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# 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
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).

## 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.

Pawel A. Penczek

category 1
FILTER
category 2
FOURIER

filter.py

# Maturity

stable
works for most people, has been tested; test cases/examples available.

# Bugs

None. It is perfect.