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Apprentice
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(The University of Texas at San Antonio)
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posted by  chobelo on 11/7/2009 12:57:37 AM  |  status: Live  |  Earned Karma: 135

geometric sum math

Course Textbook Chapter Problem Needs by
Digital Signal Processing N/A N/A N/A 11/9/2009 at 11:00:00 PM
Question Details:

I don't understand what steps they are taking in this process.  Please explain quick I have a test coming and I am lost with this problem.
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Sage
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(IIT Kharagpur)
posted by Chelsea_fan(MNK) on 11/7/2009 1:32:09 AM  |  status: Live
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Response Details:

we replace the 1,s in following steps,

in the 2nd step,


now, ejw/2/ejw/2 =1

as also, e5jw/2e-5jw/2
           =  e0= 1

so basically we are modifying the first step ...
to get the form sinθ form ..
Mentor
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posted by Abdul Rafay on 11/7/2009 10:20:39 AM  |  status: Live
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Response Details:
question is not complete, i mean last step is not correct.
eponentional is missing
Abdul Rafay
Sage
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(IIT Kharagpur)
posted by Chelsea_fan(MNK) on 11/7/2009 11:49:27 AM  |  status: Live
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Response Details:
 

now we know,
ejx=cosx+jsinx
e-jx=cosx-jsinx

∴ej5w/2=cos5ω/2+jsin5ω/2
   e-5w/2=cos5ω/2-jsin5ω/2

subtracting, ej5w/2-e-j5w/2=2jsin5ω/2

so numerator =2jsin5ω/2

again,

ejw/2=cosω/2+jsinω/2
e-jw/2=cosω/2-jsinω/2

again subtracting, ejw/2-e-jw/2=2jsinω/2

so [ej5w/2-e-j5w/2]/[ejw/2-e-jw/2]=sin5ω/2 / sinω/2
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