0.2 Filter types

So what is a filter? In general a filter is a device that discriminates, according to one or more attributes at its input, what passes through it.One example is the colour filter which absorbs light at certain wavelengths. Here we shall describe frequency-selective filters. It is called freqency-selectivebecause it discriminates among the various frequency compononents of its input. By filter design we can create filters that pass signals with frequencycomponents in some bands, and attenuates signals with content in other frequency bands.

It is customary to classify filters according to their frequency domain charachteristics. In the following we will take a look at: lowpass, highpass, bandpass, bandstop, allpassand notch filters. (All of the filters shown are discrete-time)

Ideal filter types

Lowpass

Attenuates frequencies above cutoff frequency, letting frequencies below cutoff( $f_c$ ) through, see .

Highpass

Highpass filters stops low frequencies, letting higher frequencies through, see .

Bandpass

Letting through only frequencies in a certain range, see .

Bandstop

Stopping frequencies in a certain range, see .

Allpass

Letting all frequencies through, see see .

Other filter types

Notch filter

The notch filter recognized by its perfect nulls in the frequency response,see .

Matlab files

idealFilters.m , notchFilter.m