Topic: Independant variable for integration (to do Fourier Transform)
While both Fourier series and a Fourier transform have been created and submitted, both depended on transforming a rectangular function. As such, a single integration variable was used successfully.
However, I'm trying to get a general Fourier transform to work in Graph. In doing so, I created the waveform that I wanted to transform, entered the appropriate integral and had it graph the results. After an appropriate wait, nothing gets graphed. Using shading and zoom-to-all shows no results either. I suspect the function computed comes out to be a single value which wouldn't show on the display (being an infinitesmal point).
What I need is to be able to integrate a function over a given range of one variable and plot the results over the range of another variable. Here, the integration is over time and frequency - time for the given function (a radio signal) and frequency (for the transform's results).
In this case, I can define a waveform over time of rf(x), where x ranges from 0 to 64*pi.
the real part of the Fourier transform should be ftreal(x) = integrate(re(e^1(i*x, rf(t))), t, 0, 64*pi)
Plotting ftreal(x) over 0 to 32 doesn't show anything. I don't know what Graph is trying to do with this input as it shows no intermediate steps or will list any final value(s).
Do you have any suggestions on how to make this work? Or should I look into diving into Python to extend it to add an FFT capability?
Many thanks for a remarkably powerful tool!
Jim Horn, Columbia River Gorge, USA