Method for integrated digital filters for values poles and zeros transfer function

Digital complex filters are widely used in digital signal processing. Methods for their calculation and implementation are extremely various. The serial structural circuit consisting of digital chains of second and fourth order has the most distribution. One more variant of complex filters calculation is offered in this paper, which uses the zeros and poles coordinate of transmission function of the complex filter.

Coordinates of zeros and poles of the transmission function have in the most of cases the complex values, which allows application of calculation methods of the complex filters to implement the one-order co-factors.

To illustrate this method, we consider the calculation of the complex pass-band filter using the Butterworth low-frequency prototype of the third order, which is presented as the product of co-factors of the first order containing zeros - and poles - coordinates of LF-prototype as coefficients. LF prototype-s co-factors are converted into transmission functions of digital chains of the first order LFF with complex coefficients. For this, the variables - change is fulfilled, which is used in the method of generalized bi-linear conversion. After that the frequency response displacement method is used with the help of variable change from to . Obtained transmission functions of the first-order chains with complex coefficients (using two methods) are realized in the form of structural circuits, which then are connected serially. Chains can be implemented using methods of complex arithmetic or using the conversion method for transmission function. It is shown that the complex arithmetic method requires at implementation the lesser number of arithmetic operations.