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From: Tim Wescott on 6 Aug 2010 00:54
On 08/05/2010 04:23 PM, Steve Pope wrote:
> dbd<dbd(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.

>>>>>>> LOOK HERE >>

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.
>

Discrete time question -- although the answer is just as valid in
continuous time.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
From: Steve Pope on 6 Aug 2010 01:31
Tim Wescott <tim(a)seemywebsite.com> replies to my post,

> >>>>>>> LOOK HERE >>
>
>But if I have a N sample long 50 Hz sinusoid (sampled at Fs samples per
>second),

><<<<<<<<<<
>> I find it interesting how often a continuous-time question
>> leads to a discrete-time answer on this newsgroup.

>Discrete time question -- although the answer is just as valid in
>continuous time.

Okay you're right. I should not have jumped on that one.


Steve
From: cwoptn on 6 Aug 2010 09:47
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
From: robert bristow-johnson on 6 Aug 2010 11:29
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.

r b-j

From: Tim Wescott on 6 Aug 2010 12:37
On 08/06/2010 06:47 AM, 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).

That's a good definition of the "useful communications" bandwidth. But
it's not a good definition at all of the "doesn't interfere with
adjacent channel" bandwidth.

Any time your spectrum isn't a perfect rectangle* you have to define
what you mean by bandwidth for your immediate purpose -- and be prepared
to change your definition when your immediate purposes change.

* And no real-world signal is going to have a perfectly rectangular
spectrum.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
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