[BC] dueling algorithms and audio quality

[RichardBJohnson at comcast.net]

16-bit audio is signed (twos compliment). It runs from -32767 through 0 to +32767. The peak dynamic range is therefore 32767:1 (90 dB). This is not what the ear hears, though. The ear hears the "power," so the real dynamic range is less by the peak-to-RMS ratio, i.e., 0.707 * 32767 = 23167. In other words, a sine wave with peak amplitude of +/- 32767 counts only has a RMS value of 23167 counts. 

However, we got along just fine for many years with only 70 dB of dynamic range when analog equipment was used. The difference was that very low-level analog signals were embedded in noise, which seemed natural. Digital signals, however, become granular which is unlike anything heard in nature. The solution is dither. It does not make any difference if you run 16, 18, or 24 dB converters if the equipment is designed correctly.

For instance, suppose you are going to sum the inputs of four channels to provide an output. How do you sum them? If you are exercising all 16-bits on each of the input channels, do you need four times that number of bits on the output channel? The answer is NO as long as you do the summation correctly. At least one "respected" digital board I reviewed two years ago at the NAB was designed without a clue.

If you attempt to divide the four inputs by 4 before you sum them to the output channel so you do not overload the output, you have removed the two LSBs on all four input channels! This is going to cause granulation artifacts on those channels. The "correct" solution is to use (or emulate) floating-point summation.


Cheers,
Richard B. Johnson
Book: http://www.AbominableFirebug.com/



----- Original Message -----
From: lists at loudandclean.com
To: "Broadcasters' Mailing List" <broadcast at radiolists.net>
Sent: Wednesday, October 7, 2009 2:06:38 PM (GMT-0500) Auto-Detected
Subject: Re: [BC] dueling algorithms and audio quality

    As I see it, the issues with 16 bits are (including but
not limited to):

[1] when you are down only 6 dB below "all-ones", you've lost
_half_ your quantization steps.  Instead of 65,536 "steps"
between the positive and negative peaks of the audio waveform,
you only have 32,768.  Go down another 6 dB and you only have
16,384.  So, you lose resolution really fast when you leave
any headroom at all.  But wait, we _must_ leave headroom!

[2] recent papers about the performance of D/A converters in
CD players seem to indicate that constant energy in the top
6 dB may cause error correction circuitry to activate and
never recover, introducing significant distortion.  OUCH!