[Bob Myers]

Radium wrote:

In the case of digital video, we could treat each individual sample
point location in the sampling grid (each pixel position in a frame)
the same way as if it was a sample from an individual (mono) audio
signal that continues on the same position in the next frame. For
example, a 640×480 pixel video stream shot at 30 fps would be treated
mathematically as if it consisted of 307200 parallel, individual mono
audio streams [channels] at a 30 Hz sample rate. Where does bit-
resolution enter the equation?

What you are calling "bit resolution" is more commonly
referred to as bits/sample, or in video bits/color or per
component. It "enters into the equation" in all digital
encoding systems by setting the dynamic range that can
be encoded in that system, or, if you prefer, the "accuracy"
with which each sample represents the value of the original
signal at that point. The number of bits, along with the choice
of the maximum value which can be encoded (i.e., what level
"all ones" in the sample corresponds to) determines the value
represented by the least-significant bit.


Digital linear PCM audio has the following components:

1. Sample rate [44.1 KHz for CD audio]
2. Channels [2 in stereo, 1 in monaural]
3. Bit-resolution [16-bit for CD audio]

PCM has nothing to do with it.

Sample rate in audio = frame rate in video

No. There is no real analog, in audio, to the frame
rate in video, except to the extent that the frame rate
IS a sample rate in terms of capturing one complete
2-D image at that point in time - IF that is the way the
image capture device works (and not all work this way).
More typically, the "sample rate" in audio would be
thought of as corresponding to the pixel rate in video.

Channel in audio = pixel in video

Definitely not. A "pixel" in imaging is just what the
name says - it is a "picture element," meaning one
dimensionless point-sample of the original image, at
a specific location within the image plane and, in the
case of motion video, at a specific time. A pixel is
the best analog you will find to a single sample in
the case of digital audio.

Bit-resolution in audio = ? in video

Bits per sample is bits per sample, in either case.

Is it true that unlike the-frequency-of-audio, the-frequency-of-video
has two components -- temporal and spatial?

A better way to say this is that you are concerned
with both temporal and spatial frequencies in the case of
motion video. (And, in the case of still images - as in
digital still photography - spatial frequencies only.)

II. Digital vs. Analog

Sample-rate is a digital entity.

Not really. While today most sampled systems are, in fact,
"digital" in nature (meaning that the information is encoded in
digital form), there is nothing in sampling theory which restricts
its applicability to that realm. Sampled analog systems are certainly
not very common today (unless you count certain forms of
modulation as "sampling," and in fact there are some very close
parallels there), but the theory remains the same no matter which
form of encoding is used. In any event, you must sample the
original signal at a rate equal to at least twice its bandwidth (actually,
very slightly higher, to avoid a particular degenerate case which
could occur at EXACTLY 2X the bandwidth) in order to preserve
the information in the original and avoid "aliasing."

Bob M.