Filters - Theory
Filters In this post, I want to present the theory needed for digital filter design. Firstly, a quick description of mainly used filters in the continuous domain - I want to give you some intuition in interpreting the transform functions. Next, I will present practical discretization from the '$s$' domain into the '$z$' (discrete time). Finally, a difference equation will be provided which can be directly programmed on any microprocessor. In a future post, I will show the possible implementation of described filters. In essence, the filter should block undesirable frequencies and let others pass through without distortion. For our applications, we can divide filters into 4 main categories: Low-pass filters High-pass filters Band-pass filters Notch filters Low-pass filter As the name suggests this filter allows low frequencies to pass and suppress high ones. The simplest LPF is a system with one pole: \begin{gather}H(s)=\frac{\omega_{0}}{s+\omega_{0}}\end{gather} A typ