Re: Is 44.1 KHz sample-rate enough? Yes and No.

"Mr.T" <MrT@home> writes:

"Randy Yates" <yates@xxxxxxxx> wrote in message
news:m3fxt44rfh.fsf@xxxxxxxxxxx
The best digital audio hardware is slightly less than 120dB dynamic
range.

That may be true on the ADC side, but I'm not sure it is on the DAC
side.

So for solely computer generated music you may get an extra few dB's. So
what? Still less than 144dB that Radium wants.

The statement in your original post above is reasonably correct. I was
still seeing the intimation of "impossible" from your other post to
Radium on the topic.

However, it may be POSSIBLE to reach 144 dB DR in a DAC. For example,
Figure 9 from my presentation on delta-sigma D/A conversion

http://www.digitalsignallabs.com/presentation.pdf

is based on an equation I wrote in a Matlab function (m-file). Tonight I
wrote another Matlab function which rearranged that equation to return M
(oversampling ratio) given SNR and modulator order. Using an SNR of 144
dB and a modulator order of 2 (quite conservative) I obtained a required
oversampling ratio of 1266.

At 44.1 kHz, that means we would have a 1-bit stream at 55.8 Mb/s. This
is completely reasonable given the current state of today's hardware
using, say, a Xilinx Virtex FPGA or somesuch. The MIPS required for the
interpolating filter would be well within reason as well using polyphase
filtering techniques, and a 2nd order modulator isn't too expensive in
terms of MIPS.

The bigger challenge would most likely be the analog design. But if
money were no object, then you could resort to extremes such as
cryogenically cooling the front-end amp.

This is certainly crazy for anything close to practical, but I just
wouldn't rule out "possible."

I'm still puzzled how one is going to listen to 144dB dynamic range even IF
it was possible. Any suggestions Randy?

I'm not sure what the problem would be since you can always turn the
"volume" down and let the soft parts drop into the ambient noise floor
(either thermal or acoustical). You might even get better results than
you think given the ear's ability to act like an adaptive matched filter
(e.g., you can hear a sine wave well below the noise floor).

I never intended to challenge the impracticality of it, only the
possibility. I don't believe it's IMPOSSIBLE to achieve this level of
dynamic range.
--
% Randy Yates % "Rollin' and riding and slippin' and
%% Fuquay-Varina, NC % sliding, it's magic."
%%% 919-577-9882 %
%%%% <yates@xxxxxxxx> % 'Living' Thing', *A New World Record*, ELO
http://www.digitalsignallabs.com
.

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