Time Weighting

Accurate SPL measurement requires capturing energy over specific time windows. phonometry implements exact time constants per IEC 61672-1:2013.

• Fast (fast): τ = 125 ms. Standard for noise fluctuations.
• Slow (slow): τ = 1000 ms. Standard for steady noise.
• Impulse (impulse): Asymmetric ballistics. 35 ms rise time for rapid onset capture, 1500 ms decay for readability.

import numpy as np
from phonometry import time_weighting

# Calculate energy envelope (Mean Square)
energy_envelope = time_weighting(signal, fs, mode='fast')
# dB SPL relative to 20 μPa
spl_t = 10 * np.log10(energy_envelope / (2e-5)**2)

The asymmetric Impulse ballistics use two constants — a fast attack and a slow decay — switching per sample on the sign of the change:

$$y[n] = y[n-1] + \alpha \ (x^2[n] - y[n-1]), \qquad \alpha = \begin{cases}1 - e^{-1/(f_s \cdot 0.035)} & x^2[n] > y[n-1]\\[2pt] 1 - e^{-1/(f_s \cdot 1.5)} & \text{otherwise}\end{cases}$$

The exponential detector

A sound level meter’s needle cannot follow the pressure waveform — it shows a running mean square with an exponential memory. Formally (IEC 61672-1, 3.8):

$$\tau\ \frac{dy}{dt} + y = x^2(t) \quad\Longleftrightarrow\quad y(t) = \frac{1}{\tau} \int_{-\infty}^{t} x^2(\xi)\ e^{-(t-\xi)/\tau}\ d\xi$$

a first-order low-pass on the squared signal. The time constant τ sets the trade-off: Fast (125 ms) follows speech-like fluctuations, Slow (1 s) steadies the readout for quasi-stationary noise. After a step onset the envelope reaches 63 % of its final value in one τ and ~99.8 % after 8τ — that is why level analyses discard the first instants of a recording.

time_weighting() / TimeWeighting parameters

Parameter	Type	Units	Range / default	Notes
x	1D or 2D array	pressure (any scale)	non-empty	Squared internally; output is a mean-square envelope
fs	int	Hz	> 0
mode	str	—	'fast' (default), 'slow', 'impulse'	τ = 125 ms / 1 s / 35 ms attack + 1.5 s decay
TimeWeighting(fs, mode) (class)	—	—	—	Stateful variant for streaming: process(x) carries the integrator state between blocks

The output has the units of $x^2$: take 10*log10(y / p0**2) for SPL or use the level functions, which do it for you.

Verified ballistics (IEC 61672-1 Table 4)

The Fast envelope’s response to 4 kHz tonebursts lands exactly on the standard’s reference values — enforced in CI for burst durations from 1 s down to 1 ms (F and S weightings, class 1 acceptance limits):

Initial state

By default, the exponential integrator starts from rest (y[-1] = 0). Passing initial_state=None leaves this default unspecified, while initial_state='zero' requests the same zero state explicitly. If the recorded segment begins after a steady signal is already present, you can start from the first sample energy instead:

energy_envelope = time_weighting(signal, fs, mode='fast', initial_state='first')

Block processing

For block processing, pass the last output value from the previous block as the next block’s initial_state instead of resetting each block:

state = None

for block in audio_blocks:
    energy_envelope = time_weighting(block, fs, mode='fast', initial_state=state)
    state = energy_envelope[-1]

For multichannel blocks with time on the last axis, carry one state per channel: use state = energy_envelope[..., -1]. A scalar initial_state is applied to every channel, while an array must match or broadcast to the non-time shape, such as (n_channels,) for input shaped (n_channels, n_samples).

Or let the TimeWeighting class carry the state for you:

from phonometry import TimeWeighting

tw = TimeWeighting(fs, mode='fast')
for block in audio_blocks:
    energy_envelope = tw.process(block)

Concatenated block outputs are exactly equal to a single continuous call (verified for all three modes, mono and multichannel). Call tw.reset() to start from rest again.

Performance note

The impulse mode uses an asymmetric kernel that is JIT-compiled when numba is installed (pip install phonometry[perf]). Without numba a pure-Python fallback produces identical results, just slower.

See Integrated & Statistical Levels for Leq/LN metrics built on these envelopes, and Why phonometry for the IEC 61672-1 tone-burst verification.