Fig 1.
Kolmogorov-Zurbenko filter energy and log energy transfer functions.
The energy transfer function to the left and log energy transfer function to the right for Kolmogorov-Zurbenko filters with a fixed argument of paired with
in magenta,
in red,
in yellow,
in green,
in cyan, and
in blue.
Fig 2.
Kolmogorov-Zurbenko energy transfer functions for different values of argument m with fixed argument k.
The energy transfer function for Kolmogorov-Zurbenko filters with a fixed argument of paired with
in red,
in green,
in blue,
in dashed red,
in dashed green,
in dashed blue. The ellipsis shows that there are additional KZ energy transfer functions in this region as m increases.
Fig 3.
Extended Kolmogorov-Zurbenko filter energy transfer functions.
The energy transfer function for Extended Kolmogorov-Zurbenko filters with arguments and
in black,
in magenta,
in red,
in yellow,
in green,
in cyan, and
in blue, in addition to mr within each created interval. The lines with black dashes are the only possible energy transfer functions for KZ filters in the same range of argument m at
in red,
in green, and
in blue.
Fig 4.
Example periodograms of white noise and EKZ filtered time series with even valued filter window length, and corresponding energy transfer functions.
The periodogram of a white noise time series in black and the periodograms of that same time series after applying Extended Kolmogorov-Zurbenko filters in magenta, and
in dark magenta. The energy transfer functions of an
filter is shown as the magenta curve,
in dark magenta, and the closest
, or equivalent
, filter energy transfer function displayed in red with corresponding scale on the right.
Fig 5.
Example log periodograms of white noise and EKZ filtered time series with non-integer valued filter window length, and corresponding energy transfer functions.
The log periodogram of a white noise time series in black and the periodograms of that same time series after applying Extended Kolmogorov-Zurbenko filters in yellow. The approximate energy transfer functions of the
filter is shown as the yellow curve, and the closest possible
displayed in red and
displayed in green with corresponding scale on the right.
Fig 6.
Surface pressure time series, KZ filtered time series, and EKZ filtered time series with even valued filter window length.
The Seattle, Washington surface pressure time series in black and the filtered time series in yellow,
filtered time series is in red, and the
filtered time series is in green.
Fig 7.
Precipitation time series and EKZ filtered time series with non-integer valued filter window length.
The New York City precipitation rate time series in black and the filtered time series in red.