> I suspect this is nonsense. (sorry Andrew) You do have to sample the data to
> get it into the digital domain, before you can process it. (Unless you are
> going to do an ANALOG wavelet analysis - please supply diagrams)
IANAsignalengineer, but .. =) Yes, that might be total BS. I was under the
impression from long ago when I was reading about initial research in wavelet
compression that you sample, then use the samples to form a wavelet
composition that represents the sampled data, then send the parameters of the
wavelet.
For instance, a 32 bit signal at 96kHz is more than neccesary to fully
represent an analog audio signal with no loss. So, if we sample 1s of
that audio, we use up 4 bytes * 1 channel * 96000 Hz = 384000 bytes/sec.
Now, if through wavelet analysis, it's found that the signal can be
represented by the following sinusoids superposed:
3 sin (.5t - .2)
-2 sin (1.3t + .4)
4 sin (-2.5t - .83)
For that one second of audio, those sinusoids accurately represent the
sampled data. Now, sending the data that represents those sinusoids is as
easy as sending a 32 bit IEEE floating point number for each of the 3
parameters per sinusoid, so --- for simple sinusoids, that relatively simple
signal can be represented by only 9 paramters * 4 bytes = 36 bytes for an
accurate representation of 384,000 bytes worth of sample. Nyquist's law
effectively restricts sampled audio to 1/2 the sample rate, giving a
certain minimum amount of information neccesary for transfer to transmit
that signal from one point to the other. This sort of compression breaks
the bounds of Nyquist's law in transferring, though it still limits the
actual sampling of the audio.
Am I misinterpreting the technique of wavelet compression, such that the
model and calculations which I've provided here are inaccurate, baseless,
or just plain BS? If so, how does wavelet compression actually achieve
what it does?
> appropriate ), so there will be a short delay. The computational demands are
> probably similar to ATRAC. I suspect that wavelets will not be as good as
> ATRAC for any particular data rate, as they seem to me less amenable to
> psychoacoustic coding.
Very interesting... I'm very interested in wavelet compression (as I'm sure
many others on this list might be also) ... do you have any good references
for the algorithms and mathematics behind it all?
Thanks!
/Andrew
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