On Mon, 17 Oct 2005 05:09:06 GMT, Owen Duffy wrote:

On Mon, 17 Oct 2005 03:09:11 GMT, Owen Duffy wrote:


So, theoretically:
- an ideal average responding meter should read (1-2/pi)% which is
36.3% or 8.8dB on an perfect square wave;

I think this is close to the right answer, but for the wrong reason. I
think it needs to be evaluated iteratively, and I get an answer closer
to 34.3% or 9.3dB.

An analytical approach to solution of the problem.

A unit height square wave has a fundamental component of amplitude
4/pi.

To find the area under the filtered curve, I think we are looking for
the integral from 0 to pi/2 of absolute(1-4/pi*sin(theta))). I will
divide the integral at theta=asin(pi/4) to deal with the absolute
function since the problem function is positive from 0 to asin(pi/4)
and negative from asin(pi/4) to pi/2.

Here is some Perl to evaluate the ratio:

#find the zero crossing point
$theta=asin($pi/4);
#find the area under the curve
$area=$theta-4/$pi*(-cos($theta)+cos(0)); #first part
$area+=4/$pi*(-cos($pi/2)+cos($theta))-($pi/2-$theta); #second part
#divide by area under unit square wave
$ratio=$area/($pi/2);
print "Average response ratio is $ratio \n";

And the answer is 0.3430678471... or 9.3dB. It is about 9.4dB if you
only consider the harmonics up to 50KHz.

One of you mathematical whizzes might know a better way to put this!

Owen
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