I have a set of coordinates which I transformed into a real piecewise function. The piecewise function looks as such:
as you can see, the coordinates are on the interval $[-5,5]$.
When I transform this into a Fourier transform using tempered distributions, I get:
as you can see, the peak at zero is reproduced from the piecewisefunction in the Fourier transform. However, the other peaks are symmetrized about the y axis, so they seem to be equalized.
Then, when I shift the coordinates by 5 units on the x-axis, to the interval [0,10] and preserve the y-points, I get:
which is the same as plot one, just shifted by 5 units on the x-axis.
Then, when I redo the procedure of Fourier tempered distributions, I get a completely different plot:
So this is an entirely different function.
If I am interested in the interval to the right of the high peak (at x=0 on the first plot), which of the two plots is the right one, to get a Fourier series of the interval on the right to the high peak at x=0 on top?
If this is not the best way to extract a continuous function that crosses each of the steps of the piecewise function, which method is best?
Thanks