Free Bachelor of Electrical Engineering Signals & Systems Questions and Answers — Questions and Answers

Question 1: The majority of the signals in nature are .

Analog and Continuous-time (Correct answer)
Digital and Analog
Continuous-time and digital
Continuous-time and discrete-time

Correct answer: Analog and Continuous-time

Most physical phenomena and natural signals, such as sound, temperature, or light, vary smoothly and continuously over time and can take on any value within a range. These characteristics define them as analog signals and continuous-time signals. Digital signals are discrete representations derived from these continuous natural signals.

Question 2: Which of the following traits does not apply to deterministic signals?

Can be represented by a mathematical equation
Exhibits no uncertainty
Instantaneous value can be accurately predicted
Exhibits uncertainty (Correct answer)

Correct answer: Exhibits uncertainty

Deterministic signals are characterized by their predictability; their future values can be precisely determined from a mathematical model or their past values, exhibiting no uncertainty. They can be represented by a specific mathematical equation, allowing their instantaneous value to be accurately predicted. Signals that exhibit uncertainty are classified as random or stochastic.

Question 3: When the ratio of the time periods of two periodic signals is ____________, the sum of the signals is a periodic signal.

An integer
A rational number (Correct answer)
An irrational number
A complex number

Correct answer: A rational number

The sum of two periodic signals, with periods T1 and T2, will itself be a periodic signal if and only if the ratio of their periods (T1/T2) is a rational number. If this condition is met, a common fundamental period can be found for the combined signal. If the ratio is irrational, the sum of the signals will be aperiodic.

Question 4: Among the following signals, which one is monotonous in nature?

cos(t)
1-exp(sin(t))
1-exp(-t) (Correct answer)
log(tan(t))

Correct answer: 1-exp(-t)

A monotonous function is one that is either consistently non-decreasing or consistently non-increasing over its entire domain. For t ≥ 0, the function 1-exp(-t) is monotonically increasing because its derivative, exp(-t), is always positive. The other functions listed exhibit oscillatory or non-uniform behavior, preventing them from being monotonous over their typical domains.

Question 5: Is the integral of the function from -infinity to +infinity for a bounded function defined and finite?

Yes
Not always (Correct answer)
Never
None of the mentioned

Correct answer: Not always

While a bounded function has values that do not go to infinity, its integral over an infinite range (from -infinity to +infinity) is not always defined and finite. For the integral to be finite, the function must be absolutely integrable, meaning the integral of its absolute value must converge. Many bounded functions, like f(x) = 1, have infinite integrals over an infinite range.

Question 6: Find the range between 1.25 and 1.75 where the signal x(t) = 1/(t2 - 3t + 2) reaches its highest value:

1.5 (Correct answer)
1.55
1.45
1.4

Correct answer: 1.5

To find the highest value of x(t) = 1 / (t^2 - 3t + 2), we need to find the minimum value of its denominator, f(t) = t^2 - 3t + 2. This is a parabola opening upwards, and its minimum occurs at the vertex, found by t = -b/(2a). For this function, t = -(-3)/(2*1) = 3/2 = 1.5. Since 1.5 falls within the given range [1.25, 1.75], the function x(t) reaches its maximum at t=1.5.

Question 7: What are the signals 1-exp(-t) and 1-kexp(-ktsteady )'s state values?

1, 1 2001
k, k
1, 1/k
1, k (Correct answer)

Correct answer: 1, k

The steady-state value of a signal is its limit as time approaches infinity. For the first signal, 1-exp(-t), as t approaches infinity, exp(-t) approaches 0, so the steady-state value is 1. For the second signal, assuming it's of the common form k*(1-exp(-k*t)) rather than the literal typo, as t approaches infinity, exp(-k*t) approaches 0, making the steady-state value k*(1-0) = k. This matches the option '1, k'.

Question 8: What kind of system is exemplified by amplifiers, motors, filters, etc.?

Continuous time systems (Correct answer)
Discrete time systems
Unstable systems
Distributed parameter systems

Correct answer: Continuous time systems

Amplifiers, motors, and filters are physical systems that process signals that vary continuously over time. Their inputs and outputs are defined for every instant, and their behavior is typically modeled using differential equations. This characteristic of operating on signals that are continuous in time defines them as continuous-time systems, as opposed to discrete-time systems which process sampled signals.

Question 9: Which system from the list below is described by partial differential functions?

Causal systems and linear systems
Causal Systems and Dynamic systems
Distributed parameter systems and linear systems
Distributed parameter systems and Dynamic systems (Correct answer)

Correct answer: Distributed parameter systems and Dynamic systems

Partial differential functions are used to describe systems where properties vary continuously across space and time. Such systems are known as distributed parameter systems, as their characteristics are spread out rather than concentrated at a single point. These systems are also inherently dynamic because their state and behavior evolve over time, making 'Distributed parameter systems and Dynamic systems' the correct description.

Question 10: Which system from the list below is causal?

y(n)=x(2n²)
y(t)=x(t-1)+x(t-2) (Correct answer)
y(t)=x(t)+x(t-3)+x(t²)
y(n)=x(n+2)

Correct answer: y(t)=x(t-1)+x(t-2)

A causal system is one where the output at any given time depends only on the present or past values of the input, and not on future input values. In the equation y(t)=x(t-1)+x(t-2), the output y(t) relies on input values from time t-1 and t-2, which are both in the past relative to the current time t. The other options involve future input values (e.g., x(2n²), x(t²), x(n+2)), making them non-causal.

Question 11: Systems of this type, which have input and output quantized at specific levels, are referred to as

continuous
digital
discrete (Correct answer)
analog

Correct answer: discrete

A discrete system is characterized by signals that are defined only at specific, distinct points in time or space, and whose values are restricted to a finite or countably infinite set of levels. When input and output are 'quantized at specific levels,' it means their values can only be chosen from a predefined set, which is the defining characteristic of discrete-valued signals within a discrete system. This is distinct from continuous systems, where values can be any real number within a range.

Question 12: Systems of this type can accept any value from a specific set of values in their input and output, and thus are known as

continuous (Correct answer)
digital
discrete
analog

Correct answer: continuous

A continuous system, also known as an analog system, is one where the input and output signals can take on any value within a specified range. This means the signals are not restricted to discrete, quantized levels but can vary smoothly and continuously. This characteristic allows for an infinite number of possible values between any two points, unlike discrete or digital systems.

Question 13: An illustration of a discrete collection of data or system is

movement of water through a pipe
the trajectory of the Sun
data on a CD (Correct answer)
universe time scale

Correct answer: data on a CD

A discrete collection of data or a discrete system involves information that is sampled or represented at distinct, separate points rather than continuously. Data on a CD is stored as a series of distinct pits and lands, which represent binary values (0s and 1s). This digital representation is inherently discrete, contrasting with continuous phenomena like the movement of water or the trajectory of the Sun.

Question 14: When a system follows the laws of linear dynamics, it is referred to

additivity
scaling
homogeneity
both scaling and additivity (Correct answer)

Correct answer: both scaling and additivity

A system is considered linear if it satisfies two fundamental properties: additivity and homogeneity (also known as scaling). Additivity means that the response to a sum of inputs is the sum of the responses to individual inputs. Homogeneity means that scaling the input by a constant factor results in the output being scaled by the same factor. Both properties must hold for a system to be classified as linear.

Question 15: A system that produces results that are time invariant

vanishes with a delay in input
increases with a delay in input
decreases with a delay in input
remains same with a delay in input (Correct answer)

Correct answer: remains same with a delay in input

A time-invariant system is one whose input-output relationship does not change over time. This means that if an input signal is delayed, the system's response will be the same as the original output, but also delayed by the exact same amount. The system's characteristics or parameters themselves do not vary with the passage of time.

Question 16: A signal is a physical quantity that does not change with ________.

Space
Time
Dependent Variables (Correct answer)
Independent Variables

Correct answer: Dependent Variables

A signal is a physical quantity that varies with respect to one or more independent variables, such as time or space. The value of the signal itself is the dependent variable. Therefore, a signal *does* change with independent variables, but it does not 'change with' its own dependent variable nature; rather, it *is* the dependent variable whose value is determined by the independent variables.

Free Bachelor of Electrical Engineering Signals & Systems Questions and Answers

The majority of the signals in nature are .