Design of digital nyquist filters based on the measure of squared errors at sampling points
Takuro Kida, Yutaka Fukuda · Electronics and Communications in Japan (Part I Communications) · 1987
Abstract This paper describes design methods of the digital Nyquist filters based on the squared errors of the impulse response at equally spaced sampling points except one. First of all, for a specified pole of a transfer function, we consider the pole location which causes a problem when we use the residue formula proposed by Kida and Ohsumi to minimize the above mentioned squared errors. Then, assuming about 6 to 8 degrees for the orders for transfer functions, we consider a method which gives a favorable pole arrangement. We make an examination about a simple method of determining a pole arrangement which provides a favorable characteristic such that the squared errors at equally spaced sampling points except one point are about 10−5 and that the stopband attenuation is about 50 dB. Furthermore, in order to realize a large stopband attenuation which is required in the design of digital Nyquist filters, propose a design method of a transfer function based on a quadratic programming specifying the attenuation at a point in the frequency domain specified in advance. We show its effectiveness by examples. Finally, for the design of digital Nyquist filters using an interpolation method based on the sampling theorem of non‐equal space derived by Kida and Fukuda, we consider an example which indicates that transfer functions obtained by the above two design methods are appropriate.