Multiplier-free digital filters have received widespread attention in the Digital Signal Processing (DSP) community due to their high computational speed and low cost implementation. In this thesis, three new approaches are presented for designing multiplier-free digital filters.; In the first part of the thesis, an Infinite Impulse Response (HR) filter that has periodically time-varying state-space structure in conjunction with up-sampling and down-sampling is proposed. It is a multiplier-free filter since it has power-of-2 coefficients. An algorithm similar to the error back-propagation in neural networks is derived to find the power-of-2 coefficients in the filter.; The second approach is for designing multiplier-free state-space digital filters. The state-space structure whose coefficients are power-of-2 numbers and state variables are quantized to power-of-2 numbers is employed to design the proposed multiplier-free filter. Expressions of the noise variance are formulated for the quantized state vector and the output of the filter. The transformation matrix is incorporated in these expressions. It is shown that the power-of-2 quantization effects can be minimized by properly choosing the transformation matrix.; The third approach is for designing multiplier-free Finite Impulse Response (FIR) digital filters. It is based upon the frequency sampling method and upon the use of a penalty function. A steepest-descent method is developed to minimize the cost function, which contains the frequency sampling part and the penalty function part. An FIR digital filter with power-of-2 coefficients is then achieved.; Simulation results illustrate that these three new design methods yield excellent results in designing multiplier-free digital filters.
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