# Impulse signal equation

Discussion in 'Homework Help' started by Anthony Quah, Mar 31, 2008.

1. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
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i got the frequency equation but when i read how to get the impluse equation ..i dont know how it can change to other format with exp (-2jw) disappear..in other word i dont know how the formula get there...need help to solve it..

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2. ### studiot AAC Fanatic!

Nov 9, 2007
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HI tony,

The secret is the simple factorisation of the denominator in your first expression.

You need to factors in the form (1-1/n*exp(-jw)) * (1- 1/m*exp(-jw))

where product of 1/n*1/m is 1/6 and the sum is -5/6.

1/2 and 1/3 fit this bill.

The 2 in the exponential comes from the fact that in the factorisation you multiply the two exponentials together (squaring).

Sorry I haven't the time to produce a worked through version, but if this hint does not help post again and I will.

3. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
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studiot,

i will really appreciate if you can post the work of the equation..i little confuse here :-(

4. ### studiot AAC Fanatic!

Nov 9, 2007
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If you do much transform analysis you will meet partial fractions many times. So it is worth revising the algebra of factorisation and partial fractions if you are rusty here. Also worth remembering that multiplication results in addition of exponents. So

exp(-2jw) = {exp(-2jw)}^2 [squared] = exp(-jw) times exp(-jw)

Here is the detailed working.

Sorry I haven't yet conquered getting formulae onto a post.

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5. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
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thank studiot, i just try to ask my lecturer about this question...he seem to be confuse as well..maybe by seeing ur solution he will more understand..lol...anyway really appreciate it..

6. ### studiot AAC Fanatic!

Nov 9, 2007
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It would be interesting to hear what your lecturer said about my working.

7. ### Anthony Quah Thread Starter Active Member

Dec 1, 2007
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yeah..but u have to wait til monday..my class in on monday...^^

8. ### studiot AAC Fanatic!

Nov 9, 2007
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Hello Anthony, welcome back. Now that Monday has arrived, it would still be interesting to hear what your lecturer said.

9. ### thingmaker3 Retired Moderator

May 16, 2005
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I just hate it when I fall through time warps before having my coffee. Especially when said time warp cheats me out of a weekend!