As we increase the index of our Fourier vector,
the underlying frequency increases as well.
Now, the discrete nature of the vector makes it a little bit hard to understand
the signs of the shape of the signal.
But you can see for instance here that we are in the high frequency range
because the sign of the samples changes at every step.
So the sign alternation is a tell tale sign of a high frequency sitazoid.
Finally, we reach the highest frequency that discrete time complex exponential
can have.
So here it happens for K equal to 32 where our frequency
becomes 2 pi over 64 times 32, which is equal to pi.
At this point,
we will be moving from this position to this position in the complex plane.
And this is clearly indicated by the real and imaginary components of the vector,
which are alternating plus and minus one in the real part and
identical to zero in the imaginary part.
As we go forward index, as we saw in model 2.2,
the apparent speed of the point decreases and
the direction of the rotation changes from counterclockwise to clockwise.
So here as the index increases from 32 up to 63, we see
that the apparent speed of the sinusoid decreases back to 0.
But the sign that we're past pi, as far as the angular increment at each step is
concerned, comes from the phase of the imaginary part, which is inverted with
respect to the equivalent frequency that we have seen for low values of the index.
So here, for instance, if you compare this basis vector to w of 2, you would
see that the real part is the same, but the imaginary part has a sign in version.
In w of 2, it would be like this.
