Post by steveataps on Nov 28, 2012 17:55:14 GMT -5
Hi Forum, a basic question on linear time invariant filter BER:
Does the optimum yes/no linear time invariant decision maker use ONLY the maximum value of the signal after the matched filter? Clearly that is the best SINGLE data point to use. Is there no improvement in BER if we bring in information before/after this peak?
For example, my input pulse (coming from a photon detector) looks a lot like a gaussian rise/fall. Let the peak LTI output be at sample time #10, gently rising before, gently falling after.
Is the best decision (hit/no hit) made using ONLY sample #10 versus a threshold discriminator? This would be easier to implement.
Or, would we do better if we used sample #9 and #11 in some weighted vote? It then becomes a question "ok, but is this worth the price of extra circuitry?" which is beyond the scope here.
But finally, a bonus question, what if we care more about false positives than missed events, or visa versa? What is the mathematical formalism to slant the errors one way or another? (reference?)
thank you.
Steve
p.s.
I read, and somewhat understand, the 2003 tutorial on matched filters in the time domain:
www.complextoreal.com/chapters/mft.pdf
Does the optimum yes/no linear time invariant decision maker use ONLY the maximum value of the signal after the matched filter? Clearly that is the best SINGLE data point to use. Is there no improvement in BER if we bring in information before/after this peak?
For example, my input pulse (coming from a photon detector) looks a lot like a gaussian rise/fall. Let the peak LTI output be at sample time #10, gently rising before, gently falling after.
Is the best decision (hit/no hit) made using ONLY sample #10 versus a threshold discriminator? This would be easier to implement.
Or, would we do better if we used sample #9 and #11 in some weighted vote? It then becomes a question "ok, but is this worth the price of extra circuitry?" which is beyond the scope here.
But finally, a bonus question, what if we care more about false positives than missed events, or visa versa? What is the mathematical formalism to slant the errors one way or another? (reference?)
thank you.
Steve
p.s.
I read, and somewhat understand, the 2003 tutorial on matched filters in the time domain:
www.complextoreal.com/chapters/mft.pdf