Submitted by **MEGA_AEOIU792** t3_10kgr8r
in **headphones**

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**audioen**
t1_j5soc56 wrote

Reply to comment by **No-Tune-9435** in **what information an impulse response graph provides about headphones?** by **MEGA_AEOIU792**

I think you are just wrong, and you do not seem to know what flat frequency response looks like in impulse response graph. It is one sample long singular spike, followed by perfect silence afterwards, forever. You could say that studio monitor speaker systems strive to reproduce just such an impulse, and the closer it is to a very narrow spike, the better the acoustic system. Even this headset looks like it is not that far from perfect impulse apart from some ringing afterwards which suggests it has some resonance peaks and probably highpass filtering because the impulse goes below zero, and that would indicate it cancels some of the sound it produced earlier after a time delay, which is how highpass filters generally work. I don't know, it is really hard to try to read the frequency response off impulse response.

It is completely obvious to me that time delays do not have impact on the magnitude spectrum. They have an effect on the complex spectrum because phase (and group delay) are different and are encoded in the ratio of the imaginary and real parts of the complex number which is usually not shown because phase angle is difficult to relate to anything we actually hear. In that case, group delay would show the added fixed delay just fine, though.

I can only assure you that from mathematical point of view, the impulse response and complex frequency response can be converted to each other without loss. Whether Fourier analysis is good model of human hearing is perhaps a thornier question, as this isn't quite how our ears work, but I think it is still plenty useful as a construct.

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**[deleted]**
t1_j5sqmgp wrote

[removed]

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**SoNic67**
t1_j5tfqxd wrote

Limit the mathematical model only to a couple of terms of the series, and see how "lossless" your transformation is.

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**TaliskerBay22**
t1_j5tvung wrote

I do not understand, your comment can you explain? Only thing I am saying is that the impulse response of the headphone in this graph is known to infinity as the assumption that it will continue to be 0 after the end of the plotted data is certainly a valid one. So we can pad with 0s this graph as much as we want. On the other hand the time 0 in this impulse wrong seems to be arbitrary. If somebody can pass me the data of the graph I can certainly do an FFT and get the Freq response.

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**SoNic67**
t1_j5uqz7w wrote

I am talking about people that say the FFT is equal to impulse response because... math.

FFT implies infinite bandwidth.

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**TaliskerBay22**
t1_j5vuc8d wrote

The maximum frequency of a fast Fourier transform is 1 over the sampling interval or the sampling frequency. As shown in this example https://uk.mathworks.com/help/matlab/ref/fft.html

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**SoNic67**
t1_j5vxaxg wrote

Nope.

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