Periodogram.smooth(method='boxkernel', filter_width=0.1)[source]

Smooths the power spectrum using the ‘boxkernel’ or ‘logmedian’ method.

If method is set to ‘boxkernel’, this method will smooth the power spectrum by convolving with a numpy Box1DKernel with a width of filter_width, where filter width is in units of frequency. This is best for filtering out noise while maintaining seismic mode peaks. This method requires the Periodogram to have an evenly spaced grid of frequencies. A ValueError exception will be raised if this is not the case.

If method is set to ‘logmedian’, it smooths the power spectrum using a moving median which moves across the power spectrum in a steps of

log10(x0) + 0.5 * filter_width

where filter width is in log10(frequency) space. This is best for estimating the noise background, as it filters over the seismic peaks.

Periodograms that are unsmoothed have multiplicative noise that is distributed as chi squared 2 degrees of freedom. This noise distribution has a well defined mean and median but the two are not equivalent. The mean of a chi squared 2 dof distribution is 2, but the median is 2(8/9)**3. (see In order to maintain consistency between ‘boxkernel’ and ‘logmedian’ a correction factor of (8/9)**3 is applied to (i.e., the median is divided by the factor) to the median values.

In addition to consistency with the ‘boxkernel’ method, the correction of the median values is useful when applying the periodogram flatten method. The flatten method divides the periodgram by the smoothed periodogram using the ‘logmedian’ method. By appyling the correction factor we follow asteroseismic convention that the signal-to-noise power has a mean value of unity. (note the signal-to-noise power is really the signal plus noise divided by the noise and hence should be unity in the absence of any signal)

methodstr, one of ‘boxkernel’ or ‘logmedian’

The smoothing method to use. Defaults to ‘boxkernel’.


If method = ‘boxkernel’, this is the width of the smoothing filter in units of frequency. If method = logmedian, this is the width of the smoothing filter in log10(frequency) space.

smoothed_pgPeriodogram object

Returns a new Periodogram object in which the power spectrum has been smoothed.