Linear Phase Fir Low Pass Digital Differentiator Design

Abstract

Digital Differentiatorisa vitalsignal processingtool.It isfound in manyapplications,from low frequency biomedicalequipmenttohighfrequencyradars. New developing fields such as touch screen tablets and online signature verification also has digital differentiators as basic building block. Many methods have been developed to design all types of differentiators but there is still scope of improvement in terms of parameters’ optimization. The design problem of differentiators is a challenging task. Therefore, there is strong motivation to make design process easy and efficient.

First,the design of non-recursive linear phase higher order low pass digital differentiators, satisfying given specifications, is investigated. The concept of low pass differentiation is further generalized to higher order case. The design is based on Fourier series method for design of filters along with Kaiser Window function. The procedure is then used to design first order differentiators and results are compared with currently available techniques. The proposed FIR low pass differentiator has improvement in transition width and flexibility to choose anycutoff frequency. The same technique has been demonstrated for second order design according to provided specifications. This method is used to design second order low pass differentiator for QRS detection in ECG. It is shown that the proposed system has low hardware and software complexity as compared to existing second derivative based techniques of QRS detection.

Secondly, design of fractional order linear phase FIR digital differentiators is also investigated using convex optimization.Convex optimization has been applied to many engineering applications in recent years. This approach relies on finding optimum values of convex functions (e.g. linear phase FIR filters). It also requires less number of computations due to introduction of efficient algorithms. The problem of differentiator design is first described in terms of convex optimization with different optimization variables’ options. The method is then used to design first order low pass differentiators and improvement in results is observed. The concept of low pass differentiation is further generalized to fractional order differentiators. Fractional order differentiators are designed by using minmax (Chebyshev) technique on mean square error. Design examples demonstrate easier design procedure than available fractional order differentiator design methodologies. The approach also has more flexibility in terms of specification constraints. Improvement over existing fractional order differentiators is proved using mean square error parameter in passband. Finally, fractional order differentiators are designed and used for texture enhancement of images. The designed fractional order differentiators are applied on different colour images to demonstrate various desired levels of sharpening