Graph Amplitude and Phase of x(n) and x(t)

cutesteph
Messages
62
Reaction score
0
Say x(n) = n for 0 <= n < 4 and 0 o.w.

So X(W) = Sum n=-∞ to ∞ x(n) exp(-inw) = sum from n=0 to 3 nexp(-inw)
= 0 + exp(-iw) + 2exp(-j2w) + 3 exp(-j3w)

get do I get the amplitude and phase?

Also if the signal was continuous x(t) = t for the same interval

X(W)= integral 0 to 4 texp(-iwt) dy = (4exp(-i4w)/ -iw) - (exp(-iw4) -1)/w^2

How would I graph the amplitude and phase?
 
Last edited:
Mathematics news on Phys.org
Is this related to your other thread: https://www.physicsforums.com/showthread.php?t=723594

What is it about the graph that is giving you trouble?
I presume you know how to draw axes and mark them off etc...

Perhaps you don't know how to find the real and imaginary parts of X.
Hint: http://en.wikipedia.org/wiki/Euler's_formula]Euler's[/PLAIN] formula).

Note: when you write X(W) we usually expect X to be a function of W ... which means that some W's should appear on the RHS. You appear to have X(w).
 
Last edited by a moderator:
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
Back
Top