System Properties | Signals and Systems | GATE Preparation | EC

Application This topic will be helpful to classify real-time systems based on properties like Memory, dependence on present, past and future values of inputs, behavior of system wrt time etc. This type of classification helps us to design systems based on requirement.

Explanation System can be defined as meaningful connection of devices which produces required output(s) by processing input(s). System can be represented in many ways like Transfer Function, Impulse Response, State Variables, Differential equations etc. In this lecture, some very important properties of system (s) are discussed. They are

  1. Memory
  2. Invertibility
  3. Causality
  4. Stability
  5. Linearity
  6. Time Invariance

Static and Dynamic System: Based on property of memory, system can be classified as Static and Dynamic Systems. If the System for its functionality requires memory for its operation, it is known as dynamic system otherwise it is known as static system. Invertible and Non-Invertible System: To understand the concept of Invertibility, let us consider two systems: System-1 and System-2. Let x(t) and y(t) be the input and the output of system-1 respectively. The output of system-1 , y(t), is given as input to system-2 whose output is w(t). System-1 can be said to be invertible if output of system-2 ,w(t) is same as x(t). If there is no possibility of w(t) being x(t), then system-1 is a non-invertible Systems. It is observed that when distinct inputs lead to distinct outputs, such a system is automatically a invertible system.

Causal and Non-Causal System: A System is said to be causal, when the output of system does not depend upon the future values of the input but can use present and past values of input for its functionality. Otherwise the system is non-causal in nature. All practically used systems are causal in nature when input is in real time. Incase of recorded inputs which can be used in applications of image processing etc., non-causal systems are possible.

Stable and Unstable System: A system is said to be BIBO stable, when it each and every bounded input given to the system leads to bounded output. Even for a single bounded input, if the output is unbounded, system is unstable.

Linear and Non-Linear System: A system which satisfies superposition principle is said to be Linear system otherwise the system is non linear. Superposition principle has two subparts in it. (1) Homogeneity/Scaling property (2) Addtivity. A system which is linear, satisfies both parts of superposition principle.

Time Invariant and Time Variant System: A System is said to be time invariant, when the characteristic or behavior of the system does not change with time which should be the case in many real time systems. When characteristic of system changes with time, it is known as time variant system. In order to test time invariance, the delayed input is given to the system and is expected that output of the system is also delayed by same value. In this Subject of Signals and systems that we study for Undergraduate, we restrict ourselves to Linear and Time-Invariant (LTI) System