System Functions : One-dimensional FFT
In CGRAPH, the Fourier transforms of any functions can be displayed. Any intervals of the functions can be transformed. The transformation is performed in a complex manner; the real part of the Fourier spectrum is always displayed in an interval from -* to +*. Since the transformation only yields discrete values, no continuous curve is produced. Only the calculated support values are displayed.
Unlike other graphics, the settings and graphics are located in the same window. The sampling interval can be set. The sample values are limited to powers of 2. In addition to the Fourier transform into the spectral domain, the inverse transform into the time domain is also possible.
Only functions containing the variables x, t and param are permitted, i.e. no complex numbers. Enter the desired function in the input field for the function, or select one of the existing functions by clicking on the arrow to the right of the input field.
After clicking on the Create graph button, CGRAPH displays the graph. The example shown is the Gaussian bell curve f(x) = exp(-2*x2), whose Fourier transform is again a Gaussian bell curve. In addition to the transform, the underlying function is also plotted in a different colour.
Since the transform is normalised to π, the x-axis is also normalised to π. This can be changed in the settings for the axis parameters.
The default values can be viewed in the tree on the left-hand side.
The values can be changed later. The graph is adjusted automatically, at the latest when the Create graph button is clicked. Clicking on the coloured symbol for the function, etc. allows you to quickly hide the graph from the display. Double-clicking on the text allows you to adjust the graphical representation.
The representation of the axes is also part of the tree, as the graphics for this graphic type are independent of each other and can be set separately.
Unlike other graphics, an (optional) parameter is set here using a slider below the parameter in the default area (blue arrow). You can also enter and change the parameter as a number in the default area.