Source: https://jmrplens.github.io/phonometry/buildings/rooms/room-impulse-response/ # Measuring the Room Impulse Response Every room-acoustic quantity on this site starts from the same measurement: the **impulse response** (IR) between a source and a receiver. Get it right and everything downstream (reverberation time, clarity, insulation, speech metrics) is a matter of arithmetic; get it wrong and no later processing recovers what the excitation or the microphone position threw away. This guide covers the acquisition itself, per ISO 18233: the exponential sine sweep and its deconvolution, the MLS correlation method, and where to place sources and microphones so the averaged result means something. Turning the measured IR into room parameters lives in [Room Acoustics](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/); the same IR measured either side of a partition becomes sound insulation in [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/). ## Two deterministic excitations (ISO 18233) A room behaves, to a good approximation, as a **linear time-invariant** system, so everything about it is contained in its IR. You could fire a pistol and record the tail, but a deterministic excitation played through a loudspeaker and *deconvolved* recovers the same IR with 20–30 dB more effective signal-to-noise ratio (ISO 18233). Two excitations are provided. **Exponential sine sweep (ESS, Annex B).** The instantaneous frequency rises exponentially, $$ f(t) = f_1 \left( \frac{f_2}{f_1} \right)^{t/T}, $$ so the time spent per octave is constant and the excitation mimics pink noise (constant energy per fractional-octave band). The IR is recovered by linear (zero-padded, non-circular) spectral division, $$ H = \frac{Y\ \overline{X}}{|X|^2 + \varepsilon}, $$ with a small Tikhonov term $\varepsilon$ guarding the band edges where the sweep has little energy. Because a low-to-high sweep places harmonic distortion at *negative* arrival times, distortion separates cleanly from the linear IR and is discarded by keeping only the causal part. The `"farina"` method reaches the same result by convolving the recording with the analytic inverse filter; it assumes the reference sweep was generated with the default amplitude and fade, so use the spectral method for a non-unit-amplitude or custom-fade sweep. **Maximum-length sequence (MLS, Annex A).** An order-$N$ binary sequence of length $2^N-1$ whose circular autocorrelation is a near-perfect delta; the IR follows from circular cross-correlation of the recorded period with the sequence. MLS excites at constant amplitude and is quick to average, but it is more sensitive to time variance (draughts, temperature drift) and cannot be fed as much power as a sweep. **Prefer the sweep** for rooms and partitions; reach for MLS when the excitation must be periodic or the hardware favours a two-level signal. ```python import numpy as np from scipy.signal import fftconvolve from phonometry import room fs = 48000 # A 3 s, 20 Hz - 20 kHz sweep is a good broadband room excitation # sweep: excitation you play through the loudspeaker sweep = room.sweep_signal(fs, 20.0, 20000.0, 3.0) # Deconvolve the recorded response back to the impulse response system = np.zeros(fs); system[100] = 1.0; system[2000] = 0.4 # direct + reflection # recorded: mic capture of the played sweep (here simulated by convolution with a synthetic room) recorded = fftconvolve(sweep, system) ir = room.impulse_response(recorded, sweep, fs, method="spectral") print(int(np.argmax(np.abs(ir)))) # 100: direct sound recovered ir.plot() # waveform + Schroeder envelope (figure below) # Farina inverse-filter variant (needs the sweep band) ir_f = room.impulse_response(recorded, sweep, fs, method="farina", f_range=(20.0, 20000.0)) # Periodic MLS: excite with >= 2 periods, average, cross-correlate mls = room.mls_signal(16) # length 2**16 - 1 = 65535 rec = fftconvolve(np.tile(mls, 2), system)[: 2 * mls.size] ir_m = room.mls_impulse_response(rec, mls) print(int(np.argmax(np.abs(ir_m)))) # 100 ``` `sweep_signal`/`mls_signal` return plain arrays, ready to write to a WAV file and play. `impulse_response`/`mls_impulse_response` return an `ImpulseResponseResult`, a drop-in for the raw IR array (`np.asarray(ir)`, indexing and `ir.size` all keep working, so `room_parameters(ir, fs)` is unchanged) that also carries the sample rate and method and adds an `.plot()`. Two more excitations from the transfer-function literature - complementary Golay pairs with exactly noise-free deconvolution, and sweeps shaped to an arbitrary target spectrum - live in the [system-measurement guide](https://jmrplens.github.io/phonometry/signals/spectra/system-measurement/) and return the same result types. **The two excitations.** The exponential sweep sweeps its energy up the spectrum over the whole signal, while the MLS is a flat-spectrum two-level sequence, visible as the near-constant magnitude on the right.

Show the code for this figure

```python from phonometry import room from phonometry import plot_excitation fs = 48000 sweep = room.sweep_signal(fs, 50.0, 20000.0, 1.0) # ESS excitation mls = room.mls_signal(12).astype(float) # length 2**12 - 1 # One-liner: waveform + spectrogram (sweep), sequence + flat spectrum (MLS) plot_excitation(sweep, fs, kind="sweep") plot_excitation(mls, fs, kind="mls") # By hand: the sweep spectrogram and the MLS magnitude spectrum import numpy as np import matplotlib.pyplot as plt fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4)) ax1.specgram(sweep, NFFT=1024, Fs=fs, noverlap=512) ax1.set(xlabel="Time [s]", ylabel="Frequency [Hz]", title="Sweep spectrogram") spec = np.abs(np.fft.rfft(mls)) freqs = np.fft.rfftfreq(mls.size, d=1.0 / fs) ax2.semilogx(freqs[1:], 20 * np.log10(spec[1:] / np.median(spec[1:]))) ax2.set(xlabel="Frequency [Hz]", ylabel="Magnitude [dB]", title="MLS spectrum (flat)") ```

## The recovered impulse response Deconvolving the recording gives the broadband IR: the direct sound, discrete early reflections and the decaying diffuse tail. Its `.plot()` shows the waveform above and the log-magnitude envelope with the Schroeder energy-decay curve below: the straight decay whose slope becomes the reverberation time in the [Room Acoustics guide](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/). [Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_sweep_deconvolution.webm)

Show the code for this figure

```python import numpy as np from scipy.signal import fftconvolve from phonometry import room fs = 48000 sweep = room.sweep_signal(fs, 20.0, 20000.0, 1.5) # A synthetic room: direct sound + two reflections + a decaying diffuse tail system = np.zeros(int(0.7 * fs)) system[80], system[1400], system[3100] = 1.0, 0.5, 0.32 ir = room.impulse_response(fftconvolve(sweep, system), sweep, fs, length=system.size) # One-liner: waveform + log-magnitude / Schroeder decay ir.plot() # By hand: the normalized log-magnitude envelope in dB import matplotlib.pyplot as plt h = np.asarray(ir) t = np.arange(h.size) / fs plt.plot(t, 20 * np.log10(np.abs(h) / np.max(np.abs(h)))) plt.ylim(-80, 5) plt.xlabel("Time [s]"); plt.ylabel("Level re peak [dB]") ```

### `sweep_signal()` / `inverse_filter()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `fs` | int | Hz | > 0 | Sampling frequency | | `f1` | float | Hz | > 0, at/below lowest band | Sweep start frequency | | `f2` | float | Hz | `f1 < f2 <= fs/2` | Sweep stop frequency | | `seconds` | float | s | any; longer ⇒ more SNR | Sweep duration | | `amplitude` | float | — | default `1.0` | Peak amplitude | | `fade` | float | — | `[0, 0.5)`, default `0.01` | Half-Hann fade fraction (kills start/stop transients) | ### `impulse_response()` parameters | Parameter | Type | Units | Range / default | Notes | | :--- | :--- | :--- | :--- | :--- | | `recorded` | 1D array | any | non-empty | Recorded system response | | `reference` | 1D array | any | non-empty | The emitted sweep | | `fs` | int | Hz | > 0 | Sample rate | | `method` | str | — | `'spectral'` (default) / `'farina'` | `'farina'` requires `f_range` | | `f_range` | (float, float) | Hz | default `None` | `(f1, f2)` of the sweep (Farina only) | | `regularization` | float | — | default `1e-6` | Tikhonov term as a fraction of peak spectral energy | | `length` | int, optional | samples | default `len(recorded)` | Samples of causal IR to return | | `return_full` | bool | — | default `False` | Return the full sequence (distortion in the tail) | `mls_signal(order)` takes an integer `order` in 2–20 (sequence length $2^{\text{order}}-1$); `mls_impulse_response(recorded, mls, length=None)` needs `recorded` to span an integer number of MLS periods. ## Where to measure One IR characterises a single source–receiver pair; a reported room parameter is the spatial average over several. ISO 3382-1 (performance spaces) asks for at least two source positions and microphones spaced $\geq 2$ m apart, $\geq 1$ m from any surface, at $1.2$ m (seated-ear) height; ISO 3382-2 fixes the minimum number of source, microphone and source–microphone combinations per accuracy grade (survey / engineering / precision) and asks for microphone positions that avoid symmetric placements. **Averaging across positions.** The reported per-band parameter is the arithmetic mean over all source-microphone combinations, and the spread across positions is part of the answer, not noise: quote it alongside the mean whenever it exceeds the parameter's JND (ISO 3382-1 Table A.1), because a room can meet a target on average while individual seats sit far outside it. Four placement mistakes bias the mean itself: - **Correlated positions.** Microphones closer than 2 m to each other sample nearly the same sound field twice, so the average looks more stable than it is. The 1 m minimum from any surface likewise avoids the pressure build-up near a boundary (and the comb filter of the animation below) that colours everything a too-close microphone records. [Watch the high-resolution video (WebM)](https://raw.githubusercontent.com/jmrplens/phonometry/main/.github/images/anim_comb_filtering.webm) - **Symmetric placements.** In a geometrically symmetric room, mirror-image positions receive mirror-image reflection patterns; averaging them adds no new information. This is why ISO 3382-2 asks for positions that do not sit on symmetry lines. - **Too close to the source.** Inside the direct field EDT collapses and C80 saturates upward no matter what the room does. ISO 3382-2 therefore keeps every microphone at least $d_\mathrm{min} = 2\sqrt{V/(c\,\hat T)}$ from the source, with $\hat T$ an estimate of the expected reverberation time (about 2.2 m for a 200 m³ classroom with an expected 0.5 s). - **Low-frequency luck.** Below the Schroeder frequency (see the [Room Acoustics guide](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/)) each band holds only a handful of room modes, and a microphone on a node of one of them sees a different decay than a microphone on an antinode. The spread of the 63-125 Hz bands across positions is structurally larger; the cure is more positions, not a longer excitation. Three practical limits close the chain. Playback and recording themselves — sound-card I/O, level calibration of the chain — are outside the library, which starts at the recorded array. ISO 18233's time-variance and distortion diagnostics are not implemented either: the sweep separates distortion, but no helper here quantifies it (that reading lives in the [swept-sine distortion guide](https://jmrplens.github.io/phonometry/devices/electroacoustics/swept-sine-distortion/)). And the position rules above are guidance prose: nothing checks how many positions were measured or where. ## From the impulse response onward The IR leaves this page in several directions. Band-filtered and backward-integrated it becomes the decay curve whose slope is the reverberation time: the [Room Acoustics guide](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/) picks up exactly there, and its open-plan sibling walks the [ISO 3382-3 line of workstations](https://jmrplens.github.io/phonometry/buildings/rooms/open-plan-acoustics/). Measured either side of a partition, the same sweeps feed the level differences of [field sound insulation](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/). And the harmonic distortion that the exponential sweep pushes to negative arrival times is not always discarded: read deliberately, it becomes the THD analysis of the [swept-sine distortion guide](https://jmrplens.github.io/phonometry/devices/electroacoustics/swept-sine-distortion/). ## Quick answers ### Should I measure the room impulse response with a sine sweep or an MLS? Both are ISO 18233 deconvolution methods that recover the impulse response with 20–30 dB more effective signal-to-noise ratio than an impulsive source. Prefer the exponential sine sweep (Annex B): it places harmonic distortion at negative arrival times, where it is discarded. Use MLS (Annex A) when the excitation must be periodic or the hardware favours a two-level signal; it is more sensitive to time variance. ## References - International Organization for Standardization. (2006). *Acoustics — Application of new measurement methods in building and room acoustics* (ISO 18233:2006). [iso.org catalogue](https://www.iso.org/standard/40408.html). The swept-sine and MLS acquisition this page implements. - International Organization for Standardization. (2009). *Acoustics — Measurement of room acoustic parameters — Part 1: Performance spaces* (ISO 3382-1:2009). [iso.org catalogue](https://www.iso.org/standard/40979.html). The source and microphone position requirements quoted in the where-to-measure rules. - International Organization for Standardization. (2008). *Acoustics — Measurement of room acoustic parameters — Part 2: Reverberation time in ordinary rooms* (ISO 3382-2:2008). [iso.org catalogue](https://www.iso.org/standard/36201.html). The accuracy grades, position counts and the minimum source distance behind the position-averaging discussion. ## Standards ISO 18233:2006 (application of new measurement methods: the swept-sine and MLS acquisition of impulse responses); ISO 3382-1:2009 and ISO 3382-2:2008 (the source and microphone position requirements and accuracy grades applied when planning where to measure). Validated against closed-form deconvolution identities in the [conformance report](https://jmrplens.github.io/phonometry/reference/conformance/). ## See also - [Room Acoustics](https://jmrplens.github.io/phonometry/buildings/rooms/room-acoustics/): the decay analysis and ISO 3382 parameters computed from the IR this page acquires. - [Open-Plan Office Acoustics (ISO 3382-3)](https://jmrplens.github.io/phonometry/buildings/rooms/open-plan-acoustics/): the speech-privacy line measured with the same acquisition. - [System Measurement](https://jmrplens.github.io/phonometry/signals/spectra/system-measurement/): complementary Golay pairs and spectrally shaped sweeps, returning the same result types. - [Swept-Sine Distortion & Phase](https://jmrplens.github.io/phonometry/devices/electroacoustics/swept-sine-distortion/): the Farina reading of the distortion the sweep separates. - [Field Insulation Measurement (ISO 16283)](https://jmrplens.github.io/phonometry/buildings/insulation/insulation-field/): the same measurement either side of a partition. - [Image Sources & Steady-State Field](https://jmrplens.github.io/phonometry/buildings/rooms/room-image-sources/): simulated impulse responses to rehearse the processing chain on. - API reference: [`room.impulse_response`](https://jmrplens.github.io/phonometry/reference/api/rooms/impulse-response/).