OVERVIEW

We have taken the viewpoint that a filtering device is a signal processor, capable of signal discrimination on the basis of either frequency-domain or time-domain characteristics. In the past, electronic systems predominantly used continuous-time (analog) signals, but the last decade has seen these signals replaced by discrete-time (sampled) signals in many communication, radar, seismic, and biomedical applications. A sampled signal that is additionally quantized in amplitude becomes a sequence of numbers and is called a digital signal. The filter that processes these numbers is known as a digital filter, but "numerical filter" might be a more accurate name.

The aims of digital filtering are the same as those of continuous filtering, but digital hardware is used as the basic building block rather than the more conventional analog components. The increased use of digital circuitry results from the advances in integrated circuitry. As large-scale integration (LSI) progresses and circuit chips become readily available and inexpensive, the potential of digital filtering increases. Then more functions on a single chip will be possible, resulting in digital filters occupying less space and possessing greater accuracies than conventional analog filters.

Digital filters, in addition to incorporating the benefits of integrated circuitry, offer the following advantages over analog filters.

• Finite-duration impulse responses are achievable.

• Time-varying filters are realized without any special components by simply programming a different set of numbers into the filter.

• Linear-phase filters are realizable.

• Certain realization problems, such as negative element values, and practical problems, such as inconveniently large components at low...