Frequency transformations for digital filters
It is shown that the reactance transformation for an analog filter corresponds to an all-pass function transformation in the case of a digital filter. It is further shown how this result could be used to obtain in a simple way the spectral transformations for digital filters derived by Constantinides.
2-D IIR filter design using an adaptation of the random search methodology
A number of techniques are available for generating low-pass filters [1] that help to remove additive noise from transmitted signals. Frequency transformation techniques [2,3,4] can be subsequently used to convert these filters into those with different specifications. However, they will always result in either high-pass, band-pass or band-reject filter types. However, the need may arise for designing a nonstandard filter of arbitrary specifications. This includes cases where signals in multiple bands may need to be transmitted or rejected at different attenuation levels. In this paper, we discuss a method for designing such a filter with arbitrary frequency response characteristics. The design technique is based on an adaptation of the random search method [5]. The only inputs required for this algorithm are the desired frequency response and resolution. The algorithm will create a frequency domain transfer function of the desired characteristics (both magnitude and phase). A uniform random number generator will be required for the functioning of the algorithm.
The design and applications of digital filters with complex coefficients
The digital filter with complex coefficients finds applications in the digital processing of analytic signals and complex envelopes. A theory is developed for designing such filters based on low-pass analog prototypes and digital design techniques for real filters. An example of a filter designed according to this theory is presented. The relative advantages of real and analytic signal processing are discussed. It is shown that the filtering required by either processing technique requires essentially the same amount of signal operations, which is reasonable in view of the fact that the same amount of information is processed in both classes of filter.