# Impulse Response OK ?



## alexformetal (Feb 21, 2010)

Hello,

I am a new user of the REW. My english is not perfect hence sometimes I find the Help files difficult for me to understand... but at the same time REW seems to be so interesting so far !!!

I need help about the Impulse Response graph I recorded. I simply doubt that it's a correct one, because of the lack of response below the graph (between -247ms and 0, also from +245ms). IS IT NORMAL ????? If yes, how can I interprete this result ? This graph has not the same shape as the two on the Help Files (see "Impulse Responses" pages), which are are more "full graphs" , do you see what I mean ?

Here is my Impulse Response graph:








...and this is my Frequency Response graph:









Many thanks for your help !!!

Alexis


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## alexformetal (Feb 21, 2010)

...no one can help ? ...

:dontknow:


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## Wayne A. Pflughaupt (Apr 13, 2006)

Stay tuned - I think John needs to answer this one. :T

Regards,
Wayne


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## JohnM (Apr 11, 2006)

Sorry for the delayed reply. Yes, that impulse response is normal. The noise floor of the measurement is about -65dB, which is good. The region before zero on the impulse response is where distortion products end up, which appear like small copies of the main response. Each harmonic creates its own image, progressively further back in time. For example, at about -450ms you can see a distortion image that is probably the third harmonic.


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## alexformetal (Feb 21, 2010)

Hello John,

Thank you very much for your message. I really try to understand what you were writing, but there is something not very clear to me: I don't understand why distortion occurs before 0 ? If you were telling me that distortion occurs after the impulse (ie "0"), I would say Ok, but -450ms before the impulse time seems for me very strange ! There is something I obviously didn't understand, but I do not know what.... 
Anyone coud help me ? ...so sorry for my bad english... But I really want to understand !

Alexis


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## laser188139 (Sep 19, 2009)

Bonjour Alexis,

J'aimerais bien vous répondre en français, mais ça rendrait difficile à John de me corriger. Donc je vais vous écrire en anglais.

Unfortunately my math studies were more theoretical, and I missed studying the Fourier transform and Discrete Fourier transform in school. But I found one description online that gives a couple of hints. 

First, in describing the Fourier transform itself under "Continuous Signals and the Fourier Transform", he writes:


> The mathematical expression [exp(jωt) - exp(-jωt)]/2j for a sine wave illustrates why negative frequencies are necessary. The positive and negative parts of the spectrum combine to produce a real function at a positive frequency. If the negative frequency was not there, the time function would contain an imaginary part. Negative frequencies are simply a result of the way the mathematical analysis is structured.


Second, if you look in his "Appendix A: Derivation of the Sampling Theorem", you will note that the Fourier series representation includes tn terms, where n runs from -infinity to +infinity. 

What does this have to do with your question? Note the comment, "The frequency response of a filter, or any system, is equal to the Fourier transform of its impulse response." I expect the answer to why distortion harmonics appear in negative time is related to one or both of these observations. Your question has certainly given me something to read. Easiest is just to accept John's statement as true. 

J'espère que ça vous aidera.
Bill


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## JohnM (Apr 11, 2006)

This characteristic of separating the linear and non-linear (harmonic) parts of the response is a distinguishing feature of the logarithmic swept sine method of response measurement. There is a detailed explanation in this paper.


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## laser188139 (Sep 19, 2009)

Thanks, John, for the link to the paper. It was quite interesting. (So much for my guesses.)

Alexis, you will find the discussion of why harmonic distortion components appear at negative time when using logarithmic sweeps on pages 20-21 and 45-47 of the paper. Of course, the entire paper is interesting. 

Amusez-vous bien,
Bill


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## alexformetal (Feb 21, 2010)

Hello Bill and John

SO MUCH I appreciate your precious help and your devotion !
Now I need time to read all the documents.. It's going to be long, but I will enjoy !
Many thanks...and be welcome in France someday...
(Bill, are you french-native ? J'ai l'impression que vous etes français !)

Alexis


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## laser188139 (Sep 19, 2009)

Salut Alexis,

Je ne suis pas français. C'est grâce à l'Alliance française d'Austin et à deux cours suivis à l'Institut de français à Villefranche-sur-mer que j'ai fais quelques progrès. Maintenant je saisis toute l'occasion de l'utiliser. 

Dans quel département habitez-vous ? Je n'ai pas encore choisi quelle région on visitera la prochaine fois, et je cherche toujours des suggestions. Je ne sais pas quand je pourrai retourner en France, mais on peut toujours en rêver. 

Bill


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