Tuesday, September 11, 2007

Dynamic Range and HD Audio

Recently, I responded to a comment in an AVS Forum thread where someone posted that people shouldn't get too upset if their high definition audio is converted and resampled to 16 bit/48KHz. Apparently PowerDVD, the only PC software capable of playing HD DVD or Blu-ray movies, converts and resamples all of the HD 24bit/96kHz uncompressed or losslessly compressed audio (DTS-HD, Dolby TrueHD, etc.) to 16bit/48kHz. Many people are upset and would like to find a way to play the full resolution HD audio tracks from their HTPCs. The developer of PowerDVD says they have to downsample the audio because the PC doesn't provide a secure pathway for digital or analog output. I can understand why there might be some problems with a secure pathway for digital output without something like HDCP or AACS, but I don't understand why they have to downsample the audio for analog output. Anyhow, he/she basically stated that since the highest frequency a human is capable of hearing is 20,000 Hz, even when applying the Nyquist theorem to 48 kHz, the downsampled audio can still easily reproduce all audible frequencies. Therefore, I think he/she assumed the only advantage to 24bit/96kHz HD audio is the fact they can play higher frequency sounds. Well, there's a lot more to it than that...

My response just touched on the issue of how the resolution of the audio data is related to dynamic range. There are other factors that come into play, like the tonal effects of high frequency harmonics and phase accuracy. There's also the argument that when an analog waveform is converted into digital data, the higher the sampling rate and resolution of the data, the representation of the original analog signal will be much more accurate. There are also concerns about the quality of the resampling algorithm, etc., etc.

Let me get back to the subject of this post - dynamic range. Dynamic range, when used in audio measurements, refers to the difference between the loudest undistorted sound and the quietest passages. In digital audio, the maximum possible dynamic range depends on the bit depth of the audio data.

To calculate the maximum theoretical dynamic range based on a digital audio bit depth, you multiply the log of the total bit depth by 20.

Dynamic Range = 20 * log(bit depth)

For example, CD audio has a bit depth of 16 bits. A bit is a binary unit, so they are actually referring to 2 to the power of 16, which comes to 65536 decimal units. To be more accurate, we would use 65535 because they use values from 0 to 65535.

When we apply this to the formula above, we get:
DR (16 bit CD) = 20 * log(65535) = 96dB

The maximum theoretical dynamic range for 24 bit audio comes to:
DR (24 bit) = 20 * log(16777215) = 144dB

If it is true that some classical music performances can have a dynamic range of over 110 dB, then it's also possible that an HD movie could also have this large of a dynamic range. Hopefully, there will also be some other musical performances (live or studio) that were recorded in HD and become available in HD DVD or Blu-ray that will also have this high of a dynamic range.

My point is, if the audio data is always converted down to 16 bits, we won't be able to enjoy the full dynamic range available from a high definition audio performance.


  1. i am writing just to mention that the count of numbers "0 to 65535" is 65536

  2. Yes, but the value of the largest number is 65535.