# Re: Re: function in NCL for 10-day high pass filter

From: Dennis Shea (shea AT cgd.ucar.edu)
Date: Thu Oct 27 2005 - 15:05:01 MDT

> As to my knowledge, there are *at least" two ways in NCL you can use for
band-filtering analysis (also appropriate for low-frequencey filter and
high-frequncey filter).
> 1) Fourier harmonics anal: using *ezfftf* and *ezfftb* together, which is
most tranditional and simpliest way to extract the signals you need from a time
series.
> 2) Lancos filtering:
http://www.ncl.ucar.edu/Document/Functions/Built-in/filwgts_lancos.shtml, which
also works well.

Yes, this is correct. You can do filtering via FFTs.

It is "easy" but there are some caveats.

*Conceptually*, you do the the following
^^^^^^^^^^^^

[1] Perform a forward ftt on a series, "x"
[2] Set the fourier coefficients of unwanted
frequencies to 0.0
[3] Reconstruct, the series via ezfftb.

x = random_uniform(-1, 1, 24) ; generate a series

fc = ezfftf( x ) ; (2,12)

fc(:,0:4) = 0.0 ; set low freq to 0.0
fc(:,8:11) = 0.0 ; set high freq to 0.0

xBand = ezfftb(fc) ; reconstruct band passed series

*Reality* is a bit different. :-(

[1] The time series are not infinitely long or cyclic
[2] Anytime you truncate the coefficients you get Gibbs Phenomena
[3] Not all the numbers you get back are interpretable.

(1) The FFT assumes periodic data [based on sines and cosines].
Since time series are not cyclic, the series should be *tapered*
before doing the FFT to minimize "leakage"

http://www.ncl.ucar.edu/Document/Functions/Built-in/taper.shtml

(2) Gibbs phenomena will affect results. This may/may-not be important.
It depends on the series.

(3) When weights are applied to the time series [eg, wgt_runave],
then if it is, say, an 11-point running average, the first
and last 5 points are missing. When you use the FFT approach,
numbers are returned at *every* location. Gee, isn't that
great!!! The problem is that a certain number of points
at the beginning and end of the reconstructed series
are bogus.

Let the "x" be anomailies

x = random_uniform(-1, 1, 24) ; generate a series

xTaper = taper(x, 0.1, 0)

fc = ezfftf( xTaper ) ; (2,12)

fc(:,0:4) = 0.0 ; set low freq to 0.0
fc(:,8:11) = 0.0 ; set high freq to 0.0

xBand = ezfftb(fc) ; reconstruct band passed series

Ignore the first and last "n" points. You have to
know what "n" is. One way, create a filtered series
that was generated via the wgt_runave. Then do
the same via an fft and see where they 'match up'.
I recommend setting the bogus points to _FillValue
or only explicitly the "good" points.

Good luck
D

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