Digital filter design
using the hyperbolic tangent functions
Abstract: Low and bandpass 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 cutoff
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 cutoff frequencies in the bandpass filter design. Following
the proposed scheme can easily derive the other type of the filters
(e.g. highpass).
