Digital Filter Design Techniques in the Frequency Domain

In digital filtering, the spectrum is shaped using digital components as the basic elements. Although the physical realization is different, the aims of digital filtering are, thus, the same as those for continuous filtering. It is likely that digital filtering, already in extensive use for computer simulation of analog filters, will find increasing real-time application. Real-time digital filters have several advantages over their analog counterparts: a greater degree of accuracy can be attained in their realization; a larger variety can be built since certain realization problems (akin to negative elements) do not arise; no special components are needed to realize filters with time-varying coefficients; and they are of particular utility at very low frequencies where analog components become large and unwieldy. In contrast to the linear differential equations of continuous filter theory, linear digital filter theory is based on the mathematics of linear difference equations. Using the z-transform calculus, a number of digital filter design techniques are discussed. One technique is useful in designing a digital filter whose impulse response is like that of a given analog filter, whie other techniques are suitable for designing digital filters meeting specified frequency response criteria. Another yields filters with linear phase, specified frequency response, and controlled impulse response duration. The effect of digital arithmetic on digital filter behavior is considered.