Dsign of I-D Recursive Digital Filters With Linear Phase Using Two All-Pass Filters With/Without Integer Coefficients

Digital signal processing is becoming increasingly important, and is finding applications in speech processing and telecommunications in the area of 1-D signal processing. One of the important branches 1n digital signal processing 1s digital filtering. Among the numbers of structure of digital filters, the recursive(IIR) filter is known for its computational efficiency compared to the FIR counterparts. In this thesis, an alternative approach to the direct design of 1-D recursive digital filters satisfying prescribed magnitude specifications with or without constant group delay characteristic using two all-pass filters is presented. It is known that, by this approach, the most computationally efficient realization can be obtained among IIR filters for meeting the filter specifications. The method uses unconstrained optimization techniques for the filter design to approximate both the group delay and the magnitude response of the desired filter simultaneously if the constant group delay characteristic is required. Two different approaches are chosen for the stability of the filter. In the first approach, a new stability test is used to generate the stable polynomials. In the second approach, one-variable Hurwitz polynomials(HPs) using properties of positive definite matrices are generated. Bilinear transformations are applied to the HPs to obtain the stable polynomials in z domain. The polynomials generated using the approaches explained above are imposed on the filter\u27s denominator polynomials through the variable subs ti tut ion method, hence ensuring the stability .of the designed filter. The designed filters using this method are stable in nature and neither stability check nor stabilization procedure is required. To illustrate the usefulness of the technique, the results obtained are compared with a well known direct method design using a general 1-D IIR transfer function. Once the infinite precision filter is obtained, through a procedure based on discretization and reoptimization technique we discretize all coefficients to integer values. By this algorithm, the error caused by truncating the filter coefficients is minimized. Examples are given with comparisons in order to demonstrate the usefulness of the algorithm