Introduction to digital filters and comparison with analog filters

Introduction to digital filters, part one. Advantages over analog filters.

In the figure, frequency characteristics of the ideal filters. (a) low-pass; (b) highpass; (c) band-pass; d) notch.

Higher-order analog filters are obtained by cascading various stages of the first and second order. However, the unwanted interaction between the various stages, even when they are of an active type, limits the ideal characteristics that one would like to achieve. In addition, even in the simplest active filters, there is a feedback mechanism that, if not properly controlled, can make the device unstable.

Analog low-pass filter
Analog low-pass filter. a) passive b) active

The analog filters, in addition to always maintaining considerable uncertainty about the coefficients obtained, have almost no flexibility of use and must be redesigned for each application. Digital filters, which in fact are algorithms, allow the user complete control over the characteristic parameters that can always be established with the required precision; consequently, it is possible to implement digital filters of unthinkable order with analog methods, designed for the user and reprogrammable for further applications.

To this should be added that digital filters, not being based on physical components, are free from aging processes and thermal drifts. They, if they are implemented on DSP, will have the coefficients calculable in real-time, so as to be able to vary them at will and create the so-called adaptive filters.

Features of digital filters

Summarizing what has been said so far, we can list the main characteristics of digital filters:

  • Stability. Their characteristics are independent of environmental conditions;
  • Repeatability. The values of the individual components are replaced by digital parameters;
  • Adaptability. The parameters are programmable and reconfigurable;
  • Adactivity. The calculations of the coefficients can be carried out in real time so as to obtain adaptive filters;
  • Predictability. The filter design can be easily tested through simulation;
  • High performance. They can achieve the desired frequency response without phase errors.

Categories of digital filters

Essentially, digital filters fall into two categories:

  • FIR filters. Finite Impulse Response, also called non-recursive.
  • IIR filters. Infinite Impulse Response, also called recursive.

Final note

After this introduction, in the next articles we will analyze the principles of operation of the two categories of filters mentioned, we will see the synthesis techniques and we will compare the strengths and weaknesses of FIR and IIR filters.

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