4 Dec
2011
4 Dec
'11
1:04 p.m.
On 2011 Dec 3, at 12:57 AM, Eric Smith wrote:
Brent Hilpert wrote:
I'm not sure what you mean by "representation of the signal",
although I was going to posit a similar distinction to you. I presume
you mean the phenomena - changing amplitude over time of an
electrical 'signal' (term used loosely) for instance. However a
'signal' (term used more strictly) is something intended to convey
information (content), and generally there is some prior knowledge
involved of how to interpret the phenomena to retrieve that information.
I would say that conveying discrete information through a medium or
channel is typically done with a quantised signal. The original
discussion was for a baseband/pulse signal though, the addition of
modulated-carrier mediums was an additional complexity that I didn't
feel was warranted for the discussion and brings in additional
considerations.
This does seem like one of those discussions that would be sorted out
in a minute of conversation in front of a blackboard, but over email
- with slightly different understandings or ambiguous use of words -
it ends up in an infinite regression. I'm not sure of the continuing
relevance to the original discussion but we'll see where your thought
experiment goes.
In the analogy with the FSK modem in your other
message
then: simply put, whether the demodulated signal is time-quantised
depends on the properties of the modulating signal.
I still find that I can't agree with your definition of
quantization as applied to signals. In particular, you seem to
think that quantization is a characteristic of the content of the
signal, while I consider it a characteristic of the representation
of the signal. I go to a concert hall and listen to music performed
on a
(mechanical) piano. Is the sound in the concert hall quantized?
I expect we agree it is not.
I take my Olympus LS11 PCM audio recorder with me to
the concert
hall, and with the LS11 sticking out of my shirt pocket, record the
concert from my seat, using stereo 96 kHz 24-bit sampling with the
built-in microphones.
Is the PCM recording in the flash memory of the LS11 quantized?
It is a discretely-rendered approximation of the sound.
I expect we agree it quantised.
When I get home, I play back the recording through a
DAC,
reconstruction filter, amplifier, and speaker, and listen sitting
in my easy chair. As I listen to the playback, is the signal from
the output of the speaker (sound waves) quantized?
Not likely by the time it's emanating from the speaker.
If one were looking at the output of the DAC, however, I would say it
was quantised if the discrete steps are still discernable in both
time and amplitude and one could precisely recreate the input to the
DAC, for any arbitrary input sequence (assumes a good DAC).
Once it has gone through the [limited-bandwidth,distorting,noisy]
filters, amplifier and speaker, info has been lost and you're not
going to reliably or consistently get back to arbitrary 96KHz, 24-bit
discrete data.
Is the signal impinging on my ears (sound waves)
quantized?
And we both know (my) answer to that, I expect we agree on this
question.
Note that the sound waves at my ear are not identical
to those at
the speaker, and that it would be relatively difficult to exactly
reconstruct those at the speaker from those at my ear. If you were
to say that the sound waves at the speaker are quantized, does the
distortion introduced by the "channel" the signal passes through,
between the speaker and my ear, make any difference to your opinion
as to whether the signal at my ear is quantized?
I have further questions for part two of the thought experiment,
after we've considered part one.