Design and analysis of higher order fractional step Butterworth filters

This paper presents the designing of higher order fractional low pass, high pass and band reject filters of order (n+α), where n is the integer and α is the fractional step with value 0<;α<;1 using the fractional order Laplacian, s
^α
. Firstly, the designs of low pass and high pass filters are obtained in the s-domain by evaluating the filter coefficients to satisfy Butterworth approximation. Then, these filters are used to design fractional band reject filters, which provide symmetric and asymmetric characteristics for independent control above and below the mean frequency.