Re: Fourier Transform Question for Pulsed CW and 802.11b DSSS


<radio913@xxxxxxx> wrote in message
news:1130773278.863889.128080@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>
>>
>> = 2a * sinc(wa)
>>
>
>
> I would like to see where the
> pulse repetition interval comes into
> play here (PRI), and how the spacing
> of the frequencies are 1/PRI, and how
> the spacing of the sinx/x lobes are
> 1/T, where T is the "on" period of the
> CW pulse.
>

Hello Slick,

Since we now know that a pulse with width 2a has a FT of 2a since(wa), then
to see the pulse repetition interval, find the zeros of the sinc function.
Since the sinc is a fraction with nonzero denominator, it suffices to find
the zeroes of the numerator recalling the 0/0 case at the origin needs
special handling. The zeroes of sin(x) occur at multiples of pi.

So the zeroes of sinc(wa) occur where wa = n*pi and n is an integer except
when n=0. So solve for w and you find w(n) = n*pi/a. Since n is an integer
with the aforementioned caveat, the repetition interval is simply pi/a.

IHTH,
Clay



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