[Ian Iveson]

If I take two photographs of the same size and scale, each
of a different part of a starry sky, and superimpose them,
will the result have the same characteristics as each of the
components? Will it appear to be twice as dense as a normal
starry sky? Will it appear to have areas twice as bright? If
I enlarge the composite photograph, will there come a point
when it looks like normal starry sky again? Is there such a
thing as normal starry sky? What does random look like?

One of the problems of Phil's "summing noise sources"
thread, IMHO, is that Phil began by leaping from the
frequency domain to the transient domain without due
caution. "random", "pink", "white" and "bandwidth limited"
are all features we would associate with the frequency
domain, i.e. we might show them on a graph with frequency
along the horizontal axis, and
amplitude up the vertical axis...the view of a spectrum
analyser.

"Crest Factor" on the other hand, is derived from the
transient domain, that is with time along the horizontal
axis and amplitude up the vertical. The peak voltage of a
signal as viewed on an oscilloscope is also in the transient
domain.

Mapping from one domain to the other is by no means simple.
So it seems in *my* head, anyway.

For example, if I take the outputs of two noise sources,
each of the same frequency distribution (pink, white,
whatever) and each with the same bandwidth limits, and sum
them with a mixer of very wide bandwidth, will the composite
noise signal have the same bandwidth limits as the original
two? Will it have the same frequency distribution? Will it
sound the same if I adjust it to the same level? How are
these things related to the original distribution?

If noise, viewed now on an oscilloscope, appears to have
peaks up to some maximum level "hundreds of times a second",
where does this maximum level come from? Is it related to
the frequency distribution? Phil says that "CF for band
limited pink noise is often quoted as being about 4 or 12
dB.", which expresses a relationship between the two
domains, but is it meaningful?

If this maximum level in the transient domain does not
relate to a specified feature of the distribution in the
frequency domain, then to what does it relate? It is a
constraint on the meaning of "random", obviously. So is this
"random noise" level-limited as well as bandwidth limited?

Does the level have its own distribution, and how is the
distribution of level related to the distribution of
frequencies?

Is it possible to have an "anomaly" in a relationship which
does not exist?

As you were...

Ian