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

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SUMMARY

The discussion focuses on calculating the amplitude and phase of the discrete signal x(n) = n for 0 ≤ n < 4 and the continuous signal x(t) = t over the same interval. The Fourier transform for the discrete signal is derived as X(W) = 0 + exp(-iw) + 2exp(-j2w) + 3exp(-j3w). For the continuous signal, the Fourier transform is calculated as X(W) = (4exp(-i4w)/-iw) - (exp(-iw4) - 1)/w². The conversation emphasizes the need to graph the amplitude and phase, suggesting the use of Euler's formula to extract real and imaginary parts of X.

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cutesteph
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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?
 
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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).
 
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