A novel and efficient finitely precise design of linear-phase FIR filters

For the first time, an upper degradation bound of the frequency sensitivity function in the desired frequency band due to the difference between the quantized and infinitely precise coefficients of FIR filters with filter order even is formulated, and a novel and very efficient algorithm for quantization of the coefficients is then developed as an application of the bound when digital FIR filters are needed. Of course, this approach is applicable to the case with filter order odd. The algorithm mainly features simplicity and very high efficiency in obtaining the finite word-length coefficients from the infinite precision coefficients. Also observed are some graphs which exemplify the validity of this method.