# Impulse response from frequency response

• biscuits
In summary, the individual is seeking assistance in understanding how to obtain an impulse response from a frequency response in the context of acoustics. They are comparing a theory for sound scattering with measurements in an anechoic chamber and have questions about converting the FFT of the recorded signal into an impulse response. They are advised to take the inverse transform of the transfer function and to consult a textbook for more details. They also discuss recording an MLS signal and using it to compare with the frequency response of an object placed in the chamber. They are advised to record the actual MLS input signal and acoustic output in order to get accurate results.
biscuits
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?

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

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.

biscuits said:
So, how do you think is possible to record the actual MLS?
Just record the electrical signal that drives the loudspeaker.

## What is impulse response and frequency response?

Impulse response is the output of a system when a short impulse signal is applied as input. Frequency response is the measure of how a system responds to different frequencies of input signals.

## What is the relationship between impulse response and frequency response?

The frequency response of a system can be obtained by taking the Fourier transform of the impulse response. This means that the frequency response contains information about how the system responds to different frequencies, which can be inferred from the impulse response.

## How do you calculate impulse response from frequency response?

The impulse response can be obtained by taking the inverse Fourier transform of the frequency response. This will give you a time-domain representation of how the system responds to an impulse input.

## Why is impulse response from frequency response important?

Impulse response from frequency response is important because it provides valuable information about the behavior of a system. It can help us understand the stability, linearity, and frequency selectivity of a system, which are important factors in many scientific and engineering applications.

## What are some real-world applications of impulse response from frequency response?

Impulse response from frequency response is used extensively in fields such as signal processing, acoustics, and control systems. It is used to design and analyze filters, equalizers, and other systems that process signals in the frequency domain. It is also used in the design and optimization of audio systems, such as speakers and microphones.

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