Low complexity lowpass linear-phase multiplierless FIR filter

A new class of lowpass linear-phase FIR filter function given in an explicit compact form is introduced. First, the general form of a new class of nth-order difference equations with all real coefficients equals one is proposed, and after that the simple frequency sampling structure for any odd and even orders of the filter is designed. Finally, several simulation experiments have been performed in order to compare this filter with other known filters for the same values of free real integer parameters. It should be highlighted that the new filters compare favourably even with the already existing filters, because they have an insert attenuation of 158 dB, 15.1681% lower cutoff frequency of the passband of the filter, and 18.5313% lower cutoff frequency of the stopband of the filter, for an insert loss of 100 dB.