FIR Filters

We’ve established that filters are just convolutions so we can use the fact that if:

$$x(n)\ast h(n)=y(n)$$

then:

$$Y(z)=X(z)H(z)$$

So we can use the definition:

$$H(z)=\sum _{n=0}^{\infty }h(n)z^{-n}$$

so, we know:

$$Y(z)=H(z)X(z)=\sum _{n=0}^{\infty }h(n)z^{-n}X(z)$$

Where we can say: $X(z)$ is our input signal $z^{-n}$ is a delay by n samples $h(n)$ is our factors/impulse response

So a simple circuit diagram would look like:

Example Filters:

FIR Averaging Filter FIR Linear Phase Filter