Filter Classifications in the Frequency Domain

Most signals of practical interest can be considered as a sum of complex sinusoids with different amplitudes and phases. Filters in DSP can then be designed to alter these magnitudes and phases for specific purposes, as follows.

Lowpass filter

A lowpass filter passes the spectrum around zero while attenuating the remaining high-frequency components. This is achieved by choosing the system frequency response in a manner so that the filter magnitude is $1$ at low frequencies (up to the cutoff frequency) and ideally $0$ for higher frequencies. The frequency response of an ideal lowpass filter is shown in the figure below in which ${\omega }_{Cut}$ ...