2009
Comment:

← Revision 14 as of 20130701 13:12:59 ⇥
2010
converted to 1.6 markup

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. All frequencies are in [:absolute_frequency_units:absolute frequency units] {{{`f_a`}}} and their valid range is [0:0.5].  . All frequencies are in [[absolute_frequency_unitsabsolute frequency units]] {{{`f_a`}}} and their valid range is [0:0.5]. 
Name
filt_tanb  hyperbolic tangent bandpass 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
 lowend frequency of the filter passband
 low_fall_off
 fall off of the filter at the lowend frequency
 freqh
 highend frequency of the filter passband
 high_fall_off
 fall off of the filter at the highand 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 `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_Hf_L)))]tanh[(pi(ff_H))/(2a_H(f_Hf_L))]tanh[(pi(f+f_L))/(2a_L(f_Hf_L)))]+tanh[(pi(ff_L))/(2a_L(f_Hf_L))]}`
where `f_L` if the lowend frequency of the filter passband (freql), `f_H` if the highend frequency of the filter passband (freqh), `a_L` is the fall off of the filter at the lowend frequency (low_fall_off), and `a_H` is the fall off of the filter at the highend frequency (high_fall_off).
Reference
Basokur, A. T., 1998. Digital filter design using the hyperbolic tangent functions. Journal of the Balkan Geophysical Society 1, 1418.
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.