Why the integral is zero

Hi

I wonder why when it is assumed W>>1/T in many communication or other
electrical engineering problems then integral of cos(wt) from 0 to T is
approximated to be zero?

isn't that true that this integral should be 1-cos(wT)/w 

I understand that if w is very big the integral is zero but what if w=1
and T=100 then the integral can't be approximated to zero.
Therefore why integral always approximated to be zero? Is there something
that I am missing or there is something that I am not taking into
account?

Thanks.


---------------------------------------
Posted through http://www.DSPRelated.com

On 03.12.2015 11:09, chess wrote:
> Hi

(snip)

> isn't that true that this integral should be 1-cos(wT)/w
>

No way, it's sin(wT)/w

--
Evgeny.

>On 03.12.2015 11:09, chess wrote:
>> Hi
>
>(snip)
>
>> isn't that true that this integral should be 1-cos(wT)/w
>>
>
>No way, it's sin(wT)/w
>
>--
>Evgeny.

I meant integral of sin(wT) from 0 to T? But anyway still sin(wT)/W is
also approximated to zero in telecommunication.
---------------------------------------
Posted through http://www.DSPRelated.com

On Thu, 03 Dec 2015 02:09:10 -0600, chess wrote:

> Hi
> 
> I wonder why when it is assumed W>>1/T in many communication or other
> electrical engineering problems then integral of cos(wt) from 0 to T is
> approximated to be zero?
> 
> isn't that true that this integral should be 1-cos(wT)/w
> 
> I understand that if w is very big the integral is zero but what if w=1
> and T=100 then the integral can't be approximated to zero.
> Therefore why integral always approximated to be zero? Is there
> something that I am missing or there is something that I am not taking
> into account?
> 
> Thanks.

What is your W, what is your T, where are you seeing cos(wt) integrating 
to zero in the literature?

-- 

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

chess <106766@dsprelated> wrote:
>>On 03.12.2015 11:09, chess wrote:
(snip)

>>> isn't that true that this integral should be 1-cos(wT)/w

>>No way, it's sin(wT)/w

(snip)
> I meant integral of sin(wT) from 0 to T? But anyway still sin(wT)/W is
> also approximated to zero in telecommunication.

If there is a specific origin to time, and the signal being intgegrated
(or averaged) is known to start at a specific time, then you would
need to include it.  That is, the transient solution for a 
differential equation.

But in many cases you don't know, or care, where the signal starts
or ends, but only want to know the steady state solution. 

I know that the AC power line can be represented as A sin(wt),
or A cos(wt), (use appropriate A and w for your country), but I
don't know, or care, where t=0.  Is it when the plant was
built?  Some will choose sin() or cos() specifically to avoid
this question.

If I average the power line voltage for a year, I expect the
average to be zero, not A/w. Well, A/(wT) where T = 1 year.

Any signal that it transformer or capacitor coupled is assumed
to average to zero, for long enough time, unless there is a specific
need to consider the transient solution. 

In the actual case, for long enough T, either transformer loss or
capacitor leakage will remove any initial condition.

-- glen

>On Thu, 03 Dec 2015 02:09:10 -0600, chess wrote:
>
>> Hi
>> 
>> I wonder why when it is assumed W>>1/T in many communication or other
>> electrical engineering problems then integral of cos(wt) from 0 to T
is
>> approximated to be zero?
>> 
>> isn't that true that this integral should be 1-cos(wT)/w
>> 
>> I understand that if w is very big the integral is zero but what if
w=1
>> and T0 then the integral can't be approximated to zero.
>> Therefore why integral always approximated to be zero? Is there
>> something that I am missing or there is something that I am not taking
>> into account?
>> 
>> Thanks.
>
>What is your W, what is your T, where are you seeing cos(wt) integrating

>to zero in the literature?
>
>-- 
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com

W is a angular frequency and T is duration of integration. This
approximation is used in telecommunication and communication system. 
---------------------------------------
Posted through http://www.DSPRelated.com

On Thu, 03 Dec 2015 12:48:13 -0600, chess wrote:

>>On Thu, 03 Dec 2015 02:09:10 -0600, chess wrote:
>>
>>> Hi
>>> 
>>> I wonder why when it is assumed W>>1/T in many communication or other
>>> electrical engineering problems then integral of cos(wt) from 0 to T
> is
>>> approximated to be zero?
>>> 
>>> isn't that true that this integral should be 1-cos(wT)/w
>>> 
>>> I understand that if w is very big the integral is zero but what if
> w=1
>>> and T0 then the integral can't be approximated to zero.
>>> Therefore why integral always approximated to be zero? Is there
>>> something that I am missing or there is something that I am not taking
>>> into account?
>>> 
>>> Thanks.
>>
>>What is your W, what is your T, where are you seeing cos(wt) integrating
> 
>>to zero in the literature?
>>
>>--
>>
>>Tim Wescott Wescott Design Services http://www.wescottdesign.com
> 
> W is a angular frequency and T is duration of integration. This
> approximation is used in telecommunication and communication system.

Yes, thank you.  Strangely enough I was pretty sure that was the case.  
Without some pointers to specifics in the literature, I cannot tell you 
if the authors are taking shortcuts, if you're missing something, both, 
or neither.

-- 

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

On Thu, 03 Dec 2015 12:48:13 -0600, "chess" <106766@DSPRelated> wrote:

>>On Thu, 03 Dec 2015 02:09:10 -0600, chess wrote:
>>
>>> Hi
>>> 
>>> I wonder why when it is assumed W>>1/T in many communication or other
>>> electrical engineering problems then integral of cos(wt) from 0 to T
>is
>>> approximated to be zero?
>>> 
>>> isn't that true that this integral should be 1-cos(wT)/w
>>> 
>>> I understand that if w is very big the integral is zero but what if
>w=1
>>> and T0 then the integral can't be approximated to zero.
>>> Therefore why integral always approximated to be zero? Is there
>>> something that I am missing or there is something that I am not taking
>>> into account?
>>> 
>>> Thanks.
>>
>>What is your W, what is your T, where are you seeing cos(wt) integrating
>
>>to zero in the literature?
>>
>>-- 
>>
>>Tim Wescott
>>Wescott Design Services
>>http://www.wescottdesign.com
>
>W is a angular frequency and T is duration of integration. This
>approximation is used in telecommunication and communication system. 

Thanks for the clarification.   I thought it might have been W for
bandwidth and T for symbol period.    Or sample period.   Wasn't clear
to me.

That said, I still don't get the context of the question enough to
take a stab at an answer.



Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

>Hi
>
>I wonder why when it is assumed W>>1/T in many communication or other
>electrical engineering problems then integral of cos(wt) from 0 to T is
>approximated to be zero?
>
>isn't that true that this integral should be 1-cos(wT)/w 
>
>I understand that if w is very big the integral is zero but what if w=1
>and T0 then the integral can't be approximated to zero.
>Therefore why integral always approximated to be zero? Is there
something
>that I am missing or there is something that I am not taking into
>account?
>
>Thanks.
>
>
>---------------------------------------
>Posted through http://www.DSPRelated.com

The assumption should probably be stated as W >> 2Pi / T.  Whether this
matters to you is dependent on what >> means.

Anyway, if you imagine the graph from 0 to T, the bigger W is the more
full cycles there are going to be, and the skinnier each hump will be. 
Each full cycle will net zero area, so the only non-zero values which can
arise are from the last partial cycle.  The worst case is when the last
cycle only half completes and you are off by one hump of area.

If you think of the areas under the curve as being positive valued, the
area of the last hump (when there are a lot of humps) is insignificant
compared to the area of all the humps.

This is not farfetched when it is likely you are doing a power calculation
in which you square the amplitude.

Just some thoughts.

Ced
---------------------------------------
Posted through http://www.DSPRelated.com

>>Hi
>>
>>I wonder why when it is assumed W>>1/T in many communication or other
>>electrical engineering problems then integral of cos(wt) from 0 to T is
>>approximated to be zero?
>>
>>isn't that true that this integral should be 1-cos(wT)/w 
>>
>>I understand that if w is very big the integral is zero but what if w=1
>>and T0 then the integral can't be approximated to zero.
>>Therefore why integral always approximated to be zero? Is there
>something
>>that I am missing or there is something that I am not taking into
>>account?
>>
>>Thanks.
>>
>>
>>---------------------------------------
>>Posted through http://www.DSPRelated.com
>
>The assumption should probably be stated as W >> 2Pi / T.  Whether this
>matters to you is dependent on what >> means.
>
>Anyway, if you imagine the graph from 0 to T, the bigger W is the more
>full cycles there are going to be, and the skinnier each hump will be. 
>Each full cycle will net zero area, so the only non-zero values which
can
>arise are from the last partial cycle.  The worst case is when the last
>cycle only half completes and you are off by one hump of area.
>
>If you think of the areas under the curve as being positive valued, the
>area of the last hump (when there are a lot of humps) is insignificant
>compared to the area of all the humps.
>
>This is not farfetched when it is likely you are doing a power
calculation
>in which you square the amplitude.
>
>Just some thoughts.
>
>Ced
>---------------------------------------
>Posted through http://www.DSPRelated.com

The Integral is sin(Wt)/W [0,T] which is 1/W*(sin(WT)-sin(0)) which is
exactly zero.
---------------------------------------
Posted through http://www.DSPRelated.com