Room Acoustics Measurements

From Inspired Acoustics Knowledge Base

Room acoustics measurements involve various parameters that can be measured:

• Room impulse response measurements

for calculating room acoustics parameters

• Other measurements, such as
  • Sound pressure level distribution measurements
  • Subject-based speech intelligibility measurements
  • Absorption coefficient (alpha) measurments
  • Critical distance measurements, etc.

Contents 1 Room acoustics measurements in general 2 Measuring room impulse responses 3 About indirect measurements 4 Sine sweeps 5 Equipment 6 Limitations of LTI assumptions 7 Usage of the measurement result

Room acoustics measurements in general

Modern room acoustics measurements are often based on recording and post processing Room Impulse Responses (aka RIR, or IR). An impulse response is a transfer function between the input and the output of an LTI - linear, time-invariant - system, and contains all information about it. The input in a room is a source position, a physical location where the sound is excited, while the output is a listener position, which is usually located at a relevant place where the audience is often listening. There can be several inputs and outputs defined in a room, therefore the room is a MIMO - multiple input multiple output - system.

Measuring room impulse responses

Measuring a room impulse response (RIR) involves recording an audio signal called the excitation signal to obtain the response. The response - according to the measurement method - is either the impulse response itself or an intermediate response that needs to be post processed to obtain the impulse response.

The measurement methods to obtain a room impulse response can be categorized as:

• Direct measurements with
  • Periodic Impulse Excitation (PIE method)
  • Approximation of the PIE method, other impulsive excitation (electrical sparks, starter pistol, etc.)

It would be ideal to generate an impulse and directly record it with a microphone, but there are some problems with that. Impulsive signals, such as the PIE method, which uses a periodic impulse sound excited from a loudspeaker suffers from the problem of low energy thus low signal-noise ratio in the resulting measurement even with averaging. Signals that approximate an impulse such as an electric spark or a starter pistol do not have an ideally flat frequency response and they are not very well reproducible (the excitation signal itself is different every time thus averaging is problematic). They are therefore not used in modern measurements any more.

• Indirect measurements with
  • Wideband excitation methods
    • Dual channel FFT methods with random unsynchronized noise
    • INM (interrupted noise method)
    • MLS, or other pseudo-random signals that have periodic 1-valued autocorrelation functions in terms of AC component
  • Narrowband excitation
    • Warbled tones
    • Time-delay spectrometry (TDS)
    • Sine sweeps, TSP (time-stretched pulse)
  • Variable bandwidth measurements
    • Music, speech, and other variable spectral component signals for approximating a variable bandwidth room impulse response
  • Discrete frequency measurements
    • Discrete sine method
    • Stepped sine method

About indirect measurements

The idea behind indirect measurements is the need of maximizing the energy pumped into the system of interest, the room. By maximizing the energy, better signal-noise ratio can be achieved. Maximizing can be done in three ways:

• maximizing the energy in the signal itself
• maximizing the excitation level, or
• lengthening the measurement time.

Maximizing the energy of the signal means spreading the impulse over time. Such resulting signal can be sine sweeps (known as sweep signals when synthesized in time-domain or time stretched pulse, TSP when synthesized in the frequency domain) or pseudo-random noise (e.g. maximum length sequence, MLS). Sine sweeps might have some differences in the way they sweep (linearly or exponentially in time) and they have a different spectrum (white and pink, respectively) accordingly.

For capturing acoustics, exponentially sine sweeps sweeping upwards produce good results, as speakers can be driven 'louder' with them compared to a linear sweep. On the other hand, it is possible by using exponentially sweeping signals to separate the harmonic distortion produced by the loudspeakers so that their effects will not be included in the final - base band - impulse response.

After recording an excitation signal of an indirect measurement method, post processing is needed to acquire the impulse response. This is according to the matched filter theory. In the case of MLS, calculation of the cross-correlation function by means of Fast Hadamard Transform is one of the most efficient ways to obtain the impulse response.

Sine sweeps are superior in many ways compared to MLS signals. While MLS signals produce artifacts - unwanted impulses, spikes - when harmonic distortions are present - and they are significantly present in all forms of dynamic loudspeakers -, exponential sweeps do not suffer from this problem, as the harmonic contents can be separated in time from the baseband impulse response. This is because of the fact that the time between the harmonics are constant at all frequencies in exponential sweeps. Although MLS signals may produce high theoretical signal-to-noise ratios - recall that their crest factor is 1 -, in reality they do not, because of many reasons. One of these is that the MLS method is very sensitive to phase problems in general, which occur in cases when time variance exists. Sine sweeps are not prone to this problem.

Sine sweeps

Linear sweeps have a constant sweeping speed - upwards or downwards - from the start frequency w₁ towards the end frequency w₂. Linear sweeps have a white spectrum. The time-domain equation of a linear sweep is

where A is the peak amplitude of the signal and T is its length.

Exponential sweeps have an accelerating sweeping speed and have pink spectrum. They can be synthesized in time-domain with the following formula:

Equipment

The measurement equipment and methods are defined and explained in standards (ISO 3382:1997 and ISO 18233:2006). The excitation signal comes from the loudspeaker, while the recording is performed with microphones. Both the loudspeaker and the microphone have to have known directional characteristics, preferably omni-directional, according to the standards. The equipment has to be as transparent as possible (e.g. in its frequency response) and it should be powerful enough to excite the room to achieve a good signal-noise ratio. If there are frequencies not coming out of the speaker (e.g. very low frequencies), than the impulse response acquired will miss these frequencies as well. To overcome this problem, one of the best solutions might be to use a separate subwoofer or large monitor speakers.

Limitations of LTI assumptions

In a large room, such as a cathedral or a large concert hall where air movement and temperature might vary depending on the physical location (e.g. above or below), the time invariance assumption is not correct. Therefore, measurement data can vary within the same physical measurement setup. Affected regions are often high frequencies, where not just time variance, but statistical properties of stochastic reflections/behaviors also affect the results. Different excitation signals of different measurement methods behave differently when there is significant time variance.

Usage of the measurement result

One of the most important usage of the room impulse responses are the ability to calculate the Acoustical Parameters. These are used for objective evaluation of the rooms. The other usage or RIRs is auralization, based on Convolution Reverberation, or creative reverberation - again by convolution reverberation, but with the ability to control the impulse responses.