In this work we present least squares (LS) approach to design linear phase Finite Impulse Response (FIR) filter. Since the design of FIR digital filters is non-analytic, we aim at ideal zero-phase magnitude response and minimize the weighted error in passband and stopbands. The problem of least squares can then be solved non-iteratively by solving system of linear equations. Solution of which yields impulse response that is both real and symmetric. Frequency response of the proposed LS FIR filter shows a flat passband, and higher stop-band attenuation than traditional window based FIR design and comparable attenuation with Parks–McClellan method of the same order. In addition we have implemented LS FIR filter on FPGA based VLSI architectures. Performance evaluation of proposed LS FIR design on VLSI architecture shows comparable throughput, area and power consumption compared to classical filter design approaches.

在这项工作中，我们提出了最小二乘（LS）方法来设计线性相位有限冲激响应（FIR）滤波器。由于FIR数字滤波器的设计是非分析性的，因此我们的目标是理想的零相位幅度响应，并最大程度地减小通带和阻带中的加权误差。然后，可以通过求解线性方程组来非迭代地求解最小二乘问题。解决方案产生的脉冲响应既真实又对称。所提出的LS FIR滤波器的频率响应显示出平坦的通带，并且比传统的基于窗口的FIR设计具有更高的阻带衰减，并且具有相同阶数的Parks–McClellan方法可比的衰减。此外，我们已经在基于FPGA的VLSI架构上实现了LS FIR滤波器。拟议的基于VLSI架构的LS FIR设计的性能评估表明，吞吐量相当，