FIR Linear Phase Fractional Order Digital Differentiator Design using Convex Optimization

In this paper, design of linear phase FIR digital differentiators is investigated using convex optimization. The problem of differentiator design is first described in terms of convex optimization with different optimization variables’ options, taken one at a time. The method is then used to design first order low pass differentiators and results are compared with Salesnick’s technique and Parks McClellan algorithm. The designed FIR low pass differentiator has improvement in transition width and flexibility to optimize different parameters. The concept of low pass differentiation is further generalized to fractional order differentiators. Fractional order differentiators are designed by using minmax technique on mean square error. Design examples demonstrate easy design procedure and flexibility in the process as well as improvement over existing fractional order differentiators in terms of mean square error in passband. Finally, fractional order differentiators are designed and used for texture enhancement of color images. Better texture enhancement than existing filtering approaches is established based on average gradient and entropy values. General Terms FIR Filter, Fractional order differentiator, Low pass differentiator, Full band differentiator, Image Enhancement.