From Eq.(5.7), we can see that the impulse response becomes zero after time . Therefore, a tapped delay line (Fig.5.5) can only implement finite-duration impulse responses in the sense that the non-zero portion of the impulse response must be finite. This is what is meant by the term finite impulse response (FIR). We may say that the impulse response has finite support .
Causal FIR Filters
Convolution Representation of FIR Filters