In any deterministic solution, the convergence is not at all guaranteed, whereas, the stochastic and random search algorithms are 1 shot optimization and it can hit the nearly optimized solution, with guarantee. Therefore the AI dependent evolutionary algorithms (GA, PSO, DE, BFOA) are prescribed for this type of optimization problems. Some selected evolutionary algorithms are presented for digital filter design. If the statistical characteristic of the input data varies with respect to time or the required knowledge about input data is not satisfactory, adaptive filters are needed. Adaptive filters (FIR and IIR) have attractive increasing attention due to their widespread use in many different applications such as system identification, noise cancellation, channel equalization, linear prediction, control, and modeling. In the present book, in order to achieve a global minimum solution to the fitness function related to filter transfer function, biologically inspired algorithm is used. Adaptation to classical Bacterial Foraging Optimization is employed to design stable and optimum digital filter design for signal processing and image processing applications.