With reference to impulse response of LTI systems, consider the following statements:1.The impulse response completely characterizes an LTI system.2.The output of an LTI system can be obtained by convolving input with impulse response.3.For a given system, the impulse response is unique.4.Impulse response concept is applicable only to discrete-time systems.Which of the above statements is/are correct?

Correct Answer: B - 1, 2 and 3 only

Quick Concept Explanation

The impulse response uniquely characterizes an LTI system for a specified input-output relationship because any input can be decomposed into shifted impulses and the output follows by convolution. This concept applies in both continuous and discrete time. Key relation: y(t)=x(t)*h(t); y[n]=x[n]*h[n].

Exam focus: For LTI questions, think 'impulse response + convolution'. Common trap: Impulse response is not a discrete-time-only concept.

Statement-wise Verification

• Statement 1 - Correct.
  The impulse response completely characterizes an LTI system.
  The impulse response uniquely characterizes an LTI system for a specified input-output relationship because any input can be decomposed into shifted impulses and the output follows by convolution.
• Statement 2 - Correct.
  The output of an LTI system can be obtained by convolving input with impulse response.
  The impulse response uniquely characterizes an LTI system for a specified input-output relationship because any input can be decomposed into shifted impulses and the output follows by convolution.
• Statement 3 - Correct.
  For a given system, the impulse response is unique.
  For LTI questions, think 'impulse response + convolution'.
• Statement 4 - Incorrect.
  Impulse response concept is applicable only to discrete-time systems.
  Impulse-response characterization applies to continuous- and discrete-time LTI systems

Core Concept

The impulse response uniquely characterizes an LTI system for a specified input-output relationship because any input can be decomposed into shifted impulses and the output follows by convolution. This concept applies in both continuous and discrete time.

Formula / Key Relationship

y(t)=x(t)*h(t); y[n]=x[n]*h[n].

Why the Other Options Are Wrong

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

Exam Shortcut / Approach

For LTI questions, think 'impulse response + convolution'.

Common Mistake

Impulse response is not a discrete-time-only concept.

Quick Revision

LTI Characterization by Impulse Response is linked with Impulse Response, LTI Systems and Signals and Systems. For LTI questions, think 'impulse response + convolution'.