how to interpret graphs

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Published: Mar-22-2013, updated: Mar-18-2017

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How to ‘read’ graphs

This topic had become rather long so it is split into several pages.








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  1. Anonymous says:

    Thanks Solderdude. This is exactly what many of us need to help us try to translate those graphs. The problem that I have is how to work out the ‘slope. ie where to start the line at the top and where to join it at the bottom. Presumably, it goes through the central point at 1 KHz? It’s difficult to judge the ‘average’ line!!

  2. Solderdude says:

    The line in the graph is just a general idea.
    It doesn’t have to cross the 1kHz point, may well cross at 600Hz or 2kHz.
    The idea is to draw and ‘imaginary line’ from say 100-200Hz to around 5-6kHz through these wobbles and see if it slopes upward or downward. Sometimes the graph is going up and down around the imaginary line. The more that line slopes (upwards or downwards) the more the effect of ‘cold’ or ‘warm’ voices is (and instruments also). For instruments it is hard to say unless one is very familiar with it. Everyone is familiar with voices.
    At least this is what I think you meant with your question.

  3. mkrzych says:

    Fantastic article! Would be nice to see interpretation of the impulse and square wave response graphs as well.

    • Solderdude says:

      have been meaning to write about this subject but interpreting impulse and squarewaves correctly depends a lot on what ‘corrections’ were used, what test gear was used and is quite complicated.
      A squarewave measured with a dummy head (even when compensated) can look different from a squarewave measured with a flat bed measurement rig (like I use)
      Impulse response is ‘easier’ to retreive some info from but this stands or falls with knowing the size and shape (height and width) of the ‘stimulus’ and needs to be the same or standardised in order to actually say something about the response.
      Measurements as shown now on some sites now say little by itself.
      They only say something about some ringing and as the time scale is not very clear doesn’t say at which frequency.

      As said the measurements as seen now on the web are not that ‘revealing’ of properties like ‘speed’ and ‘attack’ nor ‘decay’ of music as the plots only show the ‘problem’ areas and thus sort-of mask how other frequencies fare.

      I personally think the waterfall (when correct timing windows are used, which isn’t always the case, and distortion measurements will say more about the sonic character.

  4. Sam says:

    I’m confused. Why do 40Hz and 440Hz square wave if they just show the same thing as frequency response? Isn’t the improved 440Hz square wave with the HD650 just because it became closer to your applied compensation curve. Isn’t the HD650 40Hz square wave improved because the bass extension is flat as you equalized it it using a Kameleon?

    The same goes for impulse response if a CSD again just shows the same information. For example, the HE-400i doesn’t meet the required level but is that just a result of the frequency response not meeting the compensation curve target? If it was equalized with EQ to match the compensation curve then the impulse response would be like the HD650 one?

    I found that it is easier to read a CSD if it is a 2D graph and time is in color rather than an axis. You can never read the time axis well in 3D. Not sure if your software does that.

    • Solderdude says:

      Well square-waves do also show (parts of) the frequency response except in reverse order (the highest frequencies on the left and the lowest part of the frequency range on the right which is determined by the square-wave frequency. As there is no scale for frequency here it is difficult to read.
      On top of that the time domain (inverse of frequency) AND amplitude domain are linear. For FR plots both are logarithmic.
      So while the the amplitude domain is logarithmic in the FR graphs (30dB SPL to 100dB SPL in most plots) this means the visible range is a factor 3000.
      For the square-waves you can only look in a linear scale. The top of the squarewave is about 95 dB SPL = 0.775V peak but the scale is linear so the smallest wiggles you can effectively see is about 0.02V = about 30dB dynamic range AND linear so not in dB’s.
      The reason I use 30dB SPL in the FR plots instead of 0dB SPL is because:
      A. there is microphone noise (surrounding sounds picked up as well as electrical noise).
      B. One cannot effectively hear anything below 30dB when listening to music with average levels of 75dB SPL (A-weighted) so below 30dB SPL all is moot.

      You are correct that a CSD is also a time-domain thing as well as frequency and amplitude.
      One would say the best of all worlds.
      Alas it doesn’t tell exactly how a headphone ‘rings’ that well.
      Sure, a CSD can show that certain frequencies ring longer than the steepness of the filters used.
      This is what you see in a CSD plot.
      But is not easy to predict how it really rings in practice when there is ringing at multiple frequencies.
      You can see at which frequencies it rings and how long but not how it looks when all of these ringing is combined. And that last part is what we have to deal with.
      So the square-wave is an additional tool which tells what the reaction of the actual membrane is after a pulse (that doesn’t exist in music) is applied.

      Furthermore the stimulus is a real square-wave here, not one generated with a soundcard. It thus is MUCH faster. Also for analysis no soundcard is used, just the oscilloscope which also makes it ‘faster’ and has no ringing added of the used soundcard. Some people (not Tyll) showing ‘Dirac’ pulses etc clearly show pre- and post ringing that are NOT part of what actually happens and certainly for Dirac pulses you would have to know what you see is partly soundcard or partly ringing.
      Also, in most other Dirac pulses you really have NO clue as to how high that pulse was supposed to reach. It just has a meaning less number on the amplitude axis.
      For that reason I include the stimulus and make it longer (so not a Dirac pulse) so you can actually see how high the impulse is supposed to be. So my pulse differs here. It does, however, also come from the 0V line, just like a Dirac pulse where the squarewaves swing around 0V.

      Indeed as you say the impulse response level is totally dependent on the FR response. This is correct. These 2 are linked together.
      You can EQ them to have the same level but this would require an EQ almost exactly the opposite of what is measured.

      This is where things will go wrong if you do. The reason for that is that one would have to assume that WHAT is measured is factually correct. I do NOT believe my measurements are factually correct but can be used for comparative purposes.

      IF I were to use digital EQ and correct for all sharp dips and peaks then I would be able to get better looking FR and square-wave plots indeed.
      BUT only on my rig (flatbed, no Pinnae) and only with that specific headphone. Measure a few of them and add Pinnae and it will differ. The EQ would be totally off.
      So this is why the Kameleon uses a different approach.

      I know that when the FR measures as a horizontal line on my plot that in any well made recording everything sounds ‘real’ which tells me tonally, on average, that is correct.
      Every headphone differs, even all HD800 and HD650’s are slightly different. Yes, they may be matched L and R quite tightly but HD650 number 47586 may not measure exactly like 29368.
      They will. however, have the same average FR with wider dips and peaks at the same frequency bands.
      This is how the Kameleon works. It just compensates for the ‘average’ FR. Thus it can tonally gring some headphones closer to ‘flat’ (or at least what I think is flat) but not change narrow peaks nor dips. Nor should one want these narrow ones ‘compensated’ nor does one want multiple (sharp) peaks and dips compensated. This could potentially F-up the FR even more than when no EQ is applied.

      For the HD600/HD650 etc very little compensation is needed to get excellent FR. These really are exceptions in the headphone world. Most headphones have lots of peaks and dips and weird FR which cannot be compensated exactly.
      The reasons are:
      Do we know which peaks dips are measurement errors ?
      Do we know what is caused by compensation errors (when HATS are used) ?
      Is headphone HE400i A equal to HE400i B ?
      The Kameleon can ONLY correct one notch and some (gentle slopes) which can bring quite a few headphones closer to a more ‘realistic’ sound.
      BUT not perfect.

      A compensated HD650 will never sound the same as another compensated headphone. Even when perfect EQ were reached on one specific measurement setup.
      Simply because of errors by measurements as well as dynamic behaviour (ringing, rise/fall etc).
      So this is why I chose to only address the ‘gross’ errors and in a specific but targeted way which should work well with most headphones that are eligible for correction.
      In some it works near perfect, in others the net result will improve but not be on the same level of tonally correctness.

  5. donjoe0 says:

    Are you seriously keeping Rtings at the top of your list of 3rd-party graph databases? Those people don’t even measure transient behavior, they end up putting ridiculous gaming cans at the top of their ratings lists as “critical listening” cans alongside the HD800S and such, just based on comfort, frequency response and stereo qualities. 🙂

    • Solderdude says:

      The ratings they do are solely made on on numbers produced by all measurements and weighting also is determined by certain percentages. Their goal (which they are still refining) is to create a rating based on technical points only and devoid of subjective findings.
      I believe that some aspects of headphones are very hard to deduct from numbers/measurements.

      On the other hand they are (still) doing some research on how to ‘compensate’ their plots which I think is done better than Tyll’s efforts, even his latest efforts are not that great.

      Indeed they do not publish time related plots (square-waves, impulse, step) nor CSD or spectrum plots which I feel are also measurements that can show some aspects that aren’t very visible in other plots.

      Things I do like, that others don’t measure, are things like frequency response consistency and average standard deviation which is really interesting and sometimes explains why some find a headphone bassy and others bass shy other than by preference or source material.

      The ratings are suspect though. I personally rate the Edition X MUCH higher than the HD700. To me, for critical listening, the difference is definitely not a 8.2 and 8.1.
      If I had to rate them I would rate the Ed X a 9 or or so and the HD700 a 5.5 but am sure HD700 fanboys will rate the HD700 higher than the Ed X.
      That subjectiveness is something Rtings wants to avoid. This appears to result in strange ratings for sure.

      I give them the thumbs up for measurement consistence and ‘suite’ but feel their rating needs some adjustments. Also would like to see more time related plots there and maybe some subjective ratings like the idea from Golden Ears where they showed some ‘sliders’ below the measurements.

  6. Alex F. says:

    Very interesting, thank you very much.
    Would it be possible to share with us, which software do you use to plot those graphs, in particular the Waterfalls/CSD’s.

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