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Polar Fourier Transform

​
t
max
0.01
ω
winding
3
ω
signal
3
dc
1.1
1.1
​
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,
ω
winding
. The orange dot is at the center of mass of the wrapped time history:
1
t
2
-
t
1
t
2
∫
t
1
g(t)
-2πiwft
e
dt
,
while the green dot represents the Fourier transform (i.e. the modified center of mass):
t
2
∫
t
1
g(t)
-2πiwft
e
dt
.
For speed, the symbolic integral is computed in the Initialization Code.
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