Digital filters can be divided into two categories: one is a classical filter, the useful components in the input signal and the components you want to filter out have different frequencies.
One is a modern filter, in which the useful signal in the input signal and the frequency band of the signal to be filtered out overlap.
Classical filters can be divided into low-pass/high-pass/band-pass/band-stop filters in the frequency domain
From the time domain characteristics, digital filters can be divided into FIR (finite impulse response digital filter) and IIR (infinite impulse response digital filter)
For FIR, its output depends only on a finite number of past and present inputs.
For IIR, its output depends not only on a finite number of past and present inputs, but also on past outputs.
The digital filter generally has the following difference equation,
Among them, x(n) is the input sequence, y(n) is the output sequence, and ak and bk are the filter coefficients.
When bk=0, , is the difference equation of FIR, which we
use to express and Z transform it to get
Usually digital filters are used to realize the frequency selection function. The index requirements of the frequency selection filter are given by the amplitude-frequency characteristics, and the phase-frequency characteristics are not required. If there are phase requirements for the output waveform, such as speech synthesis, waveform transmission, etc., It is required to design a linear phase digital filter.