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From: Steve Pope on 6 Aug 2010 13:37
robert bristow-johnson <rbj(a)audioimagination.com> wrote:

>On Aug 6, 9:47�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).

>if that is how you define the bandwidth of the rectangular pulse
>signal to begin with, yes. some might define such bandwidth
>differently (e.g. the difference between the -3 dB points). there is
>no final definitive definition of bandwidth, as far as i can tell from
>the lit. different definitions pop up in different applications.

I concur. 3 dB bandwidth is one common term. Equivalent noise bandwidth
is another common term and is for most functions somewhat larger.
Yet a third term is "occupied bandwidth", an even larger measure
encompassig almost all of the signal power.

One possible confusing point: you need to look at the bandwidth
of the sinc function after it has been translated to the center
frequency defined by the sinusoid. So because of this it is a bandpass,
and not a lowpass function.

Steve
From: Greg Heath on 6 Aug 2010 13:50
On Aug 5, 7:23 pm, spop...(a)speedymail.org (Steve Pope) wrote:
> dbd  <d...(a)ieee.org> wrote:
> >On Aug 5, 3:02 pm, "cwoptn" <gopi.allu(a)n_o_s_p_a_m.gmail.com> wrote:
> >> I have a very basic question. I am little bit confused about how to know
> >> the bandwidth of a time-limited pure sinusoidal signal. I understand
> >> bandwidth is defined simply as the difference between highest frequency and
> >> lowest frequency, and the bandwidth of a infinitely long pure sinusoid if 0
> >> Hz. But if I have a N sample long 50 Hz sinusoid (sampled at Fs samples per
> >> second), how to find bandwith of this signal?
> >The bandwidth of the truncated pure sinusoid is equal to the
> >"effective noise bandwidth" (enbw) of the truncating function, often
> >given in terms of dft bins (Fs/N). For a rectangular truncation
> >function (window), the enbw is 1.0, so 1.0 x Fs / N.
> >For other truncating functions, you can look in the usual windows
> >references like:
> >On the Use of Windows for Harmonic Analysis
> >with the Discrete Fourier Transform
> >fred harris,
> >from the IEEE proceedings. available at:
> >http://web.mit.edu/xiphmont/Public/windows.pdf
> >(beware errors in some Blackman and Blackman-Harris window parameters)
>
> I find it interesting how often a continuous-time question
> leads to a discrete-time answer on this newsgroup.

I find it even more interesting how often a discrete-time
question leads to a continuous-time answer on comp.ctsp

Greg
From: Steve Pope on 6 Aug 2010 14:05
Greg Heath <heath(a)alumni.brown.edu> wrote:

>I find it even more interesting how often a discrete-time
>question leads to a continuous-time answer on comp.ctsp

Good one!

S.
From: Fred Marshall on 6 Aug 2010 17:15
cwoptn wrote:
> Hi Folks,
>
> Thank you again for all your valuable inputs. 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).
>
> Thanks again,
> -- cwoptn

I'd not say that flat out - but you may.. As I mentioned earlier, the
sinc or Dirichlet "tails" show up all over the place - also called
"spectral leakage". So then it's a matter of what's important in
defining "bandwidth".

Fred
From: Ron N. on 6 Aug 2010 19:03
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




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