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Chapter 5.5.3 equation 5.21
February 15, 2015
11:46 pm
disketto
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Hi Will,
i am maybe a bit rusty and probly missing something at the equation 5.21

What it looks to me is that the result should be sqrt( 0.25 - 0.25j^2 )

what are the passages to get to sqrt( 0.25 + 0.25 ) ? maybe considering j = sqrt(-1) ?

Thanks !

February 16, 2015
1:18 am
W Pirkle
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multiplying out you get:

|H(jw)| = 0.25 +j025 - j0.25 -j^20.25

= 0.25 -j^20.25

and j^2 = -1

so 0.25 + j0.25

- Will

February 17, 2015
6:29 am
disketto
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thanks !
but this gave me another doubt... sorry

in equation 5.65 / 5.66
so j^2 = -1

we have 0.19 + j0.27

so we should have sqrt( 0.19^2 (-) 1.27^2 ) ? that gives me 1.25
what i am missing ?

thanks again !

February 17, 2015
6:10 pm
W Pirkle
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Maybe a good calculator?

sqrt(0.19^2 + 1.27^2) = 1.284133

- Will

February 25, 2015
1:39 am
disketto
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Hi Will,
maybe i didn't explain very well....

B^2 should not be = J^2*1.27^2 ?

so if J^2 = -1

from 0.19 + J0.27
A^2+B^2 = 0.19^2 + J^2*1.27^2 we have 0.19^2 - 1.27^2 not 0.19^2 + 1.27^2

i just wanted to understand the step that i didn't get....

- Vito

March 3, 2015
9:25 pm
W Pirkle
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Hi Vito

Sorry for the delayed response - I got off on another tangent.

When you use the equation sqrt(a^2 + b^2) you don't square the j term. You only square the coefficient, b. So, j does not get squared, just b.

However, when multiplying out the polynomials for reduction, you very often will run into a j^2 term, which will evaluate to -1.

- Will

March 5, 2015
5:41 am
disketto
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oh ! i understand !

Thanks Will

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