2D and 3D Packard-Takens Autocorrelation Plots of Sinusoidal Functions

number of

points

250

sin

123

(t) amplitudes & frequencies:

a

1

5.9

ω

1

2.

a

2

3.5

ω

2

5.

a

3

3.3

ω

3

7.

autocorrelation plot type

2D

3D

2D autocorrelation plot

2D y lag

1

join points

3D autocorrelation plot

3D y lag

1

3D z lag

2

0

50

100

150

200

250

-10

-5

0

5

10

t

sin

123

(t)

sin

123

(t) = a

1

sin

1

(ω

1

t) + a

2

sin

2

(ω

2

t) + a

3

sin

3

(ω

3

t)



-10

-5

0

5

10

-10

-5

0

5

10

sin

123

(t)

sin

123

(t-lag)

three-sine 2D autocorrelation plot: lag = 1

This Demonstration shows the autocorrelations of one- to three-term sinusoidal functions plotted in two and three dimensions. You can select the function's underlying amplitudes and frequencies as well as the lags and the number of generated points. You can also choose whether or not to connect the points in the two-dimensional display only.