Understanding Lissajous Curves for Fourier Synthesis

[Sam Smith]

i have a question about Fourier synthesis and how this relates to lissajous curves.

I have two sets of test data; spatial data in the x and y directions. When I plot the x data against the y I get an ellipse. ( it represents a wing moving in a circular motion)

I am trying to recreate this shape by means of Fourier synthesis. To do this I look at the fft of my x and y data and get information about the amplitudes of the fundamental frequencies along with harmonics presents in both data sets. The real part I use as the coefficient of my cos and the imaginary as the coefficient of my sin.

And so I say

X(t) = a1* cos(2*pi*f*t) + b1* sin( 2*pi*f*t)

And

Y(t) = aa1* cos(2*pi*f*t) + bb1*sin( 2*pi*f*t) + aa2* cos(4*pi*f*t) + bb2*sin( 4*pi*f*t)

(There was just one peak in the x data and two peaks in the y)

However when I then plot x against y I get a lissajous curve. As I would expect as I am plotting sine waves against sin waves. How can I recreate the original shape? Must I somehow plot cos and sin differently?

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?