FIR filter

Definition

• ${\textstyle x[n]}$ is the input signal,
• ${\textstyle y[n]}$ is the output signal,
• ${\textstyle N}$ is the filter order; an ${\textstyle N}$-order filter has ${\textstyle N+1}$ terms on the right-hand side
• ${\textstyle b_{i}}$ is the value of the impulse response at the i'th instant for ${\textstyle 0\leq i\leq N}$ of an ${\textstyle N^{\text{th}}}$-order FIR filter. If the filter is a direct form FIR filter then ${\textstyle b_{i}}$ is also a coefficient of the filter.