LNP_TEST

The LNP_TEST function computes the Lomb Normalized Periodogram of two sample populations X and Y and tests the hypothesis that the populations represent a significant periodic signal against the hypothesis that they represent random noise. The result is a two-element vector containing the maximum peak in the Lomb Normalized Periodogram and its significance. The significance is a value in the interval [0.0, 1.0]; a small value indicates that a significant periodic signal is present.

LNP_TEST is based on the routine


fasper

described in section 13.8 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press, and is used by permission.

Arguments

X

An n -element integer, single-, or double-precision floating-point vector containing equally or unequally spaced time samples.

Y

An n -element integer, single-, or double-precision floating-point vector containing amplitudes corresponding to X _i .

Keywords

HIFAC

Use this keyword to specify the scale factor of the average Nyquist frequency. The default value is 1.

JMAX

Use this keyword to specify a named variable that will contain the index of the maximum peak in the Lomb Normalized Periodogram.

OFAC

Use this keyword to specify the oversampling factor. The default value is 4.

WK1

Use this keyword to specify a named variable that will contain a vector of increasing linear frequencies.

WK2

Use this keyword to specify a named variable that will contain a vector of values from the Lomb Normalized Periodogram corresponding to the frequencies in WK1.

Example

Define two n -element sample populations.

X = [ 1.0, 2.0, 5.0, 7.0, 8.0, 9.0, $

10.0, 11.0, 12.0, 13.0, 14.0, 15.0, $

16.0, 17.0, 18.0, 19.0, 20.0, 22.0, $

23.0, 24.0, 25.0, 26.0, 27.0, 28.0]

Y = [ 0.69502, -0.70425, 0.20632, 0.77206, -2.08339, 0.97806, $

1.77324, 2.34086, 0.91354, 2.04189, 0.53560, -2.05348, $

-0.76308, -0.84501, -0.06507, -0.12260, 1.83075, 1.41403, $

-0.26438, -0.48142, -0.50929, 0.01942, -1.29268, 0.29697]

Test the hypothesis that X and Y represent a significant periodic signal against the hypothesis that they represent random noise.

result = LNP_TEST(X, Y, WK1 = wk1, WK2 = wk2, JMAX = jmax)

PRINT, result

IDL prints:

4.69296 0.198157

The small value of the significance represents the possibility of a significant periodic signal. A larger number of samples for X and Y would produce a more conclusive result. WK1 and WK2 are both 48-element vectors containing linear frequencies and corresponding Lomb values, respectively. JMAX is the indexed location of the maximum Lomb value in WK2.