In this dissertation, a digital filter is being optimized using Particle Swarm Optimization and compared with conventional frequency sampling method of optimization. Among IIR and FIR filter, here we discuss FIR filter optimization where firstly a single particle is being studied and then iterations are done for the rest. As for FIR filter, an important point to keep in notice is that an FIR filter is designed using convolution rather than recursion which results in higher quality of stability. An FIR filter is a linear phase filter where both phase delay and group delays are constant. The PSO is a population-based algorithm where a set of potential solutions evolve to approach a convenient solution (or set of solutions) for a problem. Being an optimization method, the aim is to find the global optimum of a real-valued function (fitness function) defined in a search space. In this, a population of individuals (referred to as particles) adapts by returning stochastically toward previously successful regions. Every particle's movement is a composition of initial random velocity and two randomly weighted influences i.e. individuality (the tendency to return to the particle's best previous position) and sociality (the tendency to move towards the neighborhood's best previous position).After every cycle of iteration, a new value of velocity for each particle is calculated based on its current velocity, its distance from the previous best position, and its distance from the global best position. The new velocity value is then used to calculate the next position of the particle in the search space. We use PSO as an optimization technique to optimize the output parameters of the FIR filter. PSO initializes a group of random particles (solutions) and then searches for optimal solution by updating generated values. The particle swarm algorithm is used here in terms of social cognitive behavior. It is widely used for problem solving method in engineering. When the search space is too large to search exhaustively, population based searches may be a good alternative.

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