# Polar Fourier Transform

Polar Fourier Transform

The Fourier transform quantifies the frequency content of a signal. We do this by first converting the time history to polar coordinates. Next, the speed at which the signal is wrapped in polar coordinates is varied with the winding frequency, . The orange dot is at the center of mass of the wrapped time history:

ω

winding

1

t

2

t

1

t

2

∫

t

1

-2πiwft

e

while the green dot represents the Fourier transform (i.e. the modified center of mass):

t

2

∫

t

1

-2πiwft

e

For speed, the symbolic integral is computed in the Initialization Code.