Thanks. I've got it in this form now:
{\frac {2\,i \left( \sin \left( 4\,\omega \right) \right) ^{2}{{\rm e}^{-15/2\,i\omega}}}{\sin \left( 1/2\,\omega \right) }}
After all this I found a formula for any equation in the form u(n) - u(n-L). Thanks for the help.
Well I feel stupid. I saw this formula but like I said in my original post I thought I couldn't use it since series wasn't approaching zero. I guess I was being stupid and thinking about infinite series. Since this is finite of course I can use that.
If my math is right I get
{\frac {...
So I'm trying to find the DTFT of the following; where u(n) is the unit step function.
u \left( n \right) =\cases{0&$n<0$\cr 1&$0\leq n$\cr}
I want to find the DTFT of
u \left( n \right) -2\,u \left( n-8 \right) +u \left( n-16 \right)
Which ends up being a piecewise defined function...
Tell me if this works:
log(z-1) = log(-1) + log(1-z) = Log|-1| + i\cdotarg(-1) + log(1-z)
= 0 + i\cdot\pi + log(1-z)
So I end up with f(z) = log(1-z) + i\cdot\pi
Then I could use the principle argument because now the cut is at real values of x ≥ 1. Which is outside the inside of the...
So if I understand right from what I've got in my notes I can just start my branch at some arbitrary point say something like.
\tau<arg(w)≤\tau+2\pi
Where \tau = \pi/4 maybe?
However, then the function would not be analytic at the angle \tau on the unit circle am I right?
Homework Statement
Find a branch of log(z − 1) that is analytic inside the unit circle. What is the value of this branch at z = 0?
2. The attempt at a solution
Alright so clearly the log(z) function is analytic at all points accept for the negative real axis.
So log(z-1) will be...
Thanks both of you. I'm glad I'm not crazy. Sorry I guess I didn't mean convention. I guess it would have been better to say that its the way its done by people like me who are "anal." I'll go talk to my TA about this and get my 6 points back. He only gave me 4/10 for the question.
And it was...
Ok so I just got my test back for Linear Algebra and I was told to find a basis for the ker(A) where A = \begin{array}{cccc} 1 & 1 & 0 & 1 \\ 1 & 0 & -1 & 0 \\ 0 & 1 & 1 & 1 \\ -1 & 1 & -1 & -2 \end{array}
now I computed Ax = 0 and found x = [-t, 0 ,-t, t]^T. where x4 = t.
Then I wrote the...
I think I get it. I was reducing the matrix wrong. I think I have the correct rref of the matrix now. Take a look and let me know what you think.
Solution
Homework Statement
http://img94.imageshack.us/img94/5227/nxnmatrix.png Homework Equations
Rank(A) = the number of pivots in Matrix A.
The Attempt at a Solution
I've spent some time rewriting the matrix and other operations. I really just feel like I'm banging my head against the wall. Not...
http://img811.imageshack.us/img811/3791/001sfe.jpg
There. I know you guys love seeing work. : ]
I feel like I'm just throwing math at this problem and not really thinking about what its even asking for. I'm grasping at strings here. Saw a few relations between Δx and standard deviation and...
Homework Statement
Suppose that at one instant in time the wavefunction of a particle is
ψ(x) = \sqrt{b}e-b|x|
Estimate the uncertainty of Δx for this wavefunction.
Homework Equations
ΔxΔp ≥ h(bar)/2
h(bar) = h/2pi
The Attempt at a Solution
Do I just calculate the...
Hmmm, I guess I got confused by v(x) having cos(t) in it. My book literally says "find a function v(x), independent of 't.'
I'll keep working it. I'll return if I need help. Or if I figure it out.
http://img821.imageshack.us/img821/7901/heatp.png
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I'm having difficulty with the boundary conditions on this problem. I don't need a solution or a step by step. I've just never solved a boundary condition like this.
Its the u(pi,t) = cos(t) that is giving me...