Filter Classifications in the Frequency Domain

Learn about the classification of filters in the frequency domain according to their passbands and stopbands.

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 11 at low frequencies (up to the cutoff frequency) and ideally 00 for higher frequencies. The frequency response of an ideal lowpass filter is shown in the figure below in which ωCut\omega_{Cut} and ωS\omega_S denote the cutoff frequency and sample rate, respectively.

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