Hrvoje Babic

Efficient implementation of sharpened CIC decimation filters for software radio receivers

We propose an efficient structure for sharpened, cascaded integrator comb (CIC) based, decimation filter. Novelty of proposed structure is that it can be achieved for any decimation factor and its efficient finite impulse response (FIR) implementation form. It consists of multirate cascade of sharpened CIC filters with lower (prime) decimation factors. Every cascade stage can be implemented in nonrecursive FIR form with sharpened higher order Comb filters as building blocks. Applying polyphase decomposition, every stage can work on lower decimation rate depending of decimation factor of that stage. Additionally, due to special pole structure of filter stages in cascade, first few stages can be implemented with reduction in system order, depending of stage position and decimation ratio.

Systems with symmetric impulse response

A class of low pass systems with maximum impulse response symmetry is presented. The optimization of the rational transfer function parameters is carried out for the functions of the third to the tenth order, with two to eight zeros. The time and frequency domain properties of the systems are given and compared to the known linear phase filter approximations.

Filter families with minimum impulse response moments

The lowpass systems with minimum higher order moments of the impulse response are presented. The optimization of the transfer function parameters is carried out for functions ranging from the second to the tenth order, with zeros at infinity. Besides the system order, no other requirements are set to restrict the frequency domain behavior of the system. Time and frequency domain properties of the obtained systems for various moments are given and compared.

IIR equalizer design based on the impulse response symmetry criterion

An approach for IIR equalizer design based on the impulse response symmetry is presented. Design is based on numerical optimization. General form of the objective function is given and its special cases are analyzed. It is shown that the general form gives the best results while the special cases can be more appropriate for the implementation. Practical aspects of the implementation are considered and the choice of the optimization starting point is discussed. Methods features are illustrated by an example.

A robust method for equalizer design based on the impulse response symmetry

An approach for equalizer design based on the impulse response symmetry is presented. Design is based on nonlinear optimization. Analytical goal function is given and the appropriate choice of initial solution is proposed. Behavior of a typical error surface is discussed and compared to the surface obtained by numerically approximated goal function. Position of the symmetry line is analyzed and the goal function is modified in order to obtain theoretically the best symmetry for a given system.

IIR filters with maximum impulse response symmetry

A class of optimum IIR discrete time systems based on the impulse response symmetry criterion is presented. Optimization of rational transfer function parameters of the second to the tenth order, with (i) zeros at the origin and (ii) zeros located on the real axis, is carried out. The optimum systems have the smallest symmetry error for a given system order. In the frequency domain they approximate a constant group delay and have a quasi Gaussian amplitude response. The filter design procedure is outlined. The impulse invariance method based on continuous time systems with symmetric impulse response is also considered.

Time-domain symmetry as criterion for band-pass equalizer design

A method for band-pass equalizer design based on minimization of time-domain distortion is presented. The distortion is defined as the symmetry error of the systems response to a band-pass signal. The relationship between the used time-domain criterion and the classic criteria given in the frequency domain is considered. It is shown that some frequency-domain criteria, under certain conditions, lead to equalizers suboptimal in the sense of time-domain distortion.

Method for equalizer design based on time-domain symmetry

A method for equalizer design based on symmetry of systems response to a band-limited signal is presented. The equalizer minimizes time-domain distortion, assuming that significant signal components are contained within the specified low-pass band only. Design is based on nonlinear optimization. The objective function is given and the appropriate choice of the optimization starting point is discussed. Practical aspects of implementation are considered. Methods features are illustrated by example.

Filter families with minimum time-bandwidth products

A filter family with minimum product of the impulse response duration and the frequency bandwidth is considered. The impulse response spread is characterized by the higher order moments. For the frequency spread measure, the second order moment is used. Minimizing products of the moments, causal systems with the largest energy concentration in time for a given bandwidth are obtained. The resulting impulse response is quasi Gaussian with small and short ringing. The transfer function poles suitable for the filter design up to the eighth order are given.

System functions with minimum time-bandwidth product based on the higher order moments

Systems of finite order with minimum time-bandwidth products are considered. The time and frequency response spreads are defined by moments of the higher order in both domains. Minimizing the product of the moments, causal systems with the largest energy concentration in the time and frequency domain are obtained. The optimization is carried out for transfer functions up to the eighth order with two and four complex zeros. The moment orders are chosen from two to eight. The influence of the zeros and the moment order on system properties are considered. The complete data suitable for filter design are given.