Instead of starting from a time series with n number of samples I decided to investigate the FT as the number of samples built, starting at zero and increasing.  Of course there isn’t anything at zero, so I start my plot by putting a small zero at the centre.  Somewhere between zero and one is the event horizon, a place you can’t see in to. You don’t get to see until the first sample.  If there is just one sample, the phasor plot appears as in The 1 Shell.  The zero point is represented as a black circle, the samples as red dots.  Wherever there is a sample I draw a line from the origin passing through and emanating from the sample dot.  I call this the exclusion line.  The circle tracing the path of the sample I call a shell, so The 1 Shell shows the 1 shell.