With respect to discrete-time systems, consider the following statements:1.Discrete-time signals are defined only at integer time instants.2.Such systems are commonly implemented using digital processors.3.Difference equations are used to describe discrete-time systems.4.Discrete-time systems cannot be linear.Which of the above statements is/are correct?

Correct Answer: C - 1, 2 and 3 only

Quick Concept Explanation

A discrete-time signal is defined at discrete indices, commonly integer n, and discrete-time systems are often implemented by digital processors. Linear constant-coefficient difference equations are a standard way to describe such systems. Key relation: Example LTI form: y[n]+a1y[n−1]=b0x[n]+b1x[n−1].

Exam focus: Time discreteness and system linearity are separate properties. Common trap: Do not assume a digital/discrete system must be nonlinear.

Statement-wise Verification

• Statement 1 - Correct.
  Discrete-time signals are defined only at integer time instants.
  A discrete-time signal is defined at discrete indices, commonly integer n, and discrete-time systems are often implemented by digital processors.
• Statement 2 - Correct.
  Such systems are commonly implemented using digital processors.
  A discrete-time signal is defined at discrete indices, commonly integer n, and discrete-time systems are often implemented by digital processors.
• Statement 3 - Correct.
  Difference equations are used to describe discrete-time systems.
  Linear constant-coefficient difference equations are a standard way to describe such systems.
• Statement 4 - Incorrect.
  Discrete-time systems cannot be linear.
  Many discrete-time systems are linear and are described by linear difference equations

Core Concept

A discrete-time signal is defined at discrete indices, commonly integer n, and discrete-time systems are often implemented by digital processors. Linear constant-coefficient difference equations are a standard way to describe such systems. Discrete-time systems may be linear or nonlinear; discreteness does not determine linearity.

Formula / Key Relationship

Example LTI form: y[n]+a1y[n−1]=b0x[n]+b1x[n−1].

Why the Other Options Are Wrong

Option A is incorrect because it omits correct statement(s) 3. Option B is incorrect because it omits correct statement(s) 1. Option D is incorrect because it includes incorrect statement(s) 4.

Exam Shortcut / Approach

Time discreteness and system linearity are separate properties.

Common Mistake

Do not assume a digital/discrete system must be nonlinear.

Quick Revision

Discrete-Time Signal and System Models is linked with Difference Equations, Discrete-Time Systems and Signals and Systems. Time discreteness and system linearity are separate properties.