førsteordensfilter

Førsteordensfilter, also known as a single-pole filter, is the simplest type of analog electronic filter. It is characterized by its single reactive element, either a capacitor or an inductor, in addition to resistors. These filters are commonly implemented as either a low-pass filter or a high-pass filter.

A first-order low-pass filter allows frequencies below a certain cutoff frequency to pass through relatively unimpeded, while attenuating frequencies above this cutoff. Conversely, a first-order high-pass filter allows frequencies above the cutoff frequency to pass while attenuating those below. The cutoff frequency, often denoted as f_c, is the frequency at which the output signal's power is reduced by half, or its amplitude is reduced to approximately 70.7% of its input value.

The mathematical description of a first-order filter involves a first-order differential equation. In the frequency domain, its transfer function is a rational function of the complex variable 's' (or 'jω'), with a single pole. This characteristic gives the filter its name. First-order filters are widely used in signal processing for basic smoothing, noise reduction, and as building blocks for more complex filter designs. Their simplicity makes them easy to design and implement, though their filtering performance is less sophisticated compared to higher-order filters.