Pre Assessment Test - Basics Of Signals And Systems

1. Match the following

Laplace Transform

Z Transform

Fourier Transform

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2. Match the following basic properties with its expression

Commutative Property

Associative Property

Distributive Property

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3. Low pass filter eliminates frequencies ______________ than the cut-off frequency

Higher

Lower

A low pass filter eliminates frequencies that are higher than the cut-off frequency. This means that any frequencies above the cut-off frequency are attenuated or reduced in amplitude, while frequencies below the cut-off frequency are allowed to pass through with minimal attenuation. Therefore, the correct answer is "higher."

Explanation

A low pass filter eliminates frequencies that are higher than the cut-off frequency. This means that any frequencies above the cut-off frequency are attenuated or reduced in amplitude, while frequencies below the cut-off frequency are allowed to pass through with minimal attenuation. Therefore, the correct answer is "higher."

4. All the real time natural signals are of which type?

Discrete

Continous

Digital

Real time natural signals are analog which are always continous

Explanation

Real time natural signals are analog which are always continous

5. Is analog signals are more flexible for easy transmission?

True

False

Digital signals are more flexible to transmit than analog signals

Explanation

Digital signals are more flexible to transmit than analog signals

6. Select the conditions for the existence of Initial value theorem.

If time t approaches to infinity then the function f(t) should exists.

If time t approaches to zero then the function f(t) should vanish.

If time t approaches to zero then the function f(t) should exists.

If time t approaches to infinity then the function f(t) should vanish.

The initial value theorem states that if a function f(t) is Laplace transformable and has a finite Laplace transform F(s), then the limit of f(t) as t approaches zero exists and is equal to the initial value of F(s) at s=0. Therefore, the condition for the existence of the initial value theorem is that if time t approaches zero, then the function f(t) should exist.

Explanation

The initial value theorem states that if a function f(t) is Laplace transformable and has a finite Laplace transform F(s), then the limit of f(t) as t approaches zero exists and is equal to the initial value of F(s) at s=0. Therefore, the condition for the existence of the initial value theorem is that if time t approaches zero, then the function f(t) should exist.

7. Expand the series ->(1 + x)^−1

1 + x + x^2 + x^3 + x^4 + . . .

1 − x + 2x^2 − 3x^3 + 4x^4 − . . .

1 − x + x^2 − x^3 + x^4 − . . .

The given series is an expansion of the expression (1 + x)^-1. This can be derived using the formula for the sum of an infinite geometric series, which is a/(1 - r), where a is the first term and r is the common ratio. In this case, the first term is 1 and the common ratio is -x. Thus, the series can be written as 1 + x + x^2 + x^3 + x^4 + ... which simplifies to 1 − x + x^2 − x^3 + x^4 − ...

Explanation

The given series is an expansion of the expression (1 + x)^-1. This can be derived using the formula for the sum of an infinite geometric series, which is a/(1 - r), where a is the first term and r is the common ratio. In this case, the first term is 1 and the common ratio is -x. Thus, the series can be written as 1 + x + x^2 + x^3 + x^4 + ... which simplifies to 1 − x + x^2 − x^3 + x^4 − ...

8. High Pass Filter allows the

Frequency lesser than infinity

Frequency less than cut-off frequency

Frequency higher than infinity

Frequency higher than cut-off frequency

A high pass filter allows frequencies that are higher than the cut-off frequency to pass through while attenuating or blocking frequencies that are lower than the cut-off frequency. This means that any signal with a frequency higher than the cut-off frequency will be allowed to pass through the filter with minimal loss or distortion.

Explanation

A high pass filter allows frequencies that are higher than the cut-off frequency to pass through while attenuating or blocking frequencies that are lower than the cut-off frequency. This means that any signal with a frequency higher than the cut-off frequency will be allowed to pass through the filter with minimal loss or distortion.

9. Expand the below binomial series->(1 + x)^n

1 + nx +[n(n − 1)/2!] x^2 +[n(n − 1)(n − 2)/3!] x^3 + . . .

1 + nx +2[n(n − 1)/2!] x^2 +3[n(n − 1)(n − 2)/3!] x^3 + . . .

1 - nx +[n(n − 1)/2!] x^2 +[n(n − 1)(n − 2)/3!] x^3 + . . .

1 - nx +[n(n − 1)/2!] x^2 -[n(n − 1)(n − 2)/3!] x^3 - . . .

The given answer is the correct expansion of the binomial series (1 + x)^n. It represents the terms of the series where each term is obtained by raising x to a power and multiplying it by the corresponding coefficient. The coefficients are derived from the binomial coefficient formula, which involves the values of n and the power of x in each term. The given answer correctly follows the pattern of increasing powers of x and the corresponding coefficients based on the binomial coefficient formula.

Explanation

The given answer is the correct expansion of the binomial series (1 + x)^n. It represents the terms of the series where each term is obtained by raising x to a power and multiplying it by the corresponding coefficient. The coefficients are derived from the binomial coefficient formula, which involves the values of n and the power of x in each term. The given answer correctly follows the pattern of increasing powers of x and the corresponding coefficients based on the binomial coefficient formula.

10. In the following conditions, for which Final value doesn't exist.

If the function sF(s)has the infinite pole

If the function sF(s)has pole on origin

If the function sF(s)has no zeros

If the function sF(s)has pole at unity

If the function sF(s) has a pole on the origin, it means that the denominator of the function has a factor of (s-0), which simplifies to just s. This indicates that the function has a singularity at s=0, causing it to blow up to infinity at that point. As a result, the final value of the function does not exist.

Explanation

If the function sF(s) has a pole on the origin, it means that the denominator of the function has a factor of (s-0), which simplifies to just s. This indicates that the function has a singularity at s=0, causing it to blow up to infinity at that point. As a result, the final value of the function does not exist.

11. Transfer function of the system is defined as the

Ratio of laplace transform of input to output response

Ratio of laplace transform of input to output response with zero initial condition

Ratio of laplace transform of output to input response with zero initial condition

Ratio of laplace transform of output to input response

The transfer function of a system is defined as the ratio of the Laplace transform of the output response to the Laplace transform of the input. The inclusion of "with zero initial condition" means that the system is assumed to start from a state where there is no initial energy or activity. This assumption allows for a more accurate representation of the system's behavior in response to the input. Therefore, the correct answer is the ratio of the Laplace transform of the output to the input response with zero initial condition.

Explanation

The transfer function of a system is defined as the ratio of the Laplace transform of the output response to the Laplace transform of the input. The inclusion of "with zero initial condition" means that the system is assumed to start from a state where there is no initial energy or activity. This assumption allows for a more accurate representation of the system's behavior in response to the input. Therefore, the correct answer is the ratio of the Laplace transform of the output to the input response with zero initial condition.