Hyperbolic tangent digital filters applied to the smoothing of disturbances in the phosphate resistivity data of Morocco

Low- and band-pass filters can be designed by a combination of hyperbolic tangent functions in the frequency domain using the scaling and shifting theorems of the Fourier transforms. The corresponding filter function in the time domain can be derived analytically from the frequency domain expression. The smoothness parameters control the slopes at the cut off regions and permit the construction of a relatively short filter while reducing the oscillations of the filter response in the time domain. Different smoothness parameters can be chosen for the low and high cut off frequencies in the band-pass filter design. Following the proposed scheme can easily derive the other type of the filters.