FourierDistance {TSdist}

Fourier Coefficient based distance.

Description

Computes the distance between a pair of numerical series based on their Discrete Fourier Transforms.

Usage

FourierDistance(x, y, n = (floor(length(x) / 2) + 1))

Arguments

x

Numeric vector containing the first time series.

y

Numeric vector containing the second time series.

n

Positive integer that represents the number of Fourier Coefficients to consider. ( default=(floor(length(x) / 2) + 1) )

Details

The Euclidean distance between the first n Fourier coefficients of series x and y is computed. The series must have the same length. Furthermore, n should not be larger than the length of the series.

Value

d

The computed distance between the pair of series.

Author(s)

Usue Mori, Alexander Mendiburu, Jose A. Lozano.

References

Agrawal, R., Faloutsos, C., & Swami, A. (1993). Efficient similarity search in sequence databases. In Proceedings of the 4th International Conference of Foundations of Data Organization and Algorithms (Vol. 5, pp. 69-84).

See Also

To calculate this distance measure using ts, zoo or xts objects see TSDistances. To calculate distance matrices of time series databases using this measure see TSDatabaseDistances.

Examples

# The objects example.series1 and example.series2 are two 
# numeric series of length 100 contained in the TSdist package. 

data(example.series1)
data(example.series2)

# For information on their generation and shape see help 
# page of example.series.

help(example.series)

# Calculate the Fourier coefficient based  distance using 
# the default number of coefficients:

FourierDistance(example.series1, example.series2)

# Calculate the Fourier coefficient based  distance using 
# only the first 20 Fourier coefficients:

FourierDistance(example.series1, example.series2, n=20)