I've found that I set all my 8455 levels to 0 and have a shot at adjusting the gains by ear.
This has netted them within '2dB' of each other. I have found it strange that eclipse saw fit to use 'dB' as in increment for something that has many outside things acting on it, ie gain, speaker desn, enclosure, listneting distance, etc etc,

Further to this, as my trial period of WinMLS ran out I was using ARTA last night to double check my impulse response and I ended up with some strange settings.

Previously I had :-

LT - 1.1ms RT - 2.3ms
LM - 0.0ms RM - 1.0ms
Sub - 1.0ms (out of phase)

All in phase, bar the sub which was reversed. Set up with WinMLS impulse and using LM as my reference 0.0ms. It's the furthurest driver physically.

Double checking and last night using ARTA I tested with the Sub in phase and ended up requiring about 4ms delay on the front stage relative the sub. It does sound nicer and the sub does blend slightly better with the stage, but I'm a bit confused as to why I could possibly need 4ms on the stage over my last testing. My only thought is that previously I had set from the wrong initial wave in the impulse response on the sub. I do remember it was tricky to site the correct peak in WinMLS, but it appears to be easier on ARTA.

I don't have any screen shots, but I also noticed an initial 'blip' and then it would move over flat until the peak and trough shape I'd be expecting. I used the second section to determine the phase and Impulse delay on each driver.
I ended up with from memory :-

LT - 5.1ms RT - 6.3ms
LM - 4.1ms RM - 5.1ms
Sub - 0.0ms (in phase)

Another thing I found was that I was able to get a nicer response curve with a lot less PEQ bands with extra careful selection and an overall look at the curve, rather then concerntrating on specific peaks and dips individually.

on the subject of sub polarity and delay - sometimes if you try to go the wrong way, you are using the polarity to correct a time issue, or vice versa - it's better when you get it right, as the phase is correct for a wider range of frequencies.

I'm not sure why I needed 4ms delay to bring it back in line when in phase though Pulse-R.

The mathematics behind it suggest around 1ms delay which is what I had previously, when I get a chance I'll dom some more investigation. I prefer to have everything in electronic and acoustic phase before setting TA.

Following up on this a bit more, after getting a USB Mobile Pre powered preamp I did some more tuning recently and seem to be getting much more useable results.

I'm using ARTA software now, the demo version, IE I can't save, which kind of sucks, but I can't complain with it being free

I have a handful of new cables to make up in order to be able to neatly connect it, but it's much simpler using the USB preamp, in that I only need the laptop, mic, mic cable and interface cable to the HU and I'm off and running with a mobile RTA.

I have also noticed much better linearity and I can set the levels etc, and they move according to the estimated levels I'd expect.

I'm still finding I require 4.1ms delay on the front stage when compared to the sub. Again I haven't got my head around exactly why, but for some reason, the 4.1ms delay correlates to around 571mm pathlength difference between the sub and LH mid. The PLD isn't this far in reality, so I'm a little lost as to why the impulse response is showing this difference.

ALL speakers are in phase. I see no reason to have any driver out of phase when you have TA to fix the PLD's.

I have noticed that with ARTA and the Mobile PRE I can set the EQ more effectively, and when set to 'exp' on the FR response window can instantly see the changes be adjusting the EQ. I have found it productive to move the microphone between the LH and RH ear locations and up and down also, do watch the varying reponse due to microphone location.

Being an Omnidirectional mic, the ECM8000 doesn't change it's FR too drastically through angular movement and direction, so this makes it effective when waving the mic around by hand to get a resonable indication of FR.

I have since readjusted to reasonably flat(ish), starting a little higher in level on the bass, then tapering slightly down as the freq increases.

I also tried removing some midbass and bringing the midrange up slightly, instead of just adding to the midrange to bring it to the midbass level, but found i prefer the add and cut, rather then cut. I found that when set flat(ish) by cutting the midbass to the midrange, and then adjusting the level of the mid's up to keep this in line with the sub and tweeters, the sound was very 'flat' and lifeless. When I added to the midrange and slightly cut the midbass, the overall sound was much more airy and open and had a lot more 'life' to it when compared to the cut only. Interesting overall response curves are very similar with both.

Sub freq's travel slower, thats all I've got. I use 3.1ms of delay from sub to front stage, if thats any consolidation.

Luke

I thought sound travelled at the speed of sound...?

Don't know myself but I've seen people mention it before, but I would not be surprised if it was all rubbish.

if the sub is behind you, then the wave will be opposite compared to the phase from the midbass - so the sub should be 'out of phase' to the midbass.

also, group delay in the sub will require longer delay from the midbass to match it up.

what bothers me is phase and group delay, need to get that right before you even start on the TA.

the frequency of the wave, does not determine its speed - under the same atmospheric conditions, a 30Hz wave and a 30kHz wave will travel at exactly the same speed

the reason u delay the midbass, relative to the sub, is because of the difference in distance for each speaker to the listener

Yes I'm quite aware of the distance reasons, it's just you tend to see people recommend in dash/A pillar installs to try and get the tweeter further away then the mid next to it, and one reason I'd seen given is due to the speed of the relative freq's, much like in a high end Home Audio Tower design where the tweeter will tend to be mounted further back then the mid, and one reason you commonly see given for this is Time alignment of the drivers.

I did do some research into this last night, and yes the common answer is NO there is no difference in spped relative to freq's but a bit more reading revealed yes there can be depending on the Gas medium the sound is traveling through there can be a difference, see this quote

"The medium in which a sound wave is travelling does not always respond adiabatically, and as a result the speed of sound can vary with frequency".

The thing is though, Air which we breath is pretty damn close to being an ideal gas and behaves pretty close to adiabatically (I'll admit I have no idea what that word means LOL) but it does not behave perfectly adiabatically so there is a very very minsicule difference in speed vs freq but it's such a small difference that it's not considered relevant in equations relating speed of sound and small enough that a blanket statement like "the frequency of the wave, does not determine its speed" is pretty much considered true. The question here is, is this non adiabaticall behaviour large enough to cause say a half a millisecond difference over a meter or two, when talking about the freq's we are here.

I have no idea since I don't have the patience to sit here and do the maths, nor did I find any ratio's or equations in which to figure it out.

Luke

adiabatic = occurring without gain or loss of heat (opposed to diabatic): an adiabatic process

I think you'll find that moving the tweeter behind the mid or midbass is an attempt to mechanically line up the voice coils of the two drivers, rather than for any difference in sound speed at different frequencies. ; )

x2 matt....
luke352> yes its about time-aligning the drivers, but not in the sense that the freqs are travelling at different speeds, more that u are aligning the source of the sound from each driver

and u are right luke, when a sound wave travels though certain media, its speed can be dependent on the frequency, BUT in air, the differences between all the minuscule variations in density and humidity would have no noticeable (audible) effect on the speed of the wave

Thanks for the responses guys. I have been realyl tied with work of late so haven't had a chance to sit down and spend some time with the reasoning behind it.

I'm happy that other people are using fairly high amounts of TA on the front stage relative to the sub, I was jsut questioning the results.

On the screen the impulse response's were in phase and within 0.05ms of eachother when I set the TA using the same settings for each driver. I did find the results IE impulse delay varied with differing periods and frequencies from the generator, this didn't concern me as I'm only using it as a relative delay, not an absolute.

I found it interesting that when I did some bench testing with the mic etc, is was roughly 38-40mm of movement for each shown 0.1ms delay on the impulse response, when the predicted should be 34mm movement for each 0.1ms of delay.

I must admit, that I think it would take me 10 mins to set-up the TA accurately in a vehicle using the rig with the result being better than what took me hours upon hours or tuning by ear (after base setting from calculated distances) and mono signals etc.

Cool makes sense!



That was what I was trying to get at, I didn't realy look into it far enough to really see if the minor variations would be enough to cause a difference large enough to require a .2 of a millisecond here or there to make allowances for them. I'd actually like to see the maths that show what kind of difference there is in arrival time between say a 20hz wave and a 20khz wave, over the distance of a metre in normal air. All I found is it's small enough to not be concerned about, but the answers I found were not in relation to acoustics, so are they talking about .1 millisecond or are we talking about .1 of a nanosecond? I'm not about to loose sleep over it, but it would be interesting to know.

Manage to annoy myself even more tonight with some tuning. I am placing too much emphasis on trying to get the response fairly flat and am finding that I don't like the sound when set to reasonably flat.

When comparing the sound of PEQ 1 final and PEQ 3, I much prefer the slight increase in the bass region carrying into the midbass. The flatter of the 2, PEQ 1 final sounds a bit lifeless and loses all the nice tight impact from teh midbass region.

I've come to a reasonable compromise with response of the higher octaves by taking 6-9 samples and averaging them. I actually pan the microphone through roughly 6 or 9 positions across an imaginary line between the two ear locations.

Click to view attachment PEQ 1 Final
Click to view attachment PEQ 3

dude, why are you killing yourself to get a flat response when, by your own admission, you don't like the sound of a flat response?

just use the RTA to ferret out any serious flaws in your system, then let your ears do the rest. ja?

I'm becoming more convinced that a relatively flat RTA 'can' sound good, the challenge I'm experiencing is finding the appropriate way to tune the system in order to achieve it.

I have tuned by cutting freq only, and adding only, and boost and cutting and even though they finish fairly closely to the same response they actually sound clearly different to listen to.

Although as I said I didn't like the flatter response of the above I think the challenge will be to have a smooth 'flatish' curve that I like the sound of. Of course this really does go right out the window once the vehicle is started, I found a lot of engine/exhaust noise etc sub 100hz when I did a measurement of this.

I'm also convinced that with the CBRTA it will be possible to get a system a long way towards 'good' sound within a very short space of time, experience with the above is helping me get an idea of a good starting point and I think with a couple of hours on the CBRTA I could get a system a reasonable way to sounding 80-85% of it's ability.

Frustration is all part of the fun, and 'un'/fortunately my car isn't quiet to drive, so I can live with a system that isn't greatin between tuning sessions

keep it up then - we're all learning from your experiments

dont forget that PEQ's act as a filter, so when you apply a boost/cut you are also changing the response in the time domain as well. unless you are using something like the DEQX of course.

a flat frequnecy response must sound the best, its how we achieve that flat frequnecy response that is causing the issues, not the flat frequency response itself.

keep up the good work, but i think its time that you start looking @ the time domain response. the easiest way to do this is to create waterfall plots. experiment with these plots up to around 250Hz. using a PEQ is the best way to deal with any long decay times from any particular frequnecy.

i say this because you are saying that the PEQ loses the 'nice tight impact' from your midbass. this sounds like you have increased the decay time of your midbass.

EQ works best in the sub 250Hz region. above that, it doesn't tend to work to well because of the variations in frequency from one spot to another. i find that if i EQ, i might improve the FR in one spot, but make the FR much worse in a spot 1 inch over.

Hence, i tend to only EQ frequnecies sub 250Hz AND i also use EQ to alter my drivers response, but not so much with the cabin response.

Cheers Scorpion,

I did do a phase and magnitude response and noticed the saw tooth pattern in the phase repeated over and over. I'll try and run some CSD plots tonight and see how they pan out.

I am using EQ through the entire Freq range, reasonably intensively in the 300-900 region of the midbass/range. I have a natural peak on response when running no EQ from about 80-250hz. I can get this to blend nicely with the sub, but I find that the 250-900 ish region is down in level and needs to be brought up or the increase in midbass needs to be cut to bring it back in line level-wise.

I have noticed a drop in my sub's response for some reason. When I first did measurements a while back I was getting good response will into the 300hz region when run uncrossed. Now for some reason I am getting roll-off around 70hz. I'm not sure why, but will be double checking the install to see if the baffle hasn't worked itself loose or something, nothing else in the system has changed since the initial testing.

I do have a set of midranges that will comfortably play from 250-6/8k, but don't feel like complicating the system with a 3-way set-up just yet. I feel I should be able to get the 8's and tweeters to play fairly smoothly, but this might require a reinstall.

If one frequency was to exist at a different speed to another, given that you cannot fix the wavelength (uncontrolled variable), you'll need to change the temperature that each frequency is transmitted in, to ensure they travel at different speeds. In car audio, this is simply not possible, and therefore you cannot effectively change the speed of individual frequencies without utilising a medium.

For a one degree change in temperature, you will get ~0.004954 ms change per metre travelled for the speed of sound. In order to get an audible change (say, 0.1ms per metre) you will need to change the temperature by 21 degrees.

Therefore, to change the speed of sound of a low frequency to make it audibly different to a higher frequency, the difference in temperature would need to be 21 degrees between the subwoofer and the midbass. Seriously, not gonna happen in a car.

BMWTurbo: Have you noticed with your tuning the audible difference between peaks and nulls? I've found that whilst attempting to flatten a curve (which is a good idea, but the tools we use to do it are quite poor) the nulls can exist far larger without being detected then the peaks can.

I do like Scorps suggestion too. I've known that time response and frequency response are related through the Laplace transform (and its inverse), but I've been trying (hopelessly) to find a good phase measurement to allow me to modify the frequency without impacting on the phase response. Unfortunately, my EQ isnt phase perfect, so I think I'll start looking towards the time domain.

~thematt~ I am using smoothing and averaging otherwise I'd be forever chasing my tail. I try and limit the smoothing to 1/6th and sometimes 1/3rd octave however to get an idea of what is happening. I have been using around 6-9 times sampling for hte averaging and moving it around the general area of where the head of the listener would be. When in Spectrum mode you can clearly see the response float up and down in the 1-2k+ region as you move the mic around, below this it's little less pronounced and sub300hz you hardly see any variance.

I have found that nulls can go unnoticed response wise, much easier then peaks. The peaks seem to effect the overall response and be much more descernable then a null, I guess due to the fact that you are 'hearing' excessive levels rather then 'missing' out on some misucal information.

I realise that I'm a LONG way off getting the most from the rig I have at hand and I'm appreciative of everyones responses in here, I'm more using this thread as a record of my experiences rather then trying to 'show' anyone how to use a CBRTA. I must admit I'll have to do some more research in order to get my head around the 'time domain' and CSD's etc

you cant change amplitude without altering the phase (unless you use something such as a DEQX), but thats not wat we want really. the majority of the time, the real issues we want to deal with are resonances/standing waves, each of which act as a filter, exactly like our PEQ's do. so we use an EQ to deal with any resonances/standing waves.

thats why using lots of EQ to tune a perfectly flat response is a bad idea, because your improve the amplitude at the expense of the time domain. you want to use your EQ to improve both amplitude and time domain, hence, why we can use it on resonances and to correct inherent faults of the driver.



this is why i dont EQ much in the 250Hz+ region if i can help it. if i make a measurement (be it with mics or ears) in one spot, then EQ, i might be making big adjustments to the FR an inch over. its just so sensitive to EQ'ing that ur more likely to make a negative impact than a positive one.

the only reason why i might use EQ above 300Hz is because i've identified that the variation in response is due to a particular general aspect of the environment. a particular general aspect would be something like cabin gain because it is something that occurs no matter where i sit in the car. i can identify a particular general aspect (my own terminology btw) by plotting the drivers FR (measured 'anechocially') and overlaying that on the FR at the listening position. then i use a PEQ with a very wide band to correct an issue. i never use a narrow band on anything greater than 300Hz.



it could be because peaks tend to be resonances and therefore affect the time domain as well. the ear is very very well trained in hearing resonances. its wat we listen for in a musical instrument.



time domain is a very general term. for instance, the "time domain" anomaly in a resonance is the increase in its decay time, ie how long it takes for a frequency to die away to nothing (i've explained that badly). other time domain issues are absolute phase. its a very broad term. im still learning a bunch every day about time domain stuff. so we are both in the same boat

Well thanks to Vodaphone mobile broadband and it's rubbish coverage lost my last reply.

Anyways here goes... I started from scratch again tonight, blank canvas, reset the gains, and tuned from zero EQ, TA, levels to double check my previous results.

I started by settings gain on the amps, then did a quick level match. Once level matched roughly, I set up the microphone in the centre of the listeners ears and redid all the TA settings by using 'Impulse Response' and the variance between each driver. Again the sub was the least delayed being the reference 0.0ms delay. I got very similar reaults to previously, so this set my mind at ease re TA.

Next was to double check the levels and start on the EQing. Again I aimed for 'flat' and then reset soime of the bands and levels to what sounded best to my ears, rather then relying solely on the FR results. I found the when roughly' flat' I noticed a lack of lowend/misbass, so brought these back up. I also took more averages, 20 generally accross the area occupied by the listener and found that I needed minimal EQ on the tweeters.

I ended up with similar results to last time with respect to EQ settings, again which was interesting as I tried to take a different approach to tuning this time.

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is there a user manual or some technical reading that comes with the software that your using?

im not sure its calculating the waterfall plot the same way that i am used to.

http://www.fesb.hr/~mateljan/arta/download...user-manual.pdf

Is the user manual for the software. It's a free software, unless you wish to save from it in whcih case you need to buy the licence. I have just been using screen shots of each different response curve etc, Where if you can save the data you should be able to generate it all from a saved file.

http://www.fesb.hr/~mateljan/arta/download.htm is the ARTA download page link.

I'll be allocating some time to get my head around the manual fairly soon, it seems very powerful and using the RTA and Impulse are a simplistic approach.

Waterfall looks a bit off IMO.

Whats your window set to? You need to use a different window for bass as opposed to midrange and again another for highs.

~thematt~ I honestly don't really know, I just ran the tests with whatever settings were there.

After flicking through the ARTA manual as linked above, they all seem a bit off, I might have to redo the test's by adjusting in the Impulse Window like it suggests. This will probably change the CSD and hopefully give something like to be expected. Mine don't show any sign of the typical shape.

Is it common practice to test each driver pair in the system, each single driver, or the system as a whole? In the ARTA manual they talk about small bookshelves, which I would assume is a 2-way system, tested as a complete unit.

depends on how it is measured i guess. it looks different to me, but the graphs i usually see always have each frequency start @ 0ms, which to me, means that its not measured directly but calculated rather. those graphs look as though they are measured directly.



the window is very important when using waterfalls, because waterfalls are calculated (usually) not measured directly. see if it was measured directly, then you would have all the early reflection intereference in the first 20-30ms and then you would have reverb influence for the rest. this is what we dont want in a waterfall plot because we are looking for resonances (both driver or environmental resonances).

jump on the REW website and go through the manual there. very informative.

i measure individual drivers response when im looking @ waterfalls and then compare that with the waterfalls @ the listening position. when im doing FR, i grab individual drivers and the drivers as a system (near field) since i always have my mid and tweet placed together (i run 3-ways). i then inspect that graph and see what conclusions i can draw from the speakers crossing over together.

i also use individual drivers response and overlay that on the same graph as the FR @ the listening position.

the important thing im trying to point out is that essentially, the drivers and the environment should be analysed seperatly to determine which issue is a driver issue (so we use EQ to fix) or which issue is an environmental issue (which we fix by trying differernt baffles and different speaker locations).

we have to have the right information first before we can use the right tool to fix the problem

seriously an rta saves you five + minutes of listening, as it might take longer but any fool can spend less than an hour bumping up the eq till stuff sounds bad and find an offensive peak. its not that hard...sounds bad is bad.

dips take longer to find by ear as its whats missing and that can be like, where is waldo ?


A millisa(sp) curve/response could potentially tell you more but only if you do a chopper read and cut your fkn ears off.......


what is wrong with JUST listening to what you hear ????

You are looking for things that are heard not seen....so ditch your eyes and use your ears..*sighs*
<<<is off to LISTEN to some music
if it sounds good and measures bad, your measuring the wrong thing
peace
Cyberpunky

http://www.hometheatershack.com/roomeq/wiz...sponse.html#top

the above is how waterfalls are essentially calculated

and here is how REW creates its plots

http://www.hometheatershack.com/roomeq/wiz...#waterfallgroup

u will probably have to sign in to view those documents

does this help?

Thanks Scorpion, will print off a copy today for reference.

I suspect the window selection will be the key.

i should also add

http://en.wikipedia.org/wiki/Short-time_Fourier_transform

otherwise the above might not make much sense

http://en.wikipedia.org/wiki/Fourier_transform

i linked the mathmatical explanation, but im sure if you googled it u might get a better explanation if ur not mathmatically inclined

Ah! The Fourier Transform (and the inverse)!! I did heaps of that back at Uni, and never really connected the dots until I started looking further into Audio.

Fourier Transform: A clever mathematical method of converting from the time domain (amplitude over time) to the frequency domain (Amplitude over frequency and phase over frequency).

Also demonstrates how amplitude over time is DIRECTLY related to phase and frequency, and vice versa!! (changing one must result in the other being modified).

I have chance tonight to quickly set a smaller window in the Impulse Window and take another Burst Decay graph. This one seems to make a fair bit more sense. It's the complete system as a whole though, not individual drivers.

I'm pretty certain they are both showing reflections in the 1/2khz + region.

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i dont understand the second graph. why is it smoothed and why does it have the jump at 0.98 seconds? how can there be a step dB increase 0.98 seconds after the frequency is played?

for the first graph, can we start with a 0-250Hz range and re-graph it?

im not sure what you mean they are showing reflections? how are you determining that? the waterfall plot is determined from the Fourier transform, so the time aspect (in radians) is determined as a function of amplitude. its not actually measured. so im not sure how you are determining that there are reflections since the mic should be only picking up the direct sound

actually, what is the mid crossed at? could we get a grph of phase and group delay over the entire FR.

I was basing my logic on the following taken from the ARTA manual.

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I could be well off the mark, but I was assuming since I have my tweeters aimed directly facing up at the windscreen I could be recieving a partial direct wave and also the reflected wave from the screen which I'm using as my primary source. It seems to tie in well with the FR also, as the tweeters are crossed at 1250hz 24dB/Octave. Also my previous Burst Decay graph appeaqrs almost exactly like the example in the ARTA manaul above.

I will try and find some time to get the low end (0-250hz) CSD graph over the next few days.

ahh, ok, now i understand what the secnd graph is telling me. thats why you think that is an early reflection.

its very low for your tweet tho, do u have ur tweet crossed @ less than 1k or something? thats a very significant reflection, something like 20dB's and since it is reasonably linear, would suggest that there is no attenuation from your crossover.

i dont use waterfalls above 250Hz because im not interested in tryin to EQ out resonances any higher than that. im not sure whether REW uses multiple burst impulse or not like ARTA appears to. i do believe that the other anomalies are also reflections.

i would still be looking @ group delay and phase between the tweets and mids still. it looks as though that your tweet is crossed at around 2k and that you may be having a group delay/phase type of issue. compare the group delay or phase between your mid and tweet.

i say this because there is no "reflections" less than 1k. when there probably should be if you are recording reflections above 1k

My crossover point from mid to tweeter is 1250 hz both at 24dB/octave, in phase. It's crossed over active at the head unit.

I was going to mention re the dB scale, the mic etc is not calibrated, so I've been using it as relative only not for absolute levels. I think the actual scale would be a lot less then shown on the plots.

I will as mentioned set aside some time to do individual driver response and phase curves. I don't have these atm.

I might also try the tweeters on axis too and see how the CSD and Burst Decay plots come out after this. I could also explore the possibility of angling the tweeters further forward to try and stop any chance of direct waves coming from the dome.

measures good, sounds bad, your measuring the wrong thing...I cant believe you guys are ditching evolution for a computer graph...listen and learn...your ears dont lie

I would say evolution will be developing/including testing and measuring equipment.

'Evolving' would encompass exploring new and perhaps better(?) more accurate(?) and precise(?) ways to get the desired results.

'Ears don't lie' but the processing of what that is 'heard', is the part that varies between each listener.

If a system/process can be developed and specific tests and data used to create a similar result each and every time, this could potentially expidite the tuning process and not require the specific ability to be able to interpret in fine detail of exactly what is being 'heard'.

"Evolution" - The process of change, allowing development across generations.

"Insanity" - Doing the same thing over and over again, and expecting different results.

This is a positive thread, as it introduces and explores new concepts and ideas, and allows others to learn and develop their own understanding.

So did we manage to work out why 0.98 seconds had that bump, but isnt a reflection? Care to share?

And I'm surprised you're getting those responses with such a low Xover....

I did play around a little with the gating and generating Impulse Response graphs ~thematt~

I didn't actually save any screen shots as I was only mucknig around with it, but depending on where the gating was set I could get rid of that step in the foreground.

When I get a chance (sidelining this for the moment to resolve a slight alternator whine) I'll post up some more graphs with differing gate ranges to show what happens.

yer, im not convinced it is a reflection because there appears to be a linear relationship between dB and decay

in the graph posted from the ARTA manual, that reflection shows a non-linear relationship.

i dont know why it is doing that.

perhaps create a waterfall of just the tweet (outside where there are no reflections) and see if we can isolate it.

i found this link in the net
http://bb-measurement.tripod.com/

i agree, but you must measure the reversing phase too, that use to know whether your phase is inphase. the better dip in out of phase measure, the better in inphase measure.

in phase


out of phase (reversing my midrange)