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  1. Log Impulse Response?

    #1
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    Default Log Impulse Response?

    I'm wondering what Smaart is actually showing us when we ask for "log impulse". It can't be the log of the impulse response since the impulse response is a time function that can take on negative values. So it must either rectify (absolute value) or square it or something to make it all positive before taking the log. Curious minds... Thanks. --Frank

  2. Re: Log Impulse Response?

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    Senior Member Langston Holland's Avatar
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    Hi Frank:

    This is simpler than you can imagine, but I'm in the mood to make a mess of it. Massive corrections and general derision solicited.

    Sound is the variation of air pressure above and below the constant pressure the measurement mic happens to be in when the recording is made. The pressure recording microphones we typically use (omni's) have diaphragms that are pushed in and pulled out depending on this disturbance of atmospheric pressure. That diaphragm movement is supposed to produce an analog of this disturbance as a positive voltage when the diaphragm is pushed in and a negative voltage when pulled out. The amount of this variation in voltage is then translated into discrete numbers through the analog to digital conversion process.

    Assuming your converter has a 48kHz sample rate, this discrete number is awarded 48,000 times every second. The value this number is given follows the same polarity as the voltage transmitted by the microphone, no sound is zero, positive pressure is awarded a positive value and negative pressure is awarded a negative number. Just like the sample rate's resolution on the horizontal time axis, it's important to have good resolution on the vertical pressure axis. The latter is called bit depth.

    Assuming your converter has a 24 bit depth, that would allow a selection of 1 of 16,777,216 numbers (2^24) to be awarded to the voltage level 48,000 times every second. That's fairly busy. This 24 bit depth will fill a span between -8,388,607 and +8,388,607 with our lovely zero in the middle of this range. If you are a bad person and adjust the mic preamp gain such that the sound pressure peaks are 40dB shy of the converter's maximum values, you'll literally throw away 99% of its resolution capability. If you adjust the mic preamp so that the peaks use up all the converter's resolution and still want more, it'll clip. Watch your meters and practice good gain structure.

    To understand the "log" view of the IR one should first understand it's near twin, the "linear" view.

    The linear view of the IR as executed in Smaart is the time data displayed as a +/- percentage. Say you did a good job with your gain structure and recorded peaks within about 12dB of the converter's maximum, you would have recorded peaks of about +/- 2,000,000 of the +/- 8,388,607 available numerical resolution. In this example, you'll see IR peaks of about +/- 25 on the IR's vertical axis in Smaart (2 million / 8 million and some other numbers).

    The log view of the IR as executed in Smaart is the time data displayed as a (wait for it...) logarithm of the absolute value bit depth number. It's considered rude to attempt to take the log of a negative number or zero, so that's avoided. Thus the display will be made up of only positive numbers which still contain the full complex data of the raw IR. The displayed log values will be relative to the full resolution of the converter, in this case 8 million and those other numbers. Using up 50% of the converter's resolution will show log peaks at -6dB.

    HTH :)
    Last edited by Langston Holland; September 5th, 2012 at 06:38 AM.

  3. Re: Log Impulse Response?

    #3
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    Langston is spot on. The math involved is really quite trivial. The resultant y values of an impulse response are in linear amplitude and is what we typically display. If a log view is desired we convert to dB, which is simple as this: 20 * log10 of the absolute value. If the linear amplitude value is zero, we simply use the minimum dB value for the current bit depth. Though in a live environment it's highly unlikely to get a value of absolute zero.

  4. Re: Log Impulse Response?

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    Quote Originally Posted by Adam Black View Post
    20 * log10 of the absolute value.
    So the answer is absolute value, or full-wave rectification, as us electrical types sometimes call it. Thanks.

    Another way might have been to make impulse response into an analytic signal using a discrete Hilbert transform, converting to polar form, and taking the magnitude. But absolute value requires less computation and does the job. --Frank

  5. Re: Log Impulse Response?

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    Senior Member Langston Holland's Avatar
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    There are many ways to skin a cat, but first one has to understand the goal before choosing the method.

    Goal: Setting the reference delay such that the highest possible correlation between the stimulus and measurement signal occurs in the frequency region of interest.

    The center of this happy region will be at the bottom of Smaart's phase trace smile where it is parallel with the X axis. This is most often achieved by setting the reference delay of the stimulus to the peak of the log view of the IR.

    This is confirmed by a high value coherence trace.

    Vary the reference delay higher and lower than the value predicted by the log IR peak and watch the coherence and phase traces. Smaart's windowing methods will keep the magnitude response fairly consistent, though increasingly nervous while everything else gets ugly quickly.

    I think you'll find that Smaart gets closer to the correct reference delay time more consistently in live (ugly) situations than anything else out there.

    The ETC can be quite helpful at low frequencies where the complex energy (phase) included in the log IR can peak across wide areas, making it hard to judge arrival time.

    Going Further:

    1. http://www.excelsior-audio.com/Publications.html

    2. http://www.rationalacoustics.com/pag...ining_Schedule

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