the trade — the seesaw of Demo 0 again — you only choose where to sit on the curve. All windows below have the same length T and start at the impulse; the rectangular one is the “pure truncation” of Demo 3:
Colors: rectangular · half-Hann fade · Kaiser β=4 · Kaiser β=8 · exponential (adds artificial damping — biases the response, used deliberately e.g. on noisy tails) · your Kaiser (slider)
Middle plot: each window’s own spectrum, normalized (frequency axis in units of f·T, so the rectangular first zero sits at 1 = 1/T).
Bottom plot: the design space — the smoothing width of the kernel (its −6 dB width) against its ringing (first sidelobe). Points pinned to the bottom edge have no sidelobe: their skirt decays monotonically, so nothing rings beside a smeared feature — at the price of a wider kernel. Drag the slider and watch the blue Kaiser point slide along the frontier from “rectangular-like” (narrow, ringing) to “heavily tapered” (wide, no ringing).
The exponential window sits far to the right: no ringing, but the widest kernel of the lot — and it adds artificial damping, biasing the response. Rule of thumb: rectangular when the IR is already decayed (nothing to ring), a moderate taper when a strong tail is being cut.
Gating acts on the recovered IR, whatever produced it — and none of the excitation choices changes the 1/T limit. But they differ in SNR and in how they fail:
| Excitation | Strengths | Weaknesses | Typical use |
|---|---|---|---|
| Impulse (starter pistol, balloon, dirac-like click) | Trivial setup, no deconvolution | Very low energy → poor SNR; high peak drives speakers into nonlinearity | Quick checks, education |
| MLS (maximum-length sequence) | Fast, averages noise well, flat spectrum, no strict sync needed | Nonlinearities create spurious IR peaks; period must exceed the whole IR (time-aliasing); clock drift sensitive | Legacy tools, fast factory testing |
| Log swept sine (chirp, deconvolved with its inverse) | Best energy per measurement time → excellent SNR; harmonic distortion arrives at separate times (Farina) and can be excluded | Needs sync/trimming; longer measurement; inverse-filter care at the band edges | The modern default (REW, ARTA, …) |
Practical consequence: with a sweep you can spend seconds injecting energy exactly where the IR is weak (the late, low-level tail that gating wants to keep), which is why sweep-based gated measurements push the usable gate longest. Whatever the excitation, the chain is identical afterwards: deconvolve → IR → gate → zero-pad → interpret with Demos 1–5.
When the IR has not decayed by the time the reflection arrives, the standard advice is that you need a non-gating method. One such method follows directly from the building blocks above: the late tail is (approximately) a damped sinusoid, so measure its three parameters from the part you can see, then synthesize what would have come after the reflection. Two steps — first obtain the model, then use it:
Pick a window on the tail of the room measurement (the blue IR below; the reflection arrives at 14 ms). The tempting shortcut — reading f₀ off the window’s spectral peak — fails here: a short window of a slow tail has no clear peak (see the grey dot below).
So the fitter does a proper little
pole fit: it sweeps frequency and decay time together, least-squares fitting
e−t/τ(A·cos 2πft + B·sin 2πft) to the window, and keeps the (f₀, τ) pair that
explains it best — frequency, decay time, amplitude and phase, all from one fit:
Top: the measured room IR (the 14 ms reflection is the big spike); shaded, the fit window; in color, the fitted damped sinusoid — when the window is well chosen it hugs the data almost exactly (the true values for this synthetic speaker are f₀ = 68 Hz, τ = 11 ms).
Bottom: the spectrum of the fit window — note there is no clean peak; the grey dot is where a naive peak-pick would land, the red line is the fitted f₀.
Try dragging the window start left toward 0: the direct sound and the fast midrange modes get included, the fit R² collapses, and the fitted τ drifts — this is the whole art of pole fitting in one slider. A fit window must contain one clean decay and nothing else.
The fitted f₀, τ, A, B now define the tail completely. Splice it in where the fit window ends and run it on past the 14 ms reflection — the effective gate is now as long as you dare synthesize:
Grey: real data only, gated where the fit window ends — the 68 Hz port bump is unresolved. Blue: real data plus the tail synthesized from the fitted parameters, out to the effective gate.
With a good fit window the blue curve converges onto the dashed true response as the gate grows; with a bad fit window (drag Step 1’s start left) it converges to something confidently wrong. That is the catch, made visible: real tails are only approximately sums of damped sinusoids, and a bad fit injects plausible-looking but wrong bass — which is why this is the advanced option, not the default.
What the model tries to reconstruct in software, ground-plane and nearfield measurements give you for free. The red 1/T line is draggable.
The skill the demos build up to: before measuring, predict what a gated measurement can resolve. Two numbers collide.
The gate the speaker needs — its slowest resonance must decay to the noise floor, and a resonance at f₀ with Q has an amplitude decay time τ = Q/(πf₀), so reaching −60 dB takes ≈ 6.9·τ ≈ 2.2·Q/f₀. And the gate the room allows — the first reflection caps it, leaving a resolution floor of 1/T. Set both sides and read the verdict:
Top plot: the resonance’s decay envelope in dB against the two time limits — the reflection (red) and the gate needed to reach the decay target (green). Bottom plot: the maximum Q still fully resolvable at each frequency, given this room’s reflection delay, with your resonance marked.
Try the defaults — a Q = 10 resonance at 100 Hz in a room whose first reflection arrives at 10 ms — and watch the verdict explain why the bass of a ported bookshelf is measured nearfield rather than gated.
| Method | Bass extension | Reflection handling | Typical limitations |
|---|---|---|---|
| Gated in-room (impulse/MLS/sweep, this page) | Limited: fmin ≈ 1/T, T < first reflection (typically 100–300 Hz in small rooms) | Removed in time by truncating before they arrive | 1/T smearing; needs decayed IR before reflection; SNR of late tail |
| Ground plane (speaker & mic on the ground, outdoors) | Excellent — the full undamaged IR is usable; no low-frequency gate limit | The single ground reflection adds coherently (doubles pressure, +6 dB) instead of truncating it | Needs large open space; half-space loading; ground-bounce combing limits the upper end |
| Nearfield + splice (driver/port measured at mm distances) | Excellent — nearfield pressure follows cone velocity, practically anechoic at low frequencies | Reflections negligible due to proximity; spliced to gated far-field data above ~200–400 Hz | Valid only below baffle-diffraction region; needs radiating-area correction; multi-way summing is fiddly |
| Anechoic chamber | Down to the chamber’s low-frequency limit (absorber size, typically 80–200 Hz) | Absorbed — no gating needed, full-length IR available | Chamber cost/size; low-F limit; still a windowed environment above it |
| In-room steady state / minimum-phase + EQ | Full-band by construction — never attempts anechoic data | Not removed; accepted and equalized (careful above Schroeder frequency) | Includes room modes; not a loudspeaker property; position-dependent |
| Advanced / model-based (pole fitting, reflection-by-geometry removal, mic arrays) | Can extend below 1/T by extrapolating the decaying tail as damped sinusoids | Separated by model or spatial filtering instead of brute truncation | Assumption-heavy; rarely in consumer tools; the model-based tail extension of Demo 6 |
In practice the classic solution is a splice: nearfield for the bass, gated far-field for mids/highs — each method used exactly where its window does no harm.
This page stops at the standard advice, but the same ideas keep going. If you want the ceiling: