Linear system: A system is known as linear if and only if it possesses both homogeneity and superposition properties. Superposition implies that an input r1 (t) gives an output c1 (t) and another input r2 (t) gives the output c2 (t). If two inputs are applied together then the output will be the sum of two outputs:
r1(t) + r2(t) = c1(t) + c2(t)
If our input-output relationship is a straight line passing through the origin, then the system obeys the superposition property. The straight line passing through origin means that the output is zero (0) for zero (0) input.
If the input increases for any system K time from r1 (t) to Kr1 (t) then the magnitude of the output is also increased from c1 (t) to Kc1 (t) then this property is known as homogeneity. This property is a necessary condition for a system to be linear.
Linear system: A system is known as linear if and only if it possesses both homogeneity and superposition properties. Superposition implies that an input r1 (t) gives an output c1 (t) and another input r2 (t) gives the output c2 (t). If two inputs are applied together then the output will be the sum of two outputs:
r1(t) + r2(t) = c1(t) + c2(t)
If our input-output relationship is a straight line passing through the origin, then the system obeys the superposition property. The straight line passing through origin means that the output is zero (0) for zero (0) input.
If the input increases for any system K time from r1 (t) to Kr1 (t) then the magnitude of the output is also increased from c1 (t) to Kc1 (t) then this property is known as homogeneity. This property is a necessary condition for a system to be linear.