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I'm quite incapable of integrating SIN(x^2)/x^2 from first principles (or
any other way for that matter :-) to calculate the level of the main lobe.
Can anyone point out the best way to do this calculation ?
Dear Andy and all,
If the only problem is the calculation of the integral - try Derive. I have
an old DOS version at home. I do not have it at work at the moment, however
I found a demo (30-day trial) version of Derive5 for Windows at
http://www.derive-europe.com/ .
At http://cobjs.compu-ag.de/nonhacking/derive/ you can find a pirated(?)
German version of the software, if you prefer.
OK, assuming that you've installed it, to simply calculate the difinite
integral of sin(x^2)/(x^2) do the following:
- in the bottom line type sin(x^2)/(x^2) and Enter - the expression should
appear and should be marked (selected)
- go to menu: Calculus->Integrate
- Variable: x, select Definite, set Lower and Upper limit, press OK. A
beautiful integral sign should appear and the whole expression should be
marked (selected)
- go to Menu: Simplify->Approximate, select the desired accuracy and press
Approximate.
If you play around, you'll find a way to draw a nice plot of your
function...
73! Marek SQ5BPM
P.S. I just found the old Derive for DOS in the Internet, but... I realised
that an unexperienced user will probably get even more puzzled than when
using the German version for Windows without knowing German HI. But - you
can try it: http://www.geocities.com/andreubass/programes/derive.zip . Unzip
it to a new folder and run derive.exe. In this version you do everything
with the keyboard only, mostly by pressing letter keys. So, just to start
the VGA graphics mode, to be able to plot, do this (press the letters in
square brackets): [O]ptions [D]isplay [G]raphics [H]igh [V]GA [Enter]
multi[S]ync. Now an example, how to plot a simple function: [W]indow [S]plit
[V]ertical [W]indow [N]ext [W]indow [D]esignate [2]D-Plot [W]indow [N]ext .
Now press [A]uthor and for example type x^2 [Enter]. Now [P]lot [P]lot.
Beautiful, isn't it? To go back, press [A]lgebra. Play around. You can
reference to your previous equations by typing #n, for example to do now
sin(x^2)/(x^2), you could use [A]uthor and sin(#1)/#1, because x^2 has just
been saved under #1. To make an integral, you can use [C]alculus
[I]ntegrate, it is similar to the Windows version.
We used this nice software in the secondary school, about 10 years ago, but
I still use it when I have to quickly check something like (try it) :
lim((x^2+1)/(x^2),x,inf) and then [S]implify. In this case the result is
obvious, but this is just as an example what this software is capable of.
Remember that this software has been written to run even on an IBM PC-XT
with a Hercules "graphic card"! I know that there are much better
mathematical programs than this old Derive but... I think that the best
software is the software you know the best :D
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