Low latency IIR digital filter design by using metaheuristic optimization algorithms

Filters are particularly important class of LTI systems. Digital filters have great impact on modern signal processing due to their programmability, reusability, and capacity to reduce noise to a satisfactory level. From the past few decades, IIR digital filter design is an important research field. Design of an IIR digital filter with desired specifications leads to a no convex optimization problem. IIR digital filter which design by minimizing the error between frequency response of desired and designed filters with some constraints such as stability, linear phase, and minimum phase by meta heuristic algorithms has gained increasing attention. The aim of this paper is to develop an IIR digital filter designing method that can provide relatively good time response characterizations beside good frequency response ones. One of the most important required time characterizations of digital filters for real time applications is low latency. To design a low latency digital filter, minimization of weighted partial energy of impulse response of the filter is used, in this paper. By minimizing weighted partial energy of impulse response, energy of impulse response concentrates on its beginning, consequently low latency for responding to inputs. This property beside minimum phase property of designed filter leads to good time specifications. In the proposed cost function in order to ensure the stability margin the term maximum pole radius is used, to ensure the minimum phase state the number of zeros outside the unit circle is considered, to achieve linear phase the constant group delay is considered. Due to no convexity of proposed cost function, three meta-heuristc algorithms GA, PSO, and GSA are used for optimization processes. Reported results confirmed the efficiency and the flexibility of the proposed method for designing various types of digital filters (frequency selective, differentiator, integrator, Hilbert, equalizers, and …) with low latency in comparison with the traditional methods. Designed low pass filter by proposed method has only 1/79 sample delay, that is ideal for most of the applications.