FIR filter block diagram

In the digital signal processing system, the use of  FIR short form is one type of filter whose impulse response is of finite duration, the reason of it settles zero in finite time. This is a contrast to IIR filter design, which has internal feedback and may continue to respond indefinitely. 

A discrete time FIR filter of N number of order and the top part is an N stage delay line with total N+1 taps to shown in the figure. Each of unit delay is a Z-1 type of operator in the Z transform notation

The output y of a linear time-invariant system is determined by conveying its input signal x with its impulse response b. 

For a discrete-time FIR filter, the output is depend on a weighted sum of the current and finite number of previous values of the input signal.

The operation is described by the following equation, which defines the output sequence of y[n] in terms of its input sequence of x [n] given below.

Y[n] = b0 x[n] + b1 x[n-1]  + b2 x[n-2] …………bn x[n-N]

Y[n] =  ∑ bi x[n-i]


x[n] = input signal
y[n] = output signal