Linearity: 1st Difference Filter

Linearity: First Difference Filter

\(x_1[n]\)

\(y_1[n]\)

\(x_2[n]\)

\(y_2[n]\)

Figure 1: Two different inputs to the same system. The system is an FIR filter and therefore linear. Click on any of the above inputs, system blocks or outputs for a "close-up."

\(a x_1[n] + b x_2[n]\)

\(y_3[n]\)

Figure 2: Are the scaling and superposition properties satisfied? In other words, does \(y_3[n]=ay_1[n]+by_2[n]\)? Click on the output to find out.