Electronic Devices Peter Apostolov 12 2 2023 https://doi.org/10.6025/ed/2023/12/2/45-53 https://www.dline.info/ed/fulltext/v12n2/edv12n2_3.pdf This paper proposes an optimal third-degree polynomial, which approximates Kronecker’s delta function with high precision. The polynomial is obtained by a new approximation method, called “method with compressed cosines”. The method is based on Chebyshev’s optimality norm. The polynomial is used for narrow bandpass IIR filter design. The filter’s selectivity depends on the parameter Q without increasing the polynomial’s order. With the proposed method an IIR filter with 5(6) multipliers, a very narrow passband and a high stopband attenuation can be designed.