How software based impulse response measurements work

[1100xxben]

measure the frequency response of the system and we do not measure the impulse response of the system. The only thing that is truly measured with a software based impulse response measurement system is the time response. From there, we can de-convolve the output time response with the input time response and calculate the impulse response. The impulse response can then be cut down in time to eliminate reflections if desired, and the Fourier transform is performed to calculate the frequency response.

Sorry for the lengthy post. If you have read all the way through this, I hope you have at least learned something from it

[juddwilcox]

Re: How software based impulse response measurements work

Thanks, 1100xxben, I found this very, very insightful. I plan to print this for reference.. To use when I lose the forest for the trees.

[eyekode]

Re: How software based impulse response measurements work

Nice post, this needs to be a sticky

[dlneubec]

Re: How software based impulse response measurements work

Excellent job! Thanks for the effort.

[ani_101]

Re: How software based impulse response measurements work

thanks. this is very helpful as i am just wading through the basics of measurement taking. could you kindly walk us through a few examples? also setup for measurements is also critical as i found out.

[[email protected]]

Re: How software based impulse response measurements work

That was great, thanks.

[fprawn]

Re: How software based impulse response measurements work

I'd understood bits and pieces of this before, but now I feel like I have a much better grasp of the interactions of these concepts. Thank you very much for this.

[JRS]

Re: How software based impulse response measurements work

Thanks, cleared up a question I had recently related to the imaginary coefficients set and phase--if I understand what you said is that this info is necessary to characterize the systems response. For instance an all pass filter would have perfect amplitude response but without the phase data one would be unable to differentiate this system from one that is perfect with respect to both amplitude and phase. I also understand that speakers are minimum phase devices and so this objection may be barking up an hypothetical tree.... I am not sure that this is the case when electrical EQ is applied.

Another question that comes up is to what extent inspection of a FR graph informs exactly how a speaker will sound. Personally, even though I know that waterfalls, phase, group delay can all be derived from the impulse response, I find these helpful where others maintain that they are superflous. Curious as to your take on this,

[isaeagle4031]

Re: How software based impulse response measurements work

Admin please sticky this.

[ernperkins]

Re: How software based impulse response measurements work

Great post! On the topic of zero-padding to increase the apparent lower frequency resolution: Do you know of any speaker measurement programs that implement this feature?

Thanks...

[andy_c]

Re: How software based impulse response measurements work

So, to try and sum this all up... We do not measure the frequency response of the system and we do not measure the impulse response of the system. The only thing that is truly measured with a software based impulse response measurement system is the time response. From there, we can de-convolve the output time response with the input time response and calculate the impulse response. The impulse response can then be cut down in time to eliminate reflections if desired, and the Fourier transform is performed to calculate the frequency response.

There you have it. I noticed the same thing you were concerned about in that other thread, but didn't want to wade into it.

There is a good document available online that gets into detail of the history and current practice of these measurements. It's called "Transfer Function Measurement with Sweeps". It's a PDF file. I originally found this document in the Room EQ Wizard documentation, but I believe that in the current REW documentation, the link has either been removed or is now 404.

Edit: There is also the concern about distortion in the system under test, and how it affects the measurements. The exponential sine sweep method used in REW has the property that when the impulse response is calculated, distortion components appear in the calculated impulse response as "blips" before the true impulse response actually occurs, as if it were a non-causal system. This makes windowing necessary to take these out, but also makes distortion measurement possible. There's an article by Farina called "Advancements in impulse response measurements by sine sweeps" (PDF file) that goes into lots of detail about this.

[JRS]

Re: How software based impulse response measurements work

Thanks I learned quite a bit more about the pros and cons of various methods of measuring/calculating the IR. I am curious as to others experience--I was astonished by the mention and display of S/N figures of 80+ dB. In my neck of the woods on a really quiet day (live near a busy street) I might get high forties when averaging 32 sweeps.

[feyz]

Re: How software based impulse response measurements work

Great post! On the topic of zero-padding to increase the apparent lower frequency resolution: Do you know of any speaker measurement programs that implement this feature?

They all do, pretty much by default, but more as forcing the rest of the measured impulse into zero vs padding with zero. Because with todays computers, the input signal lengths used and the corresponding FFT window sizes give already much longer time than a gate time used in indoor measurements.

But more importantly, the relationship with gating and resolution in frequency response (FR) is not how it is described here. And no offense or nothing personal to the original poster, this incorrect and misleading explanation of relationship of gating to FR resolution has been made for a long time and being repeated for a long time now. I tried to explain the misconception and really what is the relationship throughout the years a few times, but ...

Here goes another attempt of mine:

- FR can be thought of the combined effects of several resonance structures. The sharpness of resonance peak or dip is defined by its Q (Quality) factor . A high Q factor means a sharp peak or dip in FR at that frequency, when the FR is drawn in logarithmic scale. Sharpness is opposite of smoothness.

- In addition to defining the sharpness of a peak or dip of a resonance in FR, a Q factor also determines how many CYCLES (not seconds) it takes for its impulse response to (almost) die out.

- From above, if there is a resonance with Q = 10 at 100Hz and a resonance with same Q = 10 at 1000Hz, the former one's impulse response will (practically) die out at 10 * 1/100 = 0.1 seconds, and later one's impulse response will die out at 10 * 1/1000 = 0.01 seconds.

- Because same Q sharpness in FR is same for all frequencies if logarithmic frequency scale is used, in linear frequency scale a low frequency resonance has higher sharpness with a higher frequency resonance that has the same Q.

- All sound related FR's are drawn on logarithmic frequency scale, because our hearing is logarithmic on frequency.

- Now if an impulse response is gated at say 1 second, this means FR of this cannot contain a resonance mechanism that have Q such that Q times one cycle of that frequency is greater than 1 second. In simpler form:

Q x 1/f < 1 (gate time) for any resonance that makes up the final FR.

- From above it means that, say again using 1 second gating, a resonance at 100Hz can have at most a Q of 100, but a resonance at 1000Hz can have at most a Q of 1000, and a resonance at 10KHz can have at most a Q of 10,000. In other words, with this gate it allows a resonance at 10Khz to have a sharpness of 100 times of a resonance at 100Hz on the FR in log frequency scale.

- What gating really does in FR is this restriction on Q of any resonance. This restriction on Q of any possible resonance found in the FR is basically a smoothing operation, putting a limit on sharpness, which is loss of resolution, done on the real FR that would have been without the gating used.

- BUT, note that this smoothing operation unlike 1/octave smoothing operations, is made on linear frequency scale, not on log frequency scale. 1/octave smoothing operations being on log frequency scale, smooth out equally on low and high frequency regions when FR is drawn in log scale. Gating resulting smoothing operation smooths more on lower frequency vs higher frequency when the frequency response is drawn on log scale. This is all because the Q is cycle based on impulse response, not time based, as explained above.

- Note up to here there was no mention of sampling frequency or length of FFT window etc, and such the smoothing effect (loss of resolution) of gating is independent of those.

- Note also that, this all means there is no clear cut section such as 1/gate time frequency in the FR that makes below it completely invalid and above it valid. There just is no such border! This is just plain misconception. What is there is, the lower the frequency, the more it is smoothed and the more it is likely to be not accurate, and the higher the frequency the less it is smoothed and the more likely it is accurate.

- Above assumes that having a resonance with certain Q value at any frequency value is assumed to be equally likely throughout the whole frequency region, which I think is a valid assumption.

- So in summary, if a gate of 0.01 second is used, this doesn't make in FR anything below 100Hz invalid and above valid. It means the FR has been smoothed progressively less as frequency increases. And it also means at a certain frequency, the sharpness of the curve can be at most like a resonance at same frequency that has a Q equal to frequency times 0.01.

The above can be explained also by time domain being dual of frequency domain and gating is dual of low pass filtering, but most people lose me when I mention "low pass filtering of the FR"

[Jeff B.]

Re: How software based impulse response measurements work

Ben and Feyz - thank you for excellent contributions!

My explanation on impulse response in an earlier thread was simplified just to distinguish it from, and show its relationship to, the frequency response. These detailed explanations are excellent. It has been my understanding that gating creates more of a gradual transition in measurement accuracy, but Feyz' explanation is very clear and lucid. Much appreciated from both you guys.

[eyekode]

Re: How software based impulse response measurements work

feyz, thanks for the detailed explanation. It provides some light on an issue I had with gating in holm impulse. I was wondering if combining a higher gated result _of the same measurement_ with a lower gated result could provide a way to avoid reflections in the high frequency while using accurate low frequency results.

I still think there could be some benefit for using this technique for crossover design but there is no free lunch! After your explanation it could be seen as a smoothing operation which makes more sense then increased accuracy.