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12th August 2010, 10:49 PM  #7131 
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You didn't actually read my post Elias, did you, or you simply failed to take in any of the content. Never mind, I'm sure the penny will drop with you one day. If your misconceptions have left any room for new information that doesn't fit your steady state world view and you are curious to know how transfer functions are measured here in the real world, this paper has a good overview of the various methods that requires only very basic knowledge. http://www.anselmgoertz.de/Page10383...wpenglish.PDF

12th August 2010, 11:17 PM  #7132  
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Much appreciated, Mike 

13th August 2010, 02:21 AM  #7133  
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I for myself wouldn't take that for granted  otherwise a Dirac impulse measurement would completely fail to be a valid FR measurements setup  *even in theory* (meaning  to let mere practical problems like bad signal to noise behaviour out of consideration)  which is not the case to all of my knowledge Those discussion about measurement and calculation of steady state plots tells me how difficult it is to create common ground even at long known facts when it comes to very details  good thing for me, as I can see it more relaxed that CMP concept and "FR depending on time we look at" doesn't get accepted in a single day. Michael
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Audio and Loudspeaker Design Guidelines Last edited by mige0; 13th August 2010 at 02:27 AM. 

13th August 2010, 06:31 AM  #7134 
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Mike, whilst it is good to see a sense of humour around here, selectively editing my posts to make it appear as if I said the opposite of what I actually said is misleading for others browsing the thread, as Michael's post demonstrates, and kind of dishonest. To be fair to others you should edit your post.
Michael, the comments quoted were preceded by In my view the basic misconceptions underpinning the above are: which rather changes the meaning. Mike, your earlier engine mapping analogy isn't really applicable to the discussion as engines are not LTI systems. I used to design engine, gearbox and chassis management and data acquisition systems for motorsport applications as it happens, though that was 2 decades ago. One of the most interesting engine types to deal with is twostrokes, as a single misfire has a dramatic effect on scavenging efficiency and hence the crankcase mixture  the early twostroke fuel injection systems tried a simple mapbased approach which was disastrous, as misfires caused havoc. The solution there is to model the crankcase mixture, using crankshaft acceleration as an input to the model. If that doesn't count as offtopic, even in a thread of 7,000+ posts, I don't know what does 
13th August 2010, 08:58 AM  #7135  
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Hi JohnPM,
I already can see youre more of a practical type of a person, but I'm trying to have a theoretical discussion here without that much of the restrictions of the practical world.  Elias Quote:


13th August 2010, 09:04 AM  #7136  
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Hi Michael,
"Dirac impulse measurement" does not actually measure "frequency response" but it measures impulse response in time domain. To get frequency response one needs to process the measurement as it is known. One can measure "frequency response" directly by steady state sinusoid signals, without the need to measure impulse response. Maybe it's the loose usage of terms that's causing the confusion? One have to differentiate between the actual physical measurement and the processing and presentation of the results.  Elias Quote:


13th August 2010, 09:10 AM  #7137 
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Let's consider where the approach has got so far. Most impulse responses in loudspeaker measurements decay below the noise floor of even sensitive instruments in less than a second. If we put an impulse into such a system, record 64k samples at 48kHz (1.365s) we have captured the entire impulse response. Another few ms for an FFT and we have a 64k point frequency response. Does it not strike you as contradictory that in less than 1.5s we have managed to acquire information that your steady state model suggests should take us, assuming we only allow 1s for steady state at each frequency and changing frequency takes no time, more than 18 hours? When the world does not correspond to your models, it is the models that are wrong, not the world. If your position is based on the introductory course notes you posted previously I think I can see where the misunderstanding has arisen, and I'm happy to try (again) to explain it  a mistake one person can make, many people can make  but there is no point if you are not prepared to listen.

13th August 2010, 10:28 AM  #7138 
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Here you go Elias, enjoy.
The Tale of the Transfer Function Let’s revisit the “sinusoidal steady state” course notes and stick with the same notation: lower case for time domain signals, upper case for frequency domain; a system of impulse response h(t), transfer function (Frequency Response) H(omega), driven by an input u(t) and producing an output y(t). h/H are unknown, but we would really like to know H. The notes show that if we use a sinusoid of radian frequency omega as the input then, in the steady state after the transient effects of applying the sinusoid have died away, the output consists of a sinusoid at the same frequency as the input but modified in magnitude and phase according to the value of H at that frequency. If we measure the amplitude and phase of the output relative to the input we have figured out H at one frequency. Hooray! We are on the way to finding H. But there is a problem. There are an infinite number of frequencies. And getting to steady state may take a long time, depending on how long h(t) lasts. Even if h(t) is fairly short, at infinity times a short time it is still going to take us well past teatime to fully characterise H. Elias, for one, isn’t happy. So where does the problem lie? The first place to look is probably the input signal, because a sinusoid has infinite duration – it just never stops. Let’s go to the other extreme, how about if we use an impulse? At zero duration, that is going to be pretty short. Looking more promising already. We know from the notes that Y = U H i.e. FT of output = FT of input times Transfer Function. And we also happen to know that the FT of our impulse has unit magnitude and zero phase at all frequencies, so if u is an impulse then Y = H Now that’s more like it! Since the impulse has zero duration, we only need to capture the output for the duration of the impulse response, h, and take the FT and we’re done. Not only have we found H in a very finite time, we have found it at all frequencies at once. The mathematician in us is very happy indeed, job done and still time to polish off that Reimann Hypothesis proof before tea. The Applied Mathematician in us is not so happy, however. He knows infinite amplitude, zero duration signals are a bit hard to come by in the acoustics lab, and the speakers may not react well to getting infinity up them. The techs are not likely to be too happy if we give them this method for finding H. So if zero duration signals are not so great after all, how about trying something of finite duration? In the time domain the system output is y = u * h where “*” indicates convolution. If h has finite duration, the duration of y will be the duration of u plus the duration of h. So if we capture that much of y, we have all the information the system is ever going to put out when fed u. If we capture that, and use our friend the FT again, we can figure out H from H = Y / U It will take longer than using the impulse, since we need to wait for the additional duration of our input signal u, but we still find the value of H at all frequencies at once and we’ll still get to tea in good time. Now all we need to do is pick a suitable input signal, u, of a suitably short duration. We know that dividing by zero is a nono, so our input signal needs to have a spectrum that is not zero anywhere, but beyond that we can use pretty much whatever we like as far as the Applied Mathematician is concerned. The Engineer in us is not completely happy yet. He knows that our loudspeaker and the amplifier driving it have limits, and our mic preamp has some noise, and it is not unknown for the techs to start chatting while the measurements are being made. Whatever signal we use had better not overstress the amps and speakers and have enough energy in it that the measurement noise becomes negligible. The Applied Mathematician has given us some candidates though, including a few noise sequences and sweeps, linear and logarithmic. The engineer isn’t keen on the noise sequences – they will have a high crest factor of 10dB or more (ratio of peak to average) which means the energy in the signal is going to be limited by accommodating the peaks. The sweeps are more promising, since their crest factor is only 3dB. The linear sweep has the same energy in each frequency band, but the engineer knows from the RTA that there’s more noise at low frequencies than high. The log sweep, from low frequency to high, puts more of its energy at the low end, so for a given input signal duration it should give us the best measurement result. So that settles it. The engineer picks the log sweep, measures the loudspeaker and knocks off for the day, and everyone lives happily ever after. Except Elias, who still isn’t happy. Last edited by JohnPM; 13th August 2010 at 10:38 AM. 
13th August 2010, 01:53 PM  #7139  
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John  I don't think I got anything wrong  even so I did not emphasis on your points.
What I emphasized on was to correct Mikes summarizing in laymen terms  cause I thought it does not hold *as stated*. Elias  I think I got your point to clearly distinguish in a "theoretical discussion here without that much of the restrictions of the practical world"  that "measuring" a FR by Dirac impulse actually is "calculating" the FR. But again  in laymen terms I corrected what I thought does not hold *as stated*.  Quote:
I would not doubt that FR can be measured or better "captured" by short signals (for usual LTI systems)  as said for the Dirac impulse "measurement", but you didn't drop a single word about CMP systems for now. What do *you* think is "the steady state" of a CMP system  considering as outlined  there are *several steady states* in a CMP system  and given, we define "steady state" as having no SPL change over some delta time. IMO, CMP simply does not fit *that well* into IR/FR world  at least not "in a single one". Impulse response IMO is not compromised  but FR actually is  which shades some light on the swiss knife tool of FT and its usability and limitations in audio. Michael
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Audio and Loudspeaker Design Guidelines Last edited by mige0; 13th August 2010 at 02:08 PM. 

13th August 2010, 03:28 PM  #7140  
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