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I am trying to measure the frequency response of different audio canals, e.g. tubes, hollow pipes etc.

My experimental setup looks like this: I generate an audio signal with a loudspeaker (Visaton WS 17 E 4 Ohm, datasheet: Datasheet loudspeaker which then passes through my device under test (e.g. the tube) and is then measured by a microphone (with a flat frequency response).

Unfortunately the output of my loudspeaker when measured directly (without the device under test in between) does not show a somewhat flat frequency response, on the contrary I see something like this. To obtain the graph I apply basic FFT to the output data of the microphone.

Frequency response speaker

The input signals I am using are sine sweeps and white noise. Both results in very similar results. The same applies to the audio amplifier I am using, switching to a different one changed nothing. I therefore do not believe these two to be the issue.

I wonder now what I can do to obtain sensible results after the FFT. Do you have an idea how I can either improve the output of my loudspeaker respectively what causes the peaks and valleys in it? Alternatively, is there a way to kind of "subtract" the frequency response mathematically to obtain clean results?

I am very much looking forward to hearing any suggestions because I have already invested a lot of time and I am running out of ideas.

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  • $\begingroup$ Random observation: the speaker will behave "better" if you place it in a cabinet (i suggest closed box, with sound deading fluff inside, a few liters volume). $\endgroup$
    – ghellquist
    Commented Jul 4, 2023 at 20:38

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On a high level, your setup is:

$$X \rightarrow \fbox{$H$} \xrightarrow{X.H} \fbox{$DUT$} \xrightarrow{X.H.DUT} \fbox{$Mic$} \rightarrow Y_{measured} $$

where $H$ is the loudspeaker response. I'm assuming the $Mic$ response is flat.
You therefore need to compensate your measured response $Y_{measured} = X.H.DUT$ with the inverse of the loudspeaker response: $H^{-1}$

Devil is in the detail, and inverting a transfer function comes with its own set of problems, but your loudspeaker-only measurement looks "flat" enough to at least try that simple approach. Simply multiply your measured response $Y_{measured}$ by $H^{-1}$:

$$X \rightarrow \fbox{$H$} \xrightarrow{X.H} \fbox{$DUT$} \xrightarrow{X.H.DUT} \fbox{$Mic$} \rightarrow Y_{measured} \rightarrow \fbox{$1/H$} \xrightarrow{X.DUT} Y_{compensated} $$ or, in transfer function form: $$Y_{compensated} = X.H.DUT.H^{-1} = X.DUT$$

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  • $\begingroup$ Thanks for your answer. Absolutely, you have summarised what I was trying to explain in a more mathematical way. The microphone does indeed have a fairly flat response, it is small enough to be negligible in comparison to the loudspeaker.To obtain H−1, I have to divide the measured response by the original signal and then aplly an inverse FFT to it, correct? $\endgroup$
    – Scaty
    Commented Jul 4, 2023 at 10:29
  • $\begingroup$ @Scaty no, you have $H$ already (the loudspeaker-only response). Just compute $H^{-1} = 1/H$ then multiply the DUT response by that, effectively compensating for $H$ $\endgroup$
    – Jdip
    Commented Jul 4, 2023 at 10:36
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    $\begingroup$ Of course, as my input signal is supposed to have a flat response, my measurement should already be H. Sometimes when you think about a problem for too long, you don't see the simplest contexts anymore. I will try this now and hopefully it will solve or at least significantly attenuate my problems. $\endgroup$
    – Scaty
    Commented Jul 4, 2023 at 10:51

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