# How to find the impulse response of a room using a sine sweep signal?

Using the Exponential Sine Sweep (ESS) method and my test equipment, I am trying to find the impulse response (IR) of a room which contains a great deal of sound absorbing material. Ultimately I want to calculate the reverberation time (RT60) using the IR. Of course, I know there are similar questions, but I'm asking because I think the situation is different from the one I'm in.

I create the ESS using the source control module of the front-end DAQ (LMS mobile scadas) and deliver the signal to the Omnipower sound speaker (Bruel and kajer type 4292-L) through the Amplifier (Bruel and kjaer type 2734). At the same time, sound is measured using a Mic.

The lower and upper frequency limits of the ESS signal are 20 Hz and 12800 Hz, respectively, and were generated to sweep for 20 seconds.

The schematic diagram of the measuring equipment is as follows: When measuring IR using ESS, I know that deconvolution must be performed using an inverse filter.

My understanding of this thread is that the inverse filter for the ESS method can be generated if we know the exact form of the signal which is transmitted to the speaker. However, as shown in the graph below, when the generated signal (red line) passes through the Amp, the magnitude and phase of the signal change (blue line). Therefore, it is currently difficult for me to know the exact phase information of the ESS signal transmitted to the speaker.

Anyway, I want to obtain IR using input voltage (measured form power amp, Green line) and sound pressure (Red line), which are shown as follows: To summarize my question:

Q1) Is it possible to use the generated signal that passes before the power amplifier to obtain impulse response? (It would be nice if this was possible, but it is expected that the changes in the amplitude and phase of the signal transmitted to the speaker by the amp be reflected).

Q2) If it is not feasible, is there a good way to get IR using the measured input voltage (from power am.) and response (pressure)?

Q3) In order to obtain the IR of the room, the Input is set to Voltage, but in my opinion, the Input should be the volume acceleration of the sound source or a physical quantity corresponding to it. Is there any reason why it is OKAY to calculate IR like this?

Q4) Are there any other considerations other than those mentioned above to get an accurate IR?

• Since you are capturing the signal at the input to the speaker, don't you then know the exact waveform at that node? WIth that signal and the signal at the microphone you can determine the channel between them (which will include the effects of the speaker and microphone. This post may help as well: dsp.stackexchange.com/questions/31318/… Oct 26, 2022 at 3:13

Q1) Is it possible to use generated signal that passes before the power amplifier to obtain impulse response??!

Maybe. The main problem here is that both your speaker voltage and acquired microphone signal are bandpass signals: you only excite from 20Hz to 20kHz, there is AC coupling and anti aliasing filters. That means below 20Hz and above 20 kHz you have very poor signal to noise ratio and if you try to unwind the excitation you can get a huge amount of noise amplification. This typically requires some carefully manual management and in general the calculated impulse response will have pre-ringing (i.e. isn't as causal as the real physical system).

(It would be nice if this was possible, but it is expected that the changes in the amplitude and phase of the signal transmitted to the speaker by the amp. should be reflected).

This is odd to me. You are using a very high quality (and very expensive) measurement amplifier. This should be flat as a pan cake and the smallest source of error in your system. I suspect that the phase difference you see, is really just a small frequency independent delay of class D modulator in the amp. Interestingly enough B&K doesn't spec the phase response or latency of the amp, which given the price of that thing is almost criminal negligence :-)

Q2) If it is not feasible, Is there a good way to get IR using the measured input voltage (From power amp.) and response(pressure)?

I personally prefer to use an excitation that has a well behaved inverse across the entire spectrum (from DC to Nyquist) and keep the effects of amp, A/D and D/A as part of the system. They are hard to unwind and if you use half way decent gear (as you) the impact on the measurement is minimal

Q3) In order to obtain the IR of the room, the Input is set to Voltage, but in my opinion,the Input should be the volume acceleration of the sound source or a physical quantity corresponding to it. Is there any reason why it is OKAY to calculate IR like this?

The things that you are measuring are the input voltage to the speaker and the output of the microphone which are indeed a voltages. What acoustic quantity that corresponds to, depends on the microphone & speaker. For the microphone it's either pressure or particle/volume velocity (not acceleration). As long as you are reasonably far away from a reflecting boundary these are proportional and related through the free field impedance of air.

The speaker turns the input voltage into a very complicated 3-dimensional pressure field. Trying to define a single pressure reference signal is a tricky. For direct radiators you can use "anechoic at 1m" but for the type of speaker that you are using that would be hard to justify (in my opinion), so voltage seems the best choice. At least it's well defined and reproducible.

You can certainly calibrate the entire setup, if you want to.

Q4) Are there any other considerations other than those mentioned above to get an accurate IR?

Measuring room impulse response accurately is VERY difficult. Things that need to be carefully managed and assessed are

1. Signal to noise ratio as a function of frequency. Most rooms are very noisy especially at low frequencies. There is HVAC, building vibrations, traffic noise, squeaky chairs, people talking, etc. All these needs to be monitored. Your measurement is only going to be "good" over a certain frequency range and you need to determine what the range is, so you can remove the other crap.
2. Non-linear distortions of the loudspeakers. All electromagnetic loudspeakers are somewhat non-linear and the non linearity increases with level. Finding the best excitation level is hard. Too low gives you poor SNR and too high gives a lot of THD.
3. Placement and time variance. You need to pick good spots and make sure nothing moves during the measurement.

The devious part is that none of those errors can be detected by "visual inspection". The measurement looks like a perfectly good impulse response even if it's full of actual measurement errors. So ideally you wrap a set of diagnostics around the whole process that quantifies each individual error mechanism and makes a "good/bad" call based on the requirements of your specific application. What errors can you tolerate and to what amount?

In the end you need to verify your whole setup: how can you do that? How do you know what you measured is actually "correct" or at least "good enough"?

Fortunately if all you want in the end is reverb time, this shouldn't be too hard. I strongly recommend using Schroeder integration, which is rather forgiving in terms of measurement errors.

Update on noise amplification

Your measured signal, $$M(\omega)$$ always contains some amount of noise., i.e.

$$M(\omega) = Y(\omega)+N(\omega) = H(\omega)X(\omega)+N(\omega)$$

where $$H$$ is the transfer function, $$X$$ the input signal and $$N$$ the noise spectrum (acoustic noise, line hum, etc) . You can estimate the transfer function by dividing the FFTs:

$$\hat{H}(\omega) = \frac{Y(\omega)+N(\omega)}{X(\omega)} = \frac{H(\omega)X(\omega)+N(\omega)}{X(\omega)} = H(\omega) + \frac{N(\omega)}{X(\omega)}$$

So if you have no energy at $$10Hz$$ in your excitation signal but a fair amount of noise at $$10Hz$$ you'll end up with a lot of $$10Hz$$ in your measured impulse response. Dividing something by a small number makes it very big.

• Thank you so much for taking your valuable time to provide a very detailed reply. It will be of great help to me. I have two additional questions. First, could you please explain a little more about that part? "--- if you try to unwind the excitation you can get a huge amount of noise amplification." Second, I can measure the frequency transfer function (FRF) between input voltage (v, from amp) and sound pressure (p, mic.) using decent gear (i.e. FRF(f)=p(f)/v(f), f=frequency). If i got impulse response from inverse FFT of FRF, is it equivalent to IR using ESS?? Nov 2, 2022 at 2:20
• I don't know what ESS means. I'll add a note around the Noise amplification Nov 2, 2022 at 11:05
• Sorry for not writing clearly. ESS is an Exponential sine sweep, and as I wrote in the text, I first tried to obtain the impulse response (IR) using the ESS and devolution or the inverse filter of the signal in the time domain. I would like to inquire about the equivalence of IR obtained by this method and the inverse FFT of the frequency response. Nov 4, 2022 at 2:21
• There are various ways to measure the impulse response. In a perfect environment they are all equivalent and give the same result. They do behave differently in the non-prefect real word where you have noise, non-linear distortions, time variances etc. The best choice depends on the properties of your environment and the requirements of your applications. If everything is reasonable "clean" both methods should give you very similar results, but that depends a lot on the details. Nov 4, 2022 at 17:11
• Thank you very much for your valuable reply. Nov 6, 2022 at 23:03

Q1) Is it possible to use generated signal that passes before the power amplifier to obtain impulse response??! (It would be nice if this was possible, but it is expected that the changes in the amplitude and phase of the signal transmitted to the speaker by the amp. should be reflected).

Yes. It seems that you can get the signal before and after the amplifier. With these two signals, you can measure the impulse response of the amplifier using the exact same method, and calculate a inverse filter of the amplifier system. Then measure the impulse response of the whole system (amplifier, loudspeaker, room, microphone) and apply the invers filtering.

• Thank you for taking your valuable time to reply. Amp can also be seen as a part of the overall measurement system. Is there any reason to calculate the impulse response of the Amp? Nov 2, 2022 at 2:02