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17th November 2012, 10:57 AM  #1 
diyAudio Member
Join Date: Apr 2011

Time domain distortion
I've been using the Dayton Omnimic for comparing raw drivers for some time now but time domain tests have always been pretty tough to understand for me. I'm going to start with what I think I understand and end with what I clearly don't quite get yet.
If we start by identifying dimensions of interest: 1.amplitude 2.frequency 3.time Distortion can therefore arise when the amplitude by frequency relationship is violated. This we classify as: IMD and MTD for complex signals and HD for single tone systems. The Omnimic can do HD up to 5th order. Holding the frequency fixed, amplitude by time distortion can be defined as: Delay Decay nonideal reverb? The combination of all three dimensions can depict the true signal, and the reproduced signal in its entirety. Any distortion produced is along one, two, but in reality all three dimensions. An example: true signal is two tone 50hz, and 70hz of 90db amplitude each that start at time t and end at time t+s. distorted signal takes the form of the speaker producing 100hz as well 140hz tones on top of the originals, the 70hz tone is reproduced at only 80db, both new tones produced start at time t+z and end at time t+z+s+r and so forth. I'm fairly confident we have some decent tools for amplitude and frequency distortion of many types, but where are the tests for the time domain? How important are they? If cumulative spectrum decay plots (that depict all three dimensions) store the same information as frequency response plots does that mean we can compress the problem to only two dimensions? 
17th November 2012, 11:22 AM  #2 
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It's a two dimensional problem at each point in space where the measurements are taken. Frequency and time are both related by the Fourier transform know one and you know the other. This is well known stuff for almost 200 years.
The interesting problem with transducers is the "at each point in space" bit.
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17th November 2012, 11:35 AM  #3 
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Ahh, very interesting. By the Fourier transform we then have a deterministic relationship and the three dimensions I have referred to can in fact be compressed down to two.
The "at each point in space" bit I take to mean I'm actually missing a fourth dimension. If I understand this correctly I can extend my example to say distortion can also arise if the 50hz tone is 90db only on the loveseat, while it is 80db on the couch and therefore we introduce a concept like beaming while also making the assumption that omnidirectional sound is ideal. 
17th November 2012, 11:41 AM  #4 
diyAudio Moderator

Omnidirectional is not an assumed ideal there are a lot of schools of thought about dispersion patterns, and lots of threads here discussing (heatedly!) that issue. In a sense, this is a six dimensional problem (time+amplitude or frequency+amplitude multiplied by three spatial dimensions), but that assumes point source detection, which is not the case for ears.
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17th November 2012, 11:41 AM  #5 
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In realworld measurements, the issue when transforming impulse response to amplitude frequency, phase frequency response, decay etc. is a dynamic range. It is very limited by noise (background noise or whatever) in case of single impulse, little better situation is for MLSA derived impulse response. Swept sine is still best in resolution.
In pure maths, everything can be calculated from impulse response, except for nonlinear behavior. It would be great to have a transient recorder with 20bit/10Ms/s capability. Audio signals seem to be limited at 20 kHz (which is not true), but limit of ear ITD resolution is about 2  5 us. 
17th November 2012, 11:59 AM  #6  
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Quote:
Quote:
Nonlinear behavior as in HD right? I never played with a transient recorder. Would this be equivalent to overlapping impulse responses in an effort to time align multiway speakers? 

17th November 2012, 12:37 PM  #7 
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Background noise is the limit in any measurement, unless you are determined to only use 1968 technology. It's very easy to get high resolution low noise data in 2012, even with impulses. MLS gives a huge advantage, but then you have the issue of people grumbling at you about nonexistent problems with "averaging," despite the virtues of autocorrelation.
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17th November 2012, 12:38 PM  #8 
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Precisely. That's where the "art" of loudspeaker design comes into play.
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17th November 2012, 07:28 PM  #9  
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Quote:
I've been wanting to open a similar thread but refrained to do so because I though the interest would be very limited. I've seen few attempts to do timedomain measurements when harmonic distortion is very low in an attempt to correlate subjective sound differences with objective data. unfortunately no such work I know about seems credible enough. a rather wellknown "study" was the one by Nordost where they attempted to prove that cables and other treatments make a measurable difference. unfortunately that was so obviously filled with marketing and dubious claims that it wasn't well received (for good reason, IMO). I really wish someone tried to do measurements of that kind in a credible fashion. it would be interesting to read some control theory (not necessarily applied to audio) that focuses on timedomain analysis.
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17th November 2012, 07:55 PM  #10 
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I apologize ahead of time for lingering on this 200 year old subject but I still have a lot of details to iron out.
Consider this picture from Linkwitz's site: Since the time domain can be collapsed somehow then all this time information for each frequency should be available in a frequency response plot correct? So how do I back out what the delay and energy storage is for various frequencies of a speaker using the FR plot? 
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