A method for calculating complex digital bandpass filters with a parallel structure

Abstract

A method for calculating a complex digital bandpass filter with a parallel structure from the values of zeroes and poles of the normalized LFprototype is proposed. The use of a parallel structure is convenient in implementing complex bandpass filters based on field-programmable gate arrays. The LF-prototype’s transfer function can be represented as the sum of first-order fractional rational functions with complex coefficients. Then, the LPF transfer function can be calculated as the sum of the transfer functions of digital first-order sections with complex coefficients using the method of generalized bilinear transformation. Each term is realized in the form of the proposed generalized canonical structural diagram, after which the obtained structural units are connected in parallel by means of an adder. To convert the LPF structural diagram into the bandpass filter structural diagram, the delay units in the digital sections should be replaced by complex delays, while retaining the digital section’s structural diagram. An example of calculating a complex digital filter with a parallel structure using the normalized Chebyshev Type II (inverted) LF-prototype is given. The obtained structures of low-pass and complex bandpass filters are simulated in the Micro-Cap circuit simulation environment. The simulation results have confirmed the validity of the proposed method for calculating a complex digital bandpass filter. By using complex delays it is possible to readjust the complex high-order bandpass filter's center frequency by simultaneously changing two coinciding coefficients in all complex delays. This possibility is confirmed by the relevant results of circuit simulation. The proposed calculation method makes it possible to use LF-prototypes of different orders and kinds, including those containing zeroes.