Bissoy.com
Doctors Medicines MCQs Q&A

A system provides output yi(t) when xi(t) is applied. If the system is said to be LTI then which of the following properties must satisfy? (i).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) + by2(t) (ii).If the input is x(t – T), then the output must be y (t – T) (iii).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) * by2(t) (iv).If the input is x(t – T), then the output must be y(t + T)

A system provides output yi(t) when xi(t) is applied. If the system is said to be LTI then which of the following properties must satisfy? (i).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) + by2(t) (ii).If the input is x(t – T), then the output must be y (t – T) (iii).If the input is x3 = ax1(t) + bx2(t), then output must be y3(t) = ay1(t) * by2(t) (iv).If the input is x(t – T), then the output must be y(t + T) Correct Answer (i) and (ii)

Analysis:

The defining properties of any LTI system are Linearity and Time-invariance.

  • Linearity means that the relationship between the input and the output are the result of linear differential equations, that is, differential equations employing only linear operators.
  • A linear system that maps an input x(t) to an output y(t) will map a scaled input ax(t) to an output ay(t) likewise scaled by the same factor a. And the superposition principle applies to a linear system: if the system maps inputs x1(t) and x2(t) to outputs y1(t) and y2(t) respectively, then it will map x3(t) = x1(t) + x2(t) to the output y3(t) where y3(t) = y1(t) + y2(t).
  • Time invariance means that whether we apply an input to the system now or T seconds from now, the output will be identical except for a time delay of T seconds.
  • That is, if the output due to input x(t) is y(t), then the output due to input x(t - T) is y(t - T). Hence, the system is time invariant because the output does not depend on the particular time the input is applied.

Related Questions

Consider a system whose input r and output y are related by the equation $$y\left( t \right) = \int\limits_{ - \infty }^\infty {x\left( {t - \tau } \right)} h\left( {2\tau } \right)d\tau $$
Signal Processing mcq question image
Where h(t) is shown in the graph
Which of the following four properties are possessed by the system? BIBO: Bounded input gives a bounded output
Causal: The system is causal.
LP : The system is low pass.
LTI: The system is linear and time-invariant.
If H(z) is the system function of an LTI system and HI(z) is the system function of the inverse LTI system, then which of the following is true?
Which of the following statements is/are correct? 1. A system is said to be Finite Impulse Response (FIR), if the output samples of the system depend only on the present input and a finite number of past or previous input samples. 2. If the output of a system y(n) depends only on the present input and past inputs, but not on past outputs, then it is called a non-recursive system. 3. If the output of a system y(n) depends only on the present input and past inputs, but not on past outputs, then it is called a recursive system.
A stable linear time invariant (LTI) system has a transfer function $$H\left( s \right) = {1 \over {{s^2} + s - 6}}.$$    To make this system causal it needs to be cascaded with another LTI system having a transfer function H1(s). A correct choice for H1(s) among the following options is
When a discrete time LTI system is said to be causal? must not depend on x for k>n b) Output y must not depend on x for k=n c) Output y must not depend on x for kn
If h(n) is the impulse response of an LTI system and hI(n) is the impulse response of the inverse LTI system, then which of the following is true?
In a town fair 50 people were asked which dessert they liked: ice cream, Donuts, or cupcakes. 28 said they like ice cream, 26 said they like donuts, and 26 said they like cupcakes. 8 said they like all three. 17 said they like donuts and cupcakes, 11 said they like ice cream and cupcakes. 5 said they do not like any of these. Find those people who liked ice cream and donuts but not cupcakes.
What are the properties of an LTI system posse other than Associative, Commutative and Distributive properties?
Consider the string abbccddeee. Each letter in the string must be assigned a binary code satisfying the following properties: 1. For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter. 2. For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter. Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string? 
Which of the following statements is/are correct? 1. A continuous-time system is a system in which, continuous-time input signals are applied, resulting in continuous-time output signals. 2. A system is said to be linear if it follows the superposition theorem. 3. A system is said to be non-linear if it follows the superposition theorem.