In this paper a new iterative algorithm based on least square error method (LS) called extended LS (ELSE) is proposed to automatically design linear-phase FIR filters with any desired frequency response (DFR) and limited deviations. Minimizing a cost function that is defined based on the desired filter specifications including DFR and threshold of acceptable deviations (TAD), is the main idea of ELSE. In contrast to the other typical filter designing methods, defining the transition bands is not necessary in ELSE. Moreover, ELSE regulates the convergence rate by an automated approach that was utilized in neural networks; and it approximates the filter degree using an increasing-decreasing approach. In simulations, ELSE shows significant performance compared to LS though it may be more computationally complex. Also, it supplies the application demands in all of the case studies.

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