Design of a class of multidimensional recursive digital filters using transformation techniques

It is shown that stable 3-D recursive digital filters with low-sensitivity ladder realizations can be derived from 1-D analog prototypes via spectral transformation. A major advantage of the design approach is that the initial approximation method is carried out in the analog domain utilizing the available methods, design tables, and techniques. Conversion to the discrete domain is carried out through a set of closed-form design formulas and, thus, does not require the cumbersome approach of iterative methods of optimization. The stability of the resulting digital filter reverts to that of ensuring that the employed multivariable reactance function is stable. Thus, the stability of the designed filter is guaranteed as long as all coefficients of this reactance function are positive real constants. The design method can easily be extended to realize a similar class of multidimensional recursive digital filters. Zero-phase filtering is easily obtained with the cost of only one first-octant filter realization. Another feature of the realization technique is that it lends itself to generating digital filters with tunable characteristics. By appropriately changing the parameters of the transformation function, one can adjust bandwidth along each dimension as well as the convexity of the passband hyperplane. Nevertheless, the shape of the passband region closely follows the characteristics of the multivariable reactance function. Therefore, the shape of the passband region is not completely tunable. Another drawback of this technique is that online processing for real-time data is not possible