Okay. I think I get you. You obviously know substantially more about this kind of thing than me.
you are correct about all points, except that IIRC the spectrum of the output is equal to the product of the spectrum of the "transfer function" and the spectrum of the input signal if and only if the system is stationary and i think it is not.
IMO fft should be applied to small periods of time to be meaningful, don't you think? ...i'm asking it to you because you seem to have fresh in mind the theory
ps as the lfs suspension model is linear, shouldn't be an impulse the spectrum fo the suspension transfer function?
imho its stationary under the asumption that the wheel doesnt lift from the ground
oh and if im not mistaken the transfer function is the systems spectrum (ie the fourier transform of the systems impulse response)
depends on what you want to do with it
for system identification (of time invariant systems) you want a large number of nodes along the frequency axis therefore youll use a large number of samples
for analysis of instationary proceses however (like used for adaptive prediction in (speech) coders or for utilizing psychoaccustic effects like in mp3 coding) you want shorter sets of samples (during which the process can be considered stationary) to get a better resolution in the time domain (this has to be paid with a loss in spectral resolution though ... basicaly spectral and time-domain resolution are interchangeable and have a joint upper bound much like the minimal uncertainty (to be considered the inverse of resolution) in impulse and position measurements have a joint lower bound (heisenberg))
im not sure what you mean with that question
IMHO to be stationary it would be required to lock the steer at 0° (and thus a straight road), about wheel that lift from ground, i'm not sure if ti could be the reason for non-stationary, but sounds pretty reasonable.
about the definition of "transfer function" you are right, i remembered wrong: the time domain function is the "impulsive response", my mistake
since the question that originated this thread was basically "how to find track bumps frequencies", i think only small time windows can reveal that.
it's like the human speech (which is clearly non-stationary), if you want to know the spectrum of the letter "i" inside the word "stationary" you surely don't calculate the spectrum of the word but you will apply a proper time window that surronds the "i" on the time axis and then calculate the spectrum only on that time window
basically is what i said before too, but i think specral resolution should not be an issue for suspension and track analisys
this is totally different, the spectral estimation is caused by implied limits of mathematical definitions/functions against reality. the minimum uncertainity (the heisenberg principle) is a conseguence of the fact that measuring "something" implies perturbing the system and thus it changes the system itself, so the measured value is actually the measure of the whole system "original system to be measured" + "measuring instrument".
basically i was wondering if someone (except the devs) knows more about the lfs suspension model...
steering angle ... interesting point ... but it doesnt actually change the suspension geometry (or at least not in ways which have a effect on suspension frequencies)
actually stationarity is the wrong word since it is a property of random processes ... for systems the right word would be time variant and a suspension that basically floating in mid air is obviously different from one with gorund contact
matter of fact the suspension is inherently time variant though as it has different damping depending on the direction of travel
hmmm i thought the question was "how to analyse suspension transfer functions
actually this isnt what heisenberg is about its a very common false explaination though
Very impressive :cry:
FFT is more hardcore than I though lol
FFT is more hardcore than I though lol
happy to impress you, but...you could also clarify our "uncertainity": do you want to find track bump frequencies or the suspension transfer function (ie the spectrum), or both?
if you don't stop us by answering that, we can continue for years... :P
i cannot find a better way to explain wat i mean, than the following example (i hope): think of steering enugh to bring suspension near saturation...now if you hit a bump, the suspension saturates/clips an thus you have as output a spectrum with infinite bandwidth caused by non linearity. well this is extreme, but the concept is that you are introducing an "unknown" force/signal that is biasing the system and such bias is time variant, so also the system will be time variant. imo.
yes it is clearly so, the fact is that in the last years (lol sounds like i'm an old mummy
) i work on a totally different field, so i always feel there is something important that i don't remember about this topiclet's hope the topic starter clarify us wat he wanted to know
well my example was the problem that brought to the heisenberg relationship and may seem not clear how the example fit into that, he found the relation because during his studies about quantistic theory he faced the problem of measuring at the same time speed and position of electrons. on the other hand the problem of spectral estimation is given basically by removing any "infinite" value from the formulas given by theory such as integral/series and mostly by approximating algorithms to calculate it, so it's mostrly "numeric" precision...i understand you point of view, but i don't agree and one thing that i think "prooves" it is that error forumulas and relationships about spectrum estimation are expressed in terms of part of integrals you give away or terms of series you truncated and not by the heisenberg formula, another thing: one problem is "measurement", another is "estimation/approximation" the two problems may be considered "dual" perhaps but they are generated from different causes anyway all of this may be considered one of the mathematical/phisical things that have different toughts, i believe none of us will change point of view about that, but surely it isn't a problem
im not entirely sure about this but my gut feeling says yes and no
on the topic of saturation ... yes youre right this sort of comes down to my point that the wheel should always stay in contact with the ground only in the other direction which i forgot to consider as it should never happen if the setup is fit for the track
on the bias point id say no since lfs doesnt simulate progressive springs (yet) therefore the spectrum shouldnt change with biasing
ive just thought of another thing i hadnt considered properly yet which is the time variance induced by the 2-way dampers ... obviously the different damping constants create 2 different transfer functions (tf)
to get rid of this youd either have to
1) use no dampers at all therefore youll get the pure tf of the spring and can then derive the 2 damped tfs from that
2) use the same values for both compression and bump damping and after 2 test runs with your desired values for bump and compression youll have both tfs of the time variant system
3) only analyze blocks of data where the suspension is traveling in one direction ... this will of course lead to poor spectral resolution
i could argue that the spectrum estimation problem is a measurement problem though since as you cant improve spectral resolution by higher sampling frequencies the only way to do so is by longer measurements and therefore by sacrificing temporal resolution
frankly i dont know enough about quantum physics to see if i could actually prove that both problems are the same so lets settle this with calling them dual
point (2) is the only completely correct, but is insufficient because it is a simplified sysem which is rarely used by lfs, to better model we should write down equations, but i surely don't want to do this
i think we can argue for years about that, but for the forum sake we better consider it OT...
well i'm not an expert too, but i had to study enough (too much for my taste
) of it in several courses, but i had to study much about measurement (i'm an electronic engineer) where heisenberg was a key point...but obviously could be that my teachings were biased and so am i.what comes in my mind now is a phrase that one of my professors was used to say:"the art of mathematics is giving same names to different things", well i never agreed with that, but i think it fits to our discussion
so i will follow your suggestion: let's end calling it "dual"
PS i'm still awaiting that the thread starter will answer to our doubt..."suspension" or "bumps"?
I have not finished to study all the last posts yet but to answer to the question: FFT is quite useless for me now. I wanted to use it to help me to setup my suspensions. I thought I would adapt suspension frequency to track frequency but it was wrong since track frequency is not clearly defined, and suspension frequency depends on the car.
However, FFT is useful for something, but I don't know what, it seems that it's not very helpful...
However, FFT is useful for something, but I don't know what, it seems that it's not very helpful...
well my suggestion is always the same: don't apply fft over th whole track, but divide the track into "interesting" segments i.e. each corner, segments with bumps, etc. then examine both time and frequency graphs the reason in doing this apart from possible mathematical reasons, is that you will deal with less information (divide et impera), so it may be easier to find caracteristics/behaviour on segments of track, if so then it will be up to your decision how to find the compromise that satisfies you.
as i said before, i'm not able to interpret the graphs you showed (doing fft over the whole track), so maybe you could at least give a try at doing a segmented analisys, it shouldn't hurt
well the way i see it a suspension with 2 way dampers is switching between 2 systems all the time ... so the obvious way to predict behaviour of the whole system is by first analyzing both systems seperatelly as good as possible
actually i rethought on that and came to the conclusion that dual doesnt mean basicalle the same but rather the same thing but done exactly the other way round ... therefore dual means the opposite of what we were both trying to say with it
what exactly do you mean with adapt ?
It doesn't matter now, I was in the wrong.
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Working with a suspension spectrum analyser
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