# How long should be the Room Impulse Response

I am writing a code to calculate the reverberation time of a room. I am new to the topic. I used sine sweep to excite the room and the response was recorded. Then I got the room impulse response by convolving the recorded signal with inverse sweep.Then I filtered the RIR in octave bands and did lundeby algorithm to find the point, to start backward integration.

The broad band impulse response I got was very long due to convolution(length(recorded signal)+length(inverse sweep)-1).This causes problem when I do Lundeby Algorithm. Could some one please let me know if I truncate the broad band room impulse response? How long should be the room impulse response to get good values for reverberation time? I coudn't find a literature mentioning this. I am adding a screenshot of IR.

• Could you clarify? The duration of the room's response depends on the room itself. It's a fact independent of your measurements.
– MBaz
Mar 2 at 18:25
• For determining an appropriate truncation of an impulse response, see this reference.
– Ash
Mar 2 at 19:11

The length of any room impulse response is technically infinite since it's inherently an IIR system. The reverberation time describes the decay rate. During the reverberation time the impulse response decays by 60 dB. In practice reverberation varies between a few 100 milliseconds (residentials rooms), to many seconds for large public spaces. The longest I have ever measured was about 6 seconds in monastery in Austria.

The best truncation method depends on what you want to do with the impulse response, the reverb time and how much Signal to Noise Ratio you need. Most people will try to capture everything until the decay disappears into the noise floor. That's easy enough to calculate. If you have an SNR of 80 dB and a reverb time of 1.5s you should capture at least $$t = 80dB/60dB \cdot 1.5s = 1.8s$$. You want maybe 25% or so more in the raw capture to get a good estimate of the noise floor.

Both SNR and reverb time depend significantly on frequency, so it's a good idea to do the truncations and estimations in different frequency bands.

In practice it's very difficult to get good signal to noise ratio especially at low frequencies because of acoustic background noise (which is typically "brown", i.e. $$1/f^2$$ and limited output capability of the loudspeaker. This can be partially compensated by carefully shaping the spectrum of the measurement signal and increasing the measurement time (e.g. coherent averaging). This also has to be done carefully: technically the room impulse response is time invariant but over longer time intervals something always drifts or moves (air temp, DC pressure, etc.) and you loose coherence especially at higher frequencies.

Background noise is difficult to deal with since it's hard to control. A good measurement will always require some manual management: close all windows, turn of HVAC systems, ask people in the building to be quiet for a few minutes, look for an opening in traffic noise, etc. .

In order to get a good measurement, it's best to start with a rough estimation of reverb time and SNR and use these estimates to optimize the measurement parameters for a more "high fidelity" measurement.