Signal and Systems Set 2

1. If the output of the system of the system at any 'n' depends only the present or the past values of the inputs then the system is said to be:

Linear

Non-Linear

Causal

Non-causal

A system is said to be causal if the output of the system is defined as the function shown below
y(n)=F[x(n),x(n-1),x(n-2),…] So, according to the conditions given in the question, the system is a causal system.

Explanation

A system is said to be causal if the output of the system is defined as the function shown below
y(n)=F[x(n),x(n-1),x(n-2),…] So, according to the conditions given in the question, the system is a causal system.

2. For a signal x(n) to exhibit even symmetry, it should satisfy the condition | X(-ω)|=| X(ω)|.

True

False

We know that, if a signal x(n) is real, then
X*(ω)=X(-ω)

Explanation

We know that, if a signal x(n) is real, then
X*(ω)=X(-ω)

3. The solution obtained by assuming the input x(n) of the system is zero is:

General solution

Particular solution

Complete solution

Homogenous solution

By making the input x(n)=0 we will get a homogenous difference equation and the solution of that difference equation is known as Homogenous or Complementary solution

Explanation

By making the input x(n)=0 we will get a homogenous difference equation and the solution of that difference equation is known as Homogenous or Complementary solution

4. If a power signal has its power density spectrum concentrated about zero frequency, the signal is known as:

Low frequency signal

Middle frequency signal

High frequency signal

None of the mentioned

We know that, for a low frequency signal, the power signal has its power density spectrum concentrated about zero frequency.

Explanation

We know that, for a low frequency signal, the power signal has its power density spectrum concentrated about zero frequency.

5. The discrete time function defined as u(n)=n for n≥0;=0 for n<0 is an:

Unit sample signal

Unit step signal

Unit ramp signal

None of the mentioned

When we plot the graph for the given function, we get a straight line passing through origin with a unit positive slope. So, the function is called as unit ramp signal.

Explanation

When we plot the graph for the given function, we get a straight line passing through origin with a unit positive slope. So, the function is called as unit ramp signal.

6. Zero-input response is also known as Natural or Free response.

True

False

For a zero-input response, the input is zero and the output of the system is independent of the input of the system. So, the response if such system is also known as Natural or Free response

Explanation

For a zero-input response, the input is zero and the output of the system is independent of the input of the system. So, the response if such system is also known as Natural or Free response

7. What is the output y(n) when a signal x(n)=n*u(n)is passed through a accumulator system under the conditions that it is initially relaxed?

(n2+n+1)/2

(n(n+1))/2

(n2+n+2)/2

None of the mentioned

Given that the system is initially relaxed, that is y(-1)=0
According to the equation of the accumulator,

Explanation

Given that the system is initially relaxed, that is y(-1)=0
According to the equation of the accumulator,

8. What is the zero-input response of the system described by the homogenous second order equation y(n)-3y(n-1)-4y(n-2)=0 if the initial conditions are y(-1)=5 and y(-2)=0?

(-1)n-1 + (4)n-2

(-1)n+1 + (4)n+2

(-1)n+1 + (4)n-2

None of the mentioned

Explanation: Given difference equation is y(n)-3y(n-1)-4y(n-2)=0—-(1)
Let y(n)=λn
Substituting y(n) in the given equation
=>λn – 3λn-1 – 4λn-2 = 0
=> λn-2(λ2 – 3λ – 4) = 0
the roots of the above equation are λ=-1,4
Therefore, general form of the solution of the homogenous equation is

Explanation

Explanation: Given difference equation is y(n)-3y(n-1)-4y(n-2)=0—-(1)
Let y(n)=λn
Substituting y(n) in the given equation
=>λn – 3λn-1 – 4λn-2 = 0
=> λn-2(λ2 – 3λ – 4) = 0
the roots of the above equation are λ=-1,4
Therefore, general form of the solution of the homogenous equation is