Filter design in digital signal processing

Abstract

The paper a comprehensive review and analysis of modern approaches, methods, and trends in the design of digital FIR and IIR filters in the context of digital signal processing is presented. Significant attention is focused on the analysis of methods for optimizing the filter structure, especially using algorithms such as differential evolution, which has demonstrated advantages over traditional genetic algorithms in tuning IIR filter parameters. For FIR filters, classical methods are considered, including window weighting, the least squares method, the Parks-McClellan algorithm, and the frequency sampling method. The implementation of filters in the Xilinx ISE environment using hardware description languages (VHDL) is also studied, with special attention to architectural solutions such as Wallace tree, Vedic and Booth multipliers. The designs were evaluated according to criteria such as delay, operating frequency, logic area, and power consumption. Strategic selection of implementation methodologies and design specifications is crucial to achieving efficient circuit implementation. Different design strategies for digital FIR filters using Wallace tree and Vedic multiplication have been investigated, which result in reduced delay and increased operating frequency, but increased area. In contrast, Booth design provides moderate delay, reduced number of partial products and, as a result, high-speed digital filters with finite impulse response. The key characteristics, advantages, disadvantages, and areas of application of various design methods are identified, and the role of optimization algorithms, hardware implementations, and specific requirements of individual applications (such as audio and image processing, communication systems, and power systems) in the selection and design of digital filters is explored