pippin wrote: 
> But then you've got all these high frequencies still in there on the
> analog side. Isn't the biggest problem with the high frequencies that
> power amps (especially ones filtering through intermediate frequencies
> like "Class D" amps) tend to create artifacts if you have signal in
> multiples of the audible range?
> 
> 
> 
> What kind of filters do they use? I do know that kind of stuff for
> analog filters where both the reason for their use and the negative
> impact are quite obvious.
> 
> But then... like for the windowed sinc filter you mentioned even digital
> filters are not perfectly discrete if you need finite impulse response
> and linear phase so it makes sense that they will also flatten the
> frequencies within your filter/below your cutoff frequency.
> But isn't that the same for your interpolation filter in sox? Of course,
> the interpolation filter doesn't window so it keeps all the harmonics in
> there (and creates some arbitrary new ones) but why is that better than
> leaving the simple harmonics of the 44.1 kHz samples in?
> What kind of filters does sox use?

Hi Pippin,
very good questions BTW. It turns out that with high bit depth (24) and
high sample rates relative to the bandwidth of the signal the aliases
are very low in amplitude. If this was not true a digtal filter would
not work for this purpose at all. The amplitude of the alias is
determined by the "height" of the "stair step" in the signal. At 16/44.1
those stair steps can get pretty high. Very easy to see in a scope from
a NOS DAC. The filter adds steps in between the originals steps, because
of the increased samples and the increased bit depth the height of the
steps is much less, thus producing much lower amplitude aliases. Another
way to think of it is because the bandwidth of the signal has not
changed, the maximum amount of change for a given sample is also less,
thus the maximum possible height for a stair step is also decreased.

The reason to do the digital filtering at all is that for 16/44.1 the
stair steps are large, thus producing high amplitude aliases, and those
aliases are close to the audio band. There are two methods by which an
alias can cause an image in the audio band: intermodulate with signal,
or intermodulate with another alias. It turns out that the aliases
produced by a given signal are lower in amplitude than the original
signal, thus on average the intermodulation of aliases with signals is
going to produce higher amplitude images in the audio band that alises
intermodulating with other aliases. For example a 25KHz alias
intermodulating with a 15KHz signal (thus producing a 10KHz image) will
be greater in amplitude than the same 25KHz alias intermodulating with a
35KHz alias. They both exist, but the intermodulation with the signal
will usually produce a higher amplitude image.

Now let's look at what happens with the signal upsampled to 176.4, the
aliases start at 88.2. So lets look at what happens to a 90KHz alias.
First that alias is going to be much lower amplitude in the first place
(see the above) and the lowest frequency image it can produce from
intermodulating with signal is 70KHz, way above the audio band. Now you
certainly can get images in the audio band from aliases intermodulating
with other aliases, BUT because the aliases are so much lower in
amplitude, the image between two is going to be very low in amplitude. 

The net result is that the images in the audio band are drastically
reduced (not completely eliminated) by the upsampling and filtering. A
high sample rate high bit depth original recording already has these
advantages built in. 

Now the fun part is to do this filtering in such a way that it preserves
the flavor of the original recording. 

John S.


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