# plomb

Lomb-Scargle periodogram

## Syntax

## Description

`[`

returns the Lomb-Scargle power spectral density (PSD) estimate,
`pxx`

,`f`

]
= plomb(`x`

,`t`

)`pxx`

, of a signal, `x`

, that is
sampled at the instants specified in `t`

.
`t`

must increase monotonically but need not be uniformly
spaced. All elements of `t`

must be nonnegative.
`pxx`

is evaluated at the frequencies returned in
`f`

.

If

`x`

is a vector, it is treated as a single channel.If

`x`

is a matrix, then`plomb`

computes the PSD independently for each column and returns it in the corresponding column of`pxx`

.

`x`

or `t`

can contain
`NaN`

s or `NaT`

s. These values are treated
as missing data and excluded from the spectrum computation.

`[`

estimates the PSD up to a maximum frequency, `pxx`

,`f`

]
= plomb(___,`fmax`

)`fmax`

, using
any of the input arguments from previous syntaxes. If the signal is sampled at
*N* non-`NaN`

instants, and Δ*t* is the time difference between the first and the last of them,
then `pxx`

is returned at
`round`

(`fmax`

/ *f*_{min})
points, where *f*_{min} = 1/(4 × *N* × *t _{s}*) is the smallest frequency at which

`pxx`

is
computed and the average sample time is *t*= Δ

_{s}*t*/(

*N*– 1).

`fmax`

defaults to 1/(2 × *t*), which for uniformly sampled signals corresponds to the Nyquist frequency.

_{s}`[`

specifies an integer oversampling factor, `pxx`

,`f`

]
= plomb(___,`fmax`

,`ofac`

)`ofac`

. The use of
`ofac`

to interpolate or smooth a spectrum resembles the
zero-padding technique for FFT-based methods. `pxx`

is again
returned at
`round`

(`fmax`

/*f*_{min})
frequency points, but the minimum frequency considered in this case is
1/(`ofac`

× *N* × *t _{s}*).

`ofac`

defaults to 4.`[___,`

returns the power-level threshold, `pth`

] = plomb(___,'Pd',`pdvec`

)`pth`

, such that a peak
with a value larger than `pth`

has a probability
`pdvec`

of being a true signal peak and not the result of
random fluctuations. `pdvec`

can be a vector. Every element
of `pdvec`

must be greater than 0 and smaller than 1. Each
row of `pth`

corresponds to an element of
`pdvec`

. `pth`

has the same number of
channels as `x`

. This option is not available if you specify
the output frequencies in `fvec`

.

`[`

returns the PSD estimate of `pxx`

,`w`

]
= plomb(`x`

)`x`

evaluated at a set of evenly
spaced normalized frequencies, `w`

, spanning the Nyquist
interval. Use `NaN`

s to specify missing samples. All of the
above options are available for normalized frequencies. To access them, specify
an empty array as the second input.

`plomb(___)`

with no output arguments plots the
Lomb-Scargle periodogram PSD estimate in the current figure window.

## Examples

## Input Arguments

## Output Arguments

## More About

## References

[1] Horne, James H., and Sallie L.
Baliunas. "A Prescription for Period Analysis of Unevenly Sampled Time Series."
*Astrophysical Journal.* Vol. 302, 1986, pp.
757–763.

[2] Lomb, Nicholas R. "Least-Squares Frequency Analysis of Unequally
Spaced Data." *Astrophysics and Space Science.* Vol. 39, 1976, pp.
447–462.

[3] Press, William H., and George B. Rybicki. "Fast Algorithm for
Spectral Analysis of Unevenly Sampled Data." *Astrophysical
Journal.* Vol. 338, 1989, pp. 277–280.

[4] Scargle, Jeffrey D. "Studies in Astronomical Time Series
Analysis. II. Statistical Aspects of Spectral Analysis of Unevenly Spaced Data."
*Astrophysical Journal.* Vol. 263, 1982, pp.
835–853.

## Extended Capabilities

## Version History

**Introduced in R2014b**