# Lissajous curves

Tags:
1. Oct 13, 2014

### 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?

2. Oct 18, 2014