# Impulse response from frequency response

## Main Question or Discussion Point

Hi to everybody,

I could really use some help in order to understand how to obtain an impulse response from a frequency response.

I am dealing with acoustics, but my knowledge on the particular are basic.

I am trying to compare a theory for the scattering of sound from an object with measurements in an anechoic room. The theory gives me a formula of the sound pressure scattered from an object as a function of frequency. So I am making a simulation of this and I end up with complex pressure data and the corresponding frequencies. So I assume that is the frequency response of the system. If I am not mistaken, taking the inverse Fourier transform of those data would give me the Impulse Response of the system. Please correct me if I am wrong.

Then I am trying to compare these results with measurements in an anechoic chamber. I am using an MLS signal for excitation coming from a loudspeaker and I am recording with a microphone the pressure in front of the object. Now here I am getting confused. Is the FFT of the recorded signal the frequency response of the system? And how can I convert this into an Impulse Response? The FFT of the recorded signal does not look a lot like what I expected and taking the inverse FFT of the frequency response just gives me back the recorded signal. It does not look at all like an Impulse Response.

Could you please enlighten me, on what I am doing wrong and how I can correct it?

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AlephZero
Homework Helper
The impulse response is the inverse transform of the transfer function, not the output from the system.

In other words you need to divide the FFT of the measured output by the FFT of the input signal, and then take the IFT to get the impulse response.

Any textbook on control theory or modal testing should have the details of the math.

I took a recording of an MLS signal coming from a loudspeaker in an anechoic chamber using a microphone. Then I took a second recording by placing another object inside the anechoic chamber. Holding the mic and the loudspeaker in the same position.

What I did was to divide the FFT of the second recording with the FFT of the first recording. I assumed then that the outcome of this operation is the Frequency response of the object I placed in the chamber. I then tried IFFT on the latter frequency response. Do you see reason in this?

thanks again for the input

AlephZero
Homework Helper
Hmm ... you don't know the relative phases between your two measurements, so I don't thnk you can do much with that data except compare the amplitudes of the two frequency response curves.

To get the impulse response, I think you want to record the actual MLS input signal and the acoustic output it creates, so you can match them up exactly in the time domain before you take a finite length sample and do the FFTs. The test with the chamber "empty" will give you the response of your sound transducer (which won't be perfectly "flat", of course), and the second test will add the effects of scattering and sound absorption.

AlephZero,

thanks for the explanation. I think I understand you better now.
So, how do you think is possible to record the actual MLS?
By placing the mic very close to the loudspeaker for example? The MLS signal was generated from some kind of software, I did not create the signal.

AlephZero