One of the most convenient operations in signals is linear filtering. In fact, useful information is conveyed on a certain spectral band and everything outside that band can be considered noise. Filtering it out is a good way to increase overall measurement quality. Furthermore, modern measurement systems often involve a sample and hold circuit, coupled with an analog to digital converter. As sampling is subjected to the aliasing phenomenon, this means that an analog anti-aliasing filter must always be present. In some low-performance applications, the natural low-pass behavior of sensors and amplifiers might be sufficient, but to achieve high performances, a dedicated filtering block becomes mandatory.
Filter design is a huge domain whose surface is barely scratched by this chapter. We want to provide an understanding of the problems and the terminology, as well as a design method for simple active filters.
Figure 3.1 shows the classic design flow for filter design. The first operation is called approximation. It consists of writing down a transfer function H(p) of a two-port network (in the Laplace domain):
where n(p) and g(p) are polynomials (with real coefficients of p, the Laplace variable), such that the response |H(j2πf)| of the filter matches some constraints. Usually, attenuation in some frequency bands is ...