5.1 Four types of linear-phase fir filters

Four types of linear-phase fir filters

Linear-phase FIR filter can be divided into four basic types.

When $h(n)$ is nonzero for $0\le n\le N-1$ (the length of the impulse response $h(n)$ is $N$ ), then the symmetry of the impulse response can be written as

Type i: odd-length symmetric

The frequency response of a length $N=5$ FIR Type I filter can be written as follows.

Type ii: even-length symmetric

The frequency response of a length $N=4$ FIR Type II filter can be written as follows.

Type iii: odd-length anti-symmetric

The frequency response of a length $N=5$ FIR Type III filter can be written as follows.

Type iv: even-length anti-symmetric

The frequency response of a length $N=4$ FIR Type IV filter can be written as follows.