Butterworth Filter Design

Butterworth Filter Design

Butterworth filter design is nothing but a filter approximation used to achieve ideal characteristics while transforming an analog filter response to digital filter response. 

We designed low pass and high pass filters and simulated their magnitude and frequency response using Scilab. We simulated using Scilab since it is an open source tool, but MATLAB, C as well as C++ codes are also available in abundance over the internet for the same. The most commonly found codes are written in MATLAB as it is much easier and better than Scilab.

The order of the filter and the Transfer Function were calculated after entering the various parameters of filter like: Attenuation in pass band (Ap), Attenuation in Stop band (As), Stop band frequency and Pass band frequency. Bilinear Transform Method was used to convert the Transfer Function in S-domain (Laplace Domain) to Z-domain. The obtained response was very close to ideal response as the order was greater than 10. Thus, from the obtained characteristics, we verified that, for a butterworth filter 

Passband : monotonic

Stopband : monotonic

No ripples

Wide Transition, slow roll-off  

Computing the order greater than 10 and designing a filter manually is a very cumbersome process. This is where, simulation software tools make the work easy and more efficient.