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From: dbd on 6 Aug 2010 21:28
On Aug 6, 4:03 pm, "Ron N." <rhnlo...(a)yahoo.com> wrote:
> On Aug 6, 6:47 am, "cwoptn" <gopi.allu(a)n_o_s_p_a_m.gmail.com> wrote:
>
> > So if I use rectangular
> > window of N samples as the truncating function, the bandwidth of the
> > resulting signal (for all practical purposes) is simply the main lobe width
> > of the Sinc function (corresponding to N sample long rectangular window in
> > time domain).
>
> The second lobe peaks at over 20% of the main lobe.
> Do you care about those outlying "frequencies" in your
> bandwidth requirement or definition?
>
> --
> rhn A.T nicholson d.0.t C-o-M

It is merely interesting that the effective bandwidth of the
rectangular truncation function is the same as the (half) width of the
main lobe of the Fourier transform of the truncation function. The
effective bandwidth is calculated from the application of Parseval's
theorem to the samples of the truncation function, as shown in the
cited reference, and includes the power in all sidelobes.

Dale B. Dalrymple
From: Greg Heath on 7 Aug 2010 17:34
On Aug 6, 7:03 pm, "Ron N." <rhnlo...(a)yahoo.com> wrote:
> On Aug 6, 6:47 am, "cwoptn" <gopi.allu(a)n_o_s_p_a_m.gmail.com> wrote:
>
> > So if I use rectangular
> > window of N samples as the truncating function, the bandwidth of the
> > resulting signal (for all practical purposes) is simply the main lobe width
> > of the Sinc function (corresponding to N sample long rectangular window in
> > time domain).
>
> The second lobe peaks at over 20% of the main lobe.

If the bandwidth is defined w.r.t. power, the 20% amplitude
converts to only 4% in power.

MATLAB:

figure
plot(0:0.1:10, sinc(0:0.1:10))
hold on, plot(0:0.1:10, sinc(0:0.1:10).^2,'r')

Hope this helps.

Greg

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