Re: frequency time resolution


"Ron N." <rhnlogic@xxxxxxxxx> wrote in message
news:1191972933.432482.20740@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Oct 9, 11:51 am, "Fred Marshall" <fmarshallx@xxxxxxxxxxxxxxxxxxxx>
wrote:
Here's a simple example:
If you have two purely sinousoidal responses that are 0.6Hz apart and are
both 500msec in length (exactly) then observing the distance between
zero-crossings will tell you that they are 0.6Hz apart. But, to observe
the
zero-crossing points that precisely will take a lot more samples - it
implies a wide bandwidth process being applied to a lower-bandwidth
signal.
That's the same as if the signal were wide bandwidth itself.

Knowing what you're trying to accomplish is often helpful.
I take it that you intend to compare frequency content of multiple
responses.
So, is there any physical reason to expect that there will be frequencies
that are so close together that differentiating them would be useful?
What physical mechanism in the brain is capable of differentiating
between
two 500msec purely sinusoidal responses that are .6Hz apart? Somehow I
doubt such a physical mechanism exists.

This is not in my area of expertise, but it seems like
the brains of bats might be able to discriminate some very
small phase differences in the neural firings from their
transducer apparatus in order to successfully echolocate
tiny moving lunch snacks in the dark.

An interesting book I discovered recently:
"Blip, Ping, and Buzz: Making Sense of Radar and Sonar"
by Mark Denny
Johns Hopkins University Press 2007

talks about this a bit.


Ron,

Well, I've had *some* experience with the use of wideband signals in active
sonar - and computer simulation thereof. In simulation we generated receive
beamformer output signals. Original work was done with CW pulses. As wider
bandwidths became of interest due to the availability of more processing
power then the simulators had to keep up. This meant that the bandwidth of
the simulated receive signals had to be "wide enough"

Even with CW pulses, range resolution could be had if the receiver bandwidth
was wide enough. That's because the leading edge of a pulse could be
detected with quite a bit of range resolution improvement. It takes high
SNR and wide bandwidth - which is somewhat to the point of this thread.

In the olden days, with no matched filters, the receivers could (and often
would) be full bandwidth. Good signal processing took advantage of the
bandwidth and SNR as above. With introduction of matched filters the
detectability of signals may have been improved but the resolution suffered
accordingly.

In CWFM radar the idea is to compare the frequency of the current transmit
signal with the frequency of the current received signal to determine range.
A mixer gives an LF beat signal that's proportional to frequency difference,
thus range. So I suppose that bats could do something similar. I'm not
sure about differential phase measurement in physiology of bats. But, like
the sonar, time differences might be pretty easy to detect.

Fred


.

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