# 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

``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 (

*), and*

**low_fall_off**``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.