CT Systems and DT Systems | Time invariant and time variant system

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CT and DT Systems

 A system is defined as a physical device which contains set of elements or functional blocks and that generates a response or output signal for a given input.

Classification of system:  

    The systems are classified as,             

  • Static & dynamic system  
  • Time invariant and variant system  
  • Linear and non linear system  
  • Causal and non causal system  
  • Stable and unstable system  

Static and dynamic system:  

• Static system is said to be a memoryless system. 

• The output does not depend on the past or future input. 

• It only depends on the present input for an output. 

        Eg, y(n) = x(n)  

• Dynamic system is said to be a system with memory.  

• Its output depends on the past values of input for an output.  

        Eg. Y(n) = x(n) + x(n - 1)  

• These static and dynamic systems are otherwise called memoryless and systems with  memory.

 Systems with and without memory:  

    A system is called memory less if the output at any time t (or n) depends only on the  input at time t (or n); in other words, independent of the input at times before or after t  (or n). Examples of memory less systems


Time invariant and time variant system:  

• If the time shifts in the input signals results in corresponding time shift in the output,  then the system is called as time invariant.  

• The input and output characteristics do not change with time.  

• For a continuous time system,  

        f[x(t1 – t2)] = y(t1 – t2)  

• For a discrete time system,  

        F[x(n - k)] = y(n - k)

        • If the above relation does not satisfy, then the system is said to be a time variant  system.  

        • A system is called time-invariant if the way it responds to inputs does not change over  time.

Examples of time-invariant systems:  

    The RC circuit considered earlier provided the values of R or C are constant.  


Examples of time-varying systems:  

    • The RC circuit considered earlier if the values of R or C change over time.  

    • Most physical systems are slowly time-varying due to aging, etc. Hence, they can be  considered time-invariant for certain time periods in which its behavior does not change significantly. 

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