Early Lateral Energy

The early lateral energy fraction, $J_{LF}$, represents the proportion of energy arriving from lateral directions within the first 80 ms after the arrival of the direct sound. This parameter is obtained from the impulse responses measured with a figure-of-eight pattern microphone and an omnidirectional microphone [1].

It can be calculated according to the following equation:

$$J_{LF} = \frac{\int_{0.005}^{0.080} p_L^2(t)\, dt}{\int_{0}^{0.080} p^2(t)\, dt},$$

where the numerator corresponds to the lateral energy contribution within the time window from 5 ms to 80 ms, and the denominator represents the total sound energy arriving within the first 80 ms.

The terms can be expressed as follows:

• $p_L(t)$: instantaneous sound pressure in the impulse response measured with a figure-of-eight pattern microphone;
• $p(t)$: instantaneous sound pressure in the impulse response measured with an omnidirectional microphone at the measurement point.

The figure-of-eight microphone is oriented so that its null points towards the stage source position. This ensures that it responds predominantly to lateral sound energy, with minimal influence from the direct sound. In practice, the figure-of-eight microphone can be modeled using spatial receivers by selecting one of the ambisonic signals.

Because the directivity of the figure-of-eight microphone follows a cosine pattern, the contribution of each reflection to the lateral energy varies with the square of the cosine of the incidence angle relative to the microphone’s axis of maximum sensitivity.

Thus, $J_{LF}$ is an indicator of the strength of early lateral reflections, which are closely linked to apparent source width and the listener’s spatial impression in concert halls.

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References

[1] ISO 3382-1:2009 Acoustics — Measurement of room acoustic parameters — Part 1: Performance spaces.