steve@amdimage.UUCP (Steve eidson) (08/22/85)
It's almost amusing listening to two guys from
the same company throw things at eahc other, but...
First off, in every design case I have encountered,
the digital output interpolation filter is followed by an
analog anti-alias filter. By increasing the sample rate of
the final output filter, the requirements of the analog
output filter can be reduced from a 6 to 8 pole Butterworth
down to a simple 1 or 2 pole filter. The digital filter
has better attenuation at high frequencies, thus allowing
the analog filter to roll-off much more slowly at a cutoff
frequency that is 2 or 4 times higher (depending on the
interpolation factor).
The other thing that has been ignored completely
is that most output interpolation filters I have experienced
are linear phase FIR filters. The response of a linear
phase FIR filter has no ringing. The most common filter
I have used for interpolation is the simple:
y(n) = 0.25*x(n) + 0.5*x(n-1) + 0.25*x(n-2).
Zeros are alternately inserted into the sequence to get a
factor of two increase in the output data rate, and the output
is multiplied by 2 to produce a properly scaled output.
It should also be noted that digital filters
exhibit sensitivity to coefficient truncation, just as
analog filters are sensitive to component selection. Since
multipliers are still relatively expensive for a consumer
product such as a CD player, I assume that most manufacturers
use a simple shift-and-add scheme. The example I gave above
can be implemented on most off-the-shelf CPUs. Many IIR
filters (Butterworth, Chebyschev, and elliptic) have
poles near the unit circle, which can be translated into 1-2^n,
but they are not as simple as the one-bit coefficients in
the FIR interpolation filter. I suggest that an IIR digital
filter may appear to have the same response as its analog
counterpart in an infinite precision computer simulation, but
in a real implementation, an digital filter will exhibit sensitivity
to coefficient truncation, while an analog filter will be
sensitive to the component values selected.
Another reason for choosing a digital interpolation
filter, besides time and temperature stability, is the exact
replication of a given filter from CD player to CD player.
This coupled with the fact that the analog anti-alias
filter can have much more compnent "slop", weighs in favor of the
oversampled digital approach rather than an analog approach
on mass produced players (emphasis on mass).
Sorry about the long-winded-ness, but I had to absolve myself
of this information. Any intellectual discussions are gladly
invited, any impassioned mumbo-jumbo to /dev/null.
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"...but you've got no arms and no legs,
what are you going to do, bleed all over me ..."
Steve Eidson (408) 749-2303
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