Graphing fequence of the signal

[cutesteph]

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)

How would I graph F(W)?


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 F(W) for this?

 

[Simon Bridge]

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)

How would I graph F(W)?

You wouldn't - no F(W) has been given.
You have an X(W) - which seems to be the fourier-series expansion of x(w) or something.
As it is written, it does not seem to depend on W though - but on w.
It helps if you say what things are.

Anyway - if your problem is to graph a sum of complex exponentials - you'd either plot the real and imaginary parts separately or plot the trajectory in the complex plane.

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 F(W) for this?

Again - no F(W) or any indication how it may be related to x or X. Same advise I guess.

 

[cutesteph]

I mean X(F).

 

[Simon Bridge]

I don't see any X(F) either.
What are these things supposed to represent?

 

[alphy]

To graph the frequency of the signal, you would plot the values of F(W) on the y-axis and the corresponding values of W on the x-axis. The graph would be a continuous line for the first scenario, where the signal is discrete, and a smooth curve for the second scenario, where the signal is continuous. The x-axis would range from 0 to 4, as that is the interval given in both cases. The y-axis would depend on the values of F(W), which can be calculated using the equations provided. You can also use software like MATLAB or Python to plot these graphs.