Re: Offline Rendering... still a thing?
Re: Offline Rendering... still a thing?
- Subject: Re: Offline Rendering... still a thing?
- From: Brian Willoughby <email@hidden>
- Date: Wed, 05 Aug 2015 10:08:41 -0700
On Aug 5, 2015, at 9:50 AM, Jens Alfke <email@hidden> wrote:
> On Aug 5, 2015, at 9:41 AM, Brian Willoughby <email@hidden> wrote:
>> The two most common ways to depict audio waveforms are Peak and RMS. I don't think there's any standard for displaying cube root - although I'm sure it looks interesting. I'd recommend against inventing new math for displaying audio waveforms, especially since there are well-established standards.
>
> I think we’re talking about different things. Peak and RMS describe how to reduce a time range of a waveform to a single number. What I was referring to is how to transform that number (i.e. a raw amplitude) into a volume level that’s meaningful to a human, since our ears’ response to sound pressure is highly non-linear.
>
> I did some online searching and the two common approaches seem to be either logarithmic or cube-root. I experimented with both, and the latter seemed to produce a more intuitively-correct display, to me at least. (Disclaimer: I could be mis-remembering the formula; it’s been several years since I looked at my code for it.)
Ah, yes, the raw samples correspond directly to voltages, and you can calculate power amplitude from that, but the perceived loudness is not precisely linear compared to the voltage and power in the circuit. So, yeah, Peak/RMS are different than what you're talking about.
It's very tricky to get into this area, though, because frequency content and frequency distribution significantly affect the relation between what's happening in the electronics compared to what's perceived in our brains. The formula for a pure tone at a single frequency is exponential or logarithmic. But when there are multiple frequencies the translation becomes more complex. Take a look at the Bark scale and critical bands. Of course, simpler math can get close without being precise.
The advantage of Peak and RMS is that they can be exact. The disadvantage of fancier, perception-based loudness displays is that they're much less accurate unless you have a lot of information.
Brian Willoughby
Sound Consulting
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