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.

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.

## Examples

This example tests the hypothesis that two sample, *n*-element populations X and Y represent a significant periodic signal against the hypothesis that they represent random noise:

; 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.

## Syntax

*Result* = LNP_TEST( *X*, *Y* [, /DOUBLE] [, HIFAC=*scale_factor*] [, JMAX=*variable*] [, OFAC=*value*] [, WK1=*variable*] [, WK2=*variable*] )

## Return Value

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.

## 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

### DOUBLE

Set this keyword to force the computation to be done in double-precision arithmetic.

### 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.

## Version History

4.0 |
Introduced |

## See Also

CTI_TEST, FV_TEST, KW_TEST, MD_TEST, R_TEST, RS_TEST, S_TEST, TM_TEST, XSQ_TEST