= Name =
filt_tanb - hyperbolic tangent band-pass Fourier filter
= Usage =
output = filt_tanb(image, freql, low_fall_off, freqh, high_fall_off, pad)
== Input ==
image:: input image (can be either real or Fourier)
freql:: low-end frequency of the filter pass-band
low_fall_off:: fall off of the filter at the low-end frequency
freqh:: high-end frequency of the filter pass-band
high_fall_off:: fall off of the filter at the high-and frequency
pad:: logical flag specifying whether before filtering the image should be padded with zeroes in real space to twice the size (this helps avoiding aliasing artifacts). (Default pad = False).
. All frequencies are in [[absolute_frequency_units|absolute frequency units]] {{{`f_a`}}} and their valid range is [0:0.5].
== Output ==
output:: filtered image. Output image is real when input image is real or Fourier when input image is Fourier
= Method =
Fourier transform of the input image is multiplied by a radially symmetric hyperbolic tangent filter:
. {{{`H(f) = 0.5{tanh[(pi(f+f_H))/(2a_H(f_H-f_L)))]-tanh[(pi(f-f_H))/(2a_H(f_H-f_L))]-tanh[(pi(f+f_L))/(2a_L(f_H-f_L)))]+tanh[(pi(f-f_L))/(2a_L(f_H-f_L))]}`}}}
where {{{`f_L`}}} if the low-end frequency of the filter pass-band ('''''freql'''''),
{{{`f_H`}}} if the high-end frequency of the filter pass-band ('''''freqh'''''),
{{{`a_L`}}} is the fall off of the filter at the low-end frequency ('''''low_fall_off'''''),
and {{{`a_H`}}} is the fall off of the filter at the high-end frequency ('''''high_fall_off''''').
= Reference =
Basokur, A. T., 1998. Digital filter design using the hyperbolic tangent functions. Journal of the Balkan Geophysical Society 1, 14-18.
= Author / Maintainer =
Pawel A. Penczek
= Keywords =
category 1:: FILTER
category 2:: FOURIER
= Files =
filter.py
= Maturity =
stable:: works for most people, has been tested; test cases/examples available.
= Bugs =
None. It is perfect.