Steven M. Bak

Like many, I have spent the last two days hitting the refresh button on my Yahoo NCAA Bracket.

I was curious as to how many possible bracket picks there are. Being a computer guy this is a very easy question to answer. A game is binary, you either win, or you loose. There are 63 games played. (32+16+8+4+2+1 or 11111 in binary)

Anyways 2 outcomes for each 63 games is 2^63 possibilities. Thats far, far, far more than what most people would expect.
In computer terms that is over 8 million terabytes of data!

Here is a little binary math:
2^10 = 1024 == 1000 == 1k
2^30 = 1k*1k*1k ==1 gig
2^40 = 1k*1gig == 1 tb
2^50 = 1k * 1tb
2^60 = 1k * 1k * 1tb == 1 million terrabytes
2^3 = 8

8 Million Terabytes!

Spent some time on the problem for homework in my Communication Theory Course. The problem is a Fourier Transform of a damped sinusoidal wave. I plan on adding Matlab Graphs in a couple days…

Here, g(t) is the signal in the time domain. G(f) is the transform to the frequency domain. Enjoy!

$g(t)=e^{-t}sin(2\pi{f_{c}}t)u(t)$

$G(f)=\int_{\small-\infty}^{\small\infty}e^{-t}sin(2\pi{f_{c}}t)u(t)e^{-j2\pi{f}t}dt$

$G(f)=\int_{\small0}^{\small\infty}e^{\small-t}\frac{e^{j2\pi{f_{c}}t}-e^{-j2\pi{f_{c}}t}}{2j}e^{-j2\pi{f}t}dt$

$G(f)=\frac{1}{2j}\int_{\small0}^{\small\infty}e^{j2\pi{f_{c}}t-t-j2\pi{f}t}-e^{-j2\pi{f_{c}}t-t-j2\pi{f}t}dt$

$G(f)=\frac{1}{2j}\biggl[\frac{e^{-t(-j2\pi{f_{c}}+1+j2\pi{f})}}{-j2\pi{f_{c}}+1+j2\pi{f}}\biggr]_0^{\infty}-\frac{1}{2j}\biggl[\frac{e^{-t(j2\pi{f_{c}}+1+j2\pi{f})}}{j2\pi{f_{c}}+1+j2\pi{f}}\biggr]_0^{\infty}$