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

In summary, the conversation discusses the calculation of X(W) for a given signal, using the sum and integral formulas. The question also pertains to graphing the amplitude and phase of X(W) and finding the real and imaginary parts using Euler's formula.
  • #1
cutesteph
63
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?
 
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  • #2
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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FAQ: Graph Amplitude and Phase of x(n) and x(t)

What is meant by "amplitude" and "phase" in relation to graphs of x(n) and x(t)?

Amplitude refers to the magnitude or strength of a signal, while phase refers to the relative position or timing of the signal. In the context of graphs of x(n) and x(t), amplitude and phase are used to describe the characteristics of a signal over time or discrete points.

How is amplitude represented on a graph of x(n) and x(t)?

Amplitude is typically represented on the vertical or y-axis of a graph, with larger values indicating higher amplitudes and smaller values indicating lower amplitudes. The scale of the y-axis is determined by the range of values of the signal being graphed.

Can the amplitude and phase of a signal change over time?

Yes, the amplitude and phase of a signal can change over time. This is often seen in signals that are periodic or have a repeating pattern, where the amplitude and phase may vary with each cycle of the signal.

How is phase represented on a graph of x(n) and x(t)?

Phase is typically represented on the horizontal or x-axis of a graph, with time increasing from left to right. The phase of a signal at any given point on the graph is determined by its position relative to the starting point or reference point.

How can understanding the amplitude and phase of a signal be useful for analysis?

Understanding the amplitude and phase of a signal can provide valuable information about its characteristics, such as its frequency and shape. This can be useful for identifying patterns, detecting anomalies, and predicting future behavior of a signal.

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