# 70+ Signals and Systems Solved MCQs

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1.

## Evaluate the following function in terms of t: {integral from 0 to t}{Integral from -inf to inf}d(t)

A. 1⁄t
B. 1⁄t2
C. t
D. t2
Explanation: the first integral is 1, and the overall integral evaluates to t.
2.

## The fundamental period of exp(jwt) is

A. pi/w
B. 2pi/w
C. 3pi/w
D. 4pi/w
Explanation: the function assumes the same value after t+2pi/w, hence the period would be 2pi/w.
3.

## Find the magnitude of exp(jwt). Find the boundness of sin(t) and cos(t).

A. 1, [-1,2], [-1,2]
B. 0.5, [-1,1], [-1,1]
C. 1, [-1,1], [-1,2]
D. 1, [-1,1], [-1,1]
Explanation: the sin(t)and cos(t) can be found using euler’s rule.
4.

## Find the value of {sum from -inf to inf} exp(jwn)*d[n].

A. 0
B. 1
C. 2
D. 3
Explanation: the sum will exist only for n = 0, for which the product will be 1.
5.

## Compute d[n]d[n-1] + d[n-1]d[n-2] for n = 0, 1, 2.

A. 0, 1, 2
B. 0, 0, 1
C. 1, 0, 0
D. 0, 0, 0
Explanation: only one of the values can be one at a time, others will be forced to zero, due to the delta function.
6.

## Defining u(t), r(t) and s(t) in their standard ways, are their derivatives defined at t = 0?

A. yes, yes, no
B. no, yes, no
C. no, no, yes
D. no, no, no
Explanation: none of the derivatives are defined at t=0.
7.

## Which is the correct Euler expression?

A. exp(2jt) = cos(2t) + jsin(t)
B. exp(2jt) = cos(2t) + jsin(2t)
C. exp(2jt) = cos(2t) + sin(t)
D. exp(2jt) = jcos(2t) + jsin(t)
Answer» B. exp(2jt) = cos(2t) + jsin(2t)
Explanation: euler rule: exp(jt) = cos(t) + jsin(t).
8.

## The range for unit step function for u(t – a), is

A. t < a
B. t ≤ a
C. t = a
D. t ≥ a
Explanation: a unit step signal u(t) = 1 when t ≥ 0 and 0 when t < 0
9.

## Which one of the following is not a ramp function?

A. r(t) = t when t ≥ 0
B. r(t) = 0 when t < 0
C. r(t) = ∫u(t)dt when t < 0
D. r(t) = du(t)⁄dt
Explanation: ramp function r(t) = t when t ≥ 0 and r(t) = 0 when t < 0
10.

## Unit Impulse function is obtained by using the limiting process on which among the following functions?

A. triangular function
B. rectangular function
C. signum function
D. sinc function
Explanation: unit impulse function can be obtained by using a limiting process on the rectangular pulse function. area under the rectangular pulse is equal to unity.
11.

## When is a complex exponential signal pure DC?

A. σ = 0 and Ω < 0
B. σ < 0 and Ω = 0
C. σ = 0 and Ω = 0
D. σ < 0 and Ω < 0
Answer» C. σ = 0 and Ω = 0
Explanation: a complex exponential signal is represented as x(t)= est
12.

## What is exp(ja) equal to, where j is the square root of unity?

A. cos ja + jsin a
B. sin a + jcos a
C. cos j + a sin j
D. cos a + jsin a
Answer» D. cos a + jsin a
Explanation: this is the corollary of demoivre/euler’s theorem.
13.

## What is the magnitude of exp(2+3j)?

A. exp(2.3)
B. exp(3)
C. exp(2)
D. exp(3/2)
Explanation: exp(a+b) =exp(a) * exp(b), and
14.

## What is the fundamental frequency of exp(2pi*w*j)?

A. 1pi*w
B. 2pi*w
C. w
D. 2w
Explanation: fundamental period = 2pi/w, hence fundamental frequency will be w.
15.

## Total energy possessed by a signal exp(jwt) is?

A. 2pi/w
B. pi/w
C. pi/2w
D. 2pi/3w
Explanation: energy possessed by a periodic signal is the integral of the square of the magnitude of the signal over a time period.
16.

## Sinusoidal signals multiplied by decaying exponentials are referred to as

A. amplified sinusoids
B. neutralized sinusoids
C. buffered sinusoids
D. damped sinusoids
Explanation: the decaying exponentials
17.

## What is the period of exp(2+pi*j/4)t?

A. 4
B. 8
C. 16
D. 20
Explanation: the fundamental period = 2pi/(pi/4) = 8.
18.

## exp(jwt) is periodic

A. for any w
B. for any t
C. for no w
D. for no t
Explanation: any two instants, t and t + 2pi will be equal, hence the signal will be periodic with period 2pi.
19.

## Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?

A. 8
B. 12
C. 18
D. 24
Explanation: the first signal, will repeat itself after 3 cycles. the second will repeat itself after 8 cycles. thus, both of them
20.

## exp[jwn] is periodic

A. for any w
B. for any t
C. for w=2pi*m/n
D. for t = 1/w
Explanation: discrete exponentials are periodic only for a particular choice of the fundamental frequency.
21.

## The most general form of complex exponential function is:

A. eσt
B. eΩt
C. est
D. eat
Explanation: the general form of complex exponential function is: x(t) = est where s = σ
22.

## A complex exponential signal is a decaying exponential signal when

A. Ω = 0 and σ > 0
B. Ω = 0 and σ = 0
C. Ω ≠ 0 and σ < 0
D. Ω = 0 and σ < 0
Answer» D. Ω = 0 and σ < 0
Explanation: let x(t) be the complex exponential signal
23.

## When is a complex exponential signal sinusoidal?

A. σ =0 and Ω = 0
B. σ < 0 and Ω = 0
C. σ = 0 and Ω ≠ 0
D. σ ≠ 0 and Ω ≠ 0
Answer» C. σ = 0 and Ω ≠ 0
Explanation: a signal is sinusoidal when σ = 0 and Ω ≠ 0
24.

## An exponentially growing sinusoidal signal is:

A. σ = 0 and Ω = 0
B. σ > 0 and Ω ≠ 0
C. σ < 0 and Ω ≠ 0
D. σ = 0 and Ω ≠ 0
Answer» B. σ > 0 and Ω ≠ 0
Explanation: a complex exponential signal is sinusoidal when Ω has a definite value i.e., Ω ≠ 0. it can either be growing exponential or decaying exponential based on the value of σ.
25.

## Determine the nature of the signal: x(t) = e-0.2t [cosΩt + jsinΩt].

A. exponentially decaying sinusoidal signal
B. exponentially growing sinusoidal signal
C. sinusoidal signal
D. exponential signal
Answer» A. exponentially decaying sinusoidal signal
Explanation: clearly the signal has negative exponential ⇒ decaying exponential signal. the signal also has sinusoidal component.
26.

## A signal is a physical quantity which does not vary with

A. time
B. space
C. independent variables
D. dependent variables
Explanation: a signal is a physical quantity which varies with time, space or any other independent variables. therefore, it does not vary with dependent variables.
27.

## Most of the signals found in nature are

A. continuous-time and discrete-time
B. continuous-time and digital
C. digital and analog
D. analog and continuous-time
Explanation: signals naturally are continuous-time signals. these are also known as analog signals. continuous-time or analog signals are defined for all values of time t.
28.

## Which one of the following is not a characteristic of a deterministic signal?

A. exhibits no uncertainty
B. instantaneous value can be accurately predicted
C. exhibits uncertainty
D. can be represented by a mathematical equation
Explanation: deterministic signal is one which exhibits no uncertainty and its instantaneous value can be accurately predicted from its mathematical equation. therefore, a deterministic signal doesn’t exhibit uncertainty. however, a random is always uncertain.
29.

## Sum of two periodic signals is a periodic signal when the ratio of their time periods is

A. a rational number
B. an irrational number
C. a complex number
D. an integer
Explanation: sum of two periodic signals is a periodic signal only when the ratio of their time periods is a rational number or it is the ratio of two integers. for e.g., t1/t2 = 5/7 → periodic; t1/t2 = 5 → aperiodic.
30.

## Determine the Time period of: x(t)=3 cos(20t+5)+sin(8t-3).

A. 1/10 sec
B. 1/20 sec
C. 2/5 sec d 2/4 sec
Answer» C. 2/5 sec d 2/4 sec
31.

## Determine the odd component of the signal: x(t)=cost+sint.

A. sint
B. 2sint
C. cost
D. 2cost
Explanation: here is the explanation.
32.

## Is the signal sin(t) anti-symmetric?

A. yes
B. no
Explanation: a signal is said to be anti- symmetric or odd signal when it satisfies the following condition:
33.

## For an energy signal

A. e=0
B. p= ∞
C. e= ∞
D. p=0
Explanation: a signal is called an energy signal if the energy satisfies 0<e< ∞ and power p=0.
34.

## Determine the power of the signal: x(t) = cos(t).

A. 1/2
B. 1
C. 3/2
D. 2
Explanation: To determine the power of the given signal x(t) = cos(t), we need to calculate the average power over time.

The power of a continuous-time signal x(t) can be calculated using the formula:

P = (1/T) * ∫[T] |x(t)|^2 dt

Where T is the period of the signal.

In this case, the signal x(t) = cos(t) is a periodic signal with a period of 2π. So we need to evaluate the integral over one period, from 0 to 2π.

P = (1/(2π)) * ∫[0 to 2π] |cos(t)|^2 dt

Using the trigonometric identity cos^2(t) = (1 + cos(2t))/2, we can simplify the integral:

P = (1/(2π)) * ∫[0 to 2π] (1 + cos(2t))/2 dt

P = (1/(2π)) * [t/2 + (sin(2t))/4] evaluated from 0 to 2π

P = (1/(2π)) * [(2π/2 + (sin(4π))/4) - (0/2 + (sin(0))/4)]

P = (1/(2π)) * (π + 0 - 0) = 1/2

Therefore, the power of the signal x(t) = cos(t) is 1/2.

The correct answer is A. 1/2.
35.

## Is the following signal an energy signal? x(t) = u(t) – u(t – 1)

A. yes
B. no
Explanation: here is the explanation.
36.

## A signal is anti-causal if

A. x(t) = 0 for t = 0
B. x(t) = 1 for t < 0
C. x(t) = 1 for t > 0
D. x(t) = 0 for t > 0
Answer» D. x(t) = 0 for t > 0
Explanation: a signal is said to be anti- causal when x(t) = 0 for t > 0.
37.

## Is the signal x(t)= eat u(t) causal?

A. yes
B. no
Explanation: a signal is said to be causal if it is 0 for t < 0.
38.

## Is the signal x(n) = u(n + 4) – u(n – 4) causal?

A. yes
B. no
Explanation: a signal is said to be causal if it is 0 for t < 0.
39.

## The type of systems which are characterized by input and the output capable of taking any value in a particular set of values are called as

A. analog
B. discrete
C. digital
D. continuous
Explanation: continuous systems have a restriction on the basis of the upper bound and lower bound, but within this set, the input and output can assume any value. thus, there are infinite values attainable in this system
40.

## An example of a discrete set of information/system is

A. the trajectory of the sun
B. data on a cd
C. universe time scale
D. movement of water through a pipe
Answer» B. data on a cd
Explanation: the rest of the parameters are continuous in nature. data is stored in the form of discretized bits on cds.
41.

## A system which is linear is said to obey the rules of

A. scaling
D. homogeneity
Explanation: a system is said to be additive and scalable in order to be classified as a linear system.
42.

## A time invariant system is a system whose output

A. increases with a delay in input
B. decreases with a delay in input
C. remains same with a delay in input
D. vanishes with a delay in input
Answer» C. remains same with a delay in input
Explanation: a time invariant system’s output should be directly related to the time of the output. there should be no scaling, i.e. y(t) = f(x(t)).
43.

## Should real time instruments like oscilloscopes be time invariant?

A. yes
B. sometimes
C. never
D. they have no relation with time variance
Explanation: oscilloscopes should be time invariant, i.e they should work the same way everyday, and the output should not change with the time at which it is operated.
44.

## All real time systems concerned with the concept of causality are

A. non causal
B. causal
C. neither causal nor non causal
D. memoryless
Explanation: all real time systems are causal, since they cannot have perception of the future, and only depend on their memory.
45.

## A system is said to be defined as non causal, when

A. the output at the present depends on the input at an earlier time
B. the output at the present does not depend on the factor of time at all
C. the output at the present depends on the input at the current time
D. the output at the present depends on the input at a time instant in the future
Answer» D. the output at the present depends on the input at a time instant in the future
Explanation: a non causal system’s output is said to depend on the input at a time in the future.
46.

## When we take up design of systems, ideally how do we define the stability of a system?

A. a system is stable, if a bounded input gives a bounded output, for some values of the input
B. a system is unstable, if a bounded input gives a bounded output, for all values of the input
C. a system is stable, if a bounded input gives a bounded output, for all values of the input
D. a system is unstable, if a bounded input gives a bounded output, for some values of the input
Answer» C. a system is stable, if a bounded input gives a bounded output, for all values of the input
Explanation: for designing a system, it should be kept in mind that the system does not blow out for a finite input. thus, every finite input should give a finite output.
47.

## All causal systems must have the component of

A. memory
B. time invariance
C. stability
D. linearity
Explanation: causal systems depend on the functional value at an earlier time, compelling the system to possess memory.
48.

## What are fourier coefficients?

A. the terms that are present in a fourier series
B. the terms that are obtained through fourier series
C. the terms which consist of the fourier series along with their sine or cosine values
D. the terms which are of resemblance to fourier transform in a fourier series are called fourier series coefficients
Answer» C. the terms which consist of the fourier series along with their sine or cosine values
Explanation: the terms which consist of the fourier series along with their sine or cosine values are called fourier coefficients. fourier coefficients are present in both exponential and trigonometric fourier series.
49.

## Which are the fourier coefficients in the following?

A. a0, an and bn
B. an
C. bn
D. an and bn
Answer» A. a0, an and bn
Explanation: these are the fourier coefficients in a trigonometric fourier series. a0 = 1/t∫x(t)dt
50.

## Do exponential fourier series also have fourier coefficients to be evaluated.

A. true
B. false
Explanation: the fourier coefficient is : xn = 1/t∫x(t)e-njwtdt.
51.

## The fourier series coefficients of the signal are carried from –T/2 to T/2.

A. true
B. false
Explanation: yes, the coefficients evaluation can be done from –t/2 to t/2. it is done for the simplification of the signal.
52.

## What is the polar form of the fourier series?

A. x(t) = c0 + ∑cncos(nwt+ϕn)
B. x(t) = c0 + ∑cncos(ϕn)
C. x(t) = ∑cncos(nwt+ϕn)
D. x(t) = c0+ ∑cos(nwt+ϕn)
Answer» A. x(t) = c0 + ∑cncos(nwt+ϕn)
Explanation: x(t) = c0 + ∑cncos(nwt+ϕn), is the polar form of the fourier series.
53.

## What is a line spectrum?

A. plot showing magnitudes of waveforms are called line spectrum
B. plot showing each of harmonic amplitudes in the wave is called line spectrum
C. plot showing each of harmonic amplitudes in the wave is called line spectrum
D. plot showing each of harmonic amplitudes called line spectrum
Answer» B. plot showing each of harmonic amplitudes in the wave is called line spectrum
Explanation: the plot showing each of harmonic amplitudes in the wave is called line spectrum. the line rapidly decreases for waves with rapidly convergent series.
54.

## Fourier series is not true in case of discrete time signals.

A. true
B. false
Explanation: fourier series is also true in
55.

## What is the disadvantage of exponential Fourier series?

A. it is tough to calculate
B. it is not easily visualized
C. it cannot be easily visualized as sinusoids
D. it is hard for manipulation
Answer» C. it cannot be easily visualized as sinusoids
Explanation: the major disadvantage of exponential fourier series is that it cannot be easily visualized as sinusoids. moreover, it is easier to calculate and easy for manipulation leave aside the disadvantage.
56.

## Fourier series uses which domain representation of signals?

A. time domain representation
B. frequency domain representation
C. both combined
D. neither depends on the situation
Explanation: fourier series uses frequency domain representation of signals.
57.

## How does Fourier series make it easier to represent periodic signals?

A. harmonically related
B. periodically related
C. sinusoidally related
D. exponentially related
Explanation: fourier series makes it easier to represent periodic signals as it is a mathematical tool that allows the representation of any periodic signals as the sum of harmonically related sinusoids.
58.

## Which of the following is correct regarding to impulse signal?

A. x[n]δ[n] = x[0]δ[n]
B. x[n]δ[n] = δ[n]
C. x[n]δ[n] = x[n]
D. x[n]δ[n] = x[0]
Explanation: when the input x[n] is multiplied with an impulse signal, the result will be impulse signal with magnitude of x[n] at that time.
59.

## Weighted superposition of time-shifted impulse responses is termed as                for discrete-time signals.

A. convolution integral
B. convolution multiple
C. convolution sum
D. convolution
Explanation: weighted superposition of time-shifted impulse responses is called
60.

## Find the convolution sum of sequences x1[n] = (1, 2, 3) and x2[n] = (2, 1, 4).

A. {2, 5, 12, 11, 12}
B. {2, 12, 5, 11, 12}
C. {2, 11, 5, 12, 12}
D. {-2, 5,-12, 11, 12}
Answer» A. {2, 5, 12, 11, 12}
Explanation: x1[n] = δ(n)+2δ(n-1)+3δ(n-2) and x2[n] = 2δ(n)+δ(n-1)+4δ(n-2)
61.

## The Fourier series for the function f (x) = sin2x is

A. 0.5 + 0.5 sin 2x
B. 0.5 – 0.5 sin 2x
C. 0.5 + 0.5 cos 2x
D. 0.5 – 0.5 cos 2x
Answer» D. 0.5 – 0.5 cos 2x
Explanation: f(x) = sin2x now, f(x) = sin2x =  1−cos2x
62.

## The type of systems which are characterized by input and the output capable of taking any value in a particular set of values are called as

A. analog
B. discrete
C. digital
D. continuous
Explanation: we know that continuous systems have a restriction on the basis of the upper bound and lower bound. however within this set, the input and output can assume any value. hence, there are infinite values attainable in this system.
63.

## Then, y[k] = x[3k-2] is

A. y[k] = 1, for k = 0, 1 and 0 otherwise
B. y[k] = 1, for k = 1 and -1 for k=-1
C. y[k] = 1, for k = 0, 1 and -1 otherwise
D. y[k] = 1, for k = 0, 1 and 0 otherwise
Answer» A. y[k] = 1, for k = 0, 1 and 0 otherwise
Explanation: y[k] = x [3k-2] now, y [0] = x [-2] = 1
64.

## The system described by the difference equation y(n) – 2y(n-1) + y(n-2) = X(n) – X(n-1) has y(n) = 0 and n<0. If x (n) = δ(n), then y (z) will be?

A. 2
B. 1
C. 0
D. -1
Explanation: given equation = y (n) – 2y (n- 1) + y (n-2) = x (n) – x (n-1) has y (n) = 0
65.

## A Discrete signal is said to be even or symmetric if X(-n) is equal to

A. x(n)
B. 0
C. –x(n)
D. –x(-n)
Explanation: we know that any signal be it discrete or continuous is said to be even or
66.

## Impulse response is the output of               system due to impulse input applied at time=0?

A. linear
B. time varying
C. time invariant
D. linear and time invariant
Answer» D. linear and time invariant
Explanation: impulse response is the output of lti system due to impulse input applied at time = 0 or n=0. behaviour of an lti system is characterised by the impulse response.
67.

## For a causal L.T.I. system, the impulse response is 0 for

A. t<0
B. t=0
C. t>0
D. always
Explanation: since the system is causal, the impulse response won’t exist for t<0. this is because the output of the system should not depend on future inputs. thus only option t<0 is correct.
68.

## The convolution of a discrete signal with itself is

A. squaring the signal
B. doubling the signal
D. is not possible
Explanation: this is proved by the fact that since discrete signals can be thought of as a one variable polynomial with the coefficients, along with the order, representing the amplitude, at an instant equal to the order of the variable, of the signal- they are simply multiplied during convolution.
69.

## The convolution of a function with an impulse function delayed to an instant 3 in time results in

A. an advance in the function by 3 units in time
B. the function itself
C. a delay in the function by 3 units in time
D. cannot be determined
Answer» C. a delay in the function by 3 units in time
Explanation: the convolution of an impulse function with a function results in the function itself. but if the impulse function is delayed, the output will also get delayed by
70.

## A continuous signal can be represented as the product of an impulse function and the signal itself.

A. true
B. false
Explanation: the continuous signal can be represented as an integral of impulses. this representation buries it down to the form of convolution of two signal where one signal is the impulse function while the other is the continuous signal. hence, the above statement is true.
71.

## What is the Scope value if the signal generator has a frequency of 2 Hz only?

A. an attenuated signal of same frequency
B. the entire signal at the same frequency
C. the entire signal at reduced frequency
D. an attenuated signal at reduced frequency
Answer» A. an attenuated signal of same frequency
Explanation: the above transfer function is that of a high pass filter. the cut-off frequency for allowing signals is 3hz but the given signal frequency is that of 2hz only. if the frequency of the signal generator was more than 2hz- the output would’ve been entire signal at the same frequency but for
72.

## If two LTI systems with impulse response h1 (t) and h2 (t) and are connected in parallel then output is given by

A. y(t) = x(t) *(h1(t) + h2(t))
B. y(t) = x(t) + (h1(t) + h2(t))
C. y(t) = x(t) * (h1(t) h2(t))
D. y(t) = (x(t) * h1(t)) + h2(t)
Answer» A. y(t) = x(t) *(h1(t) + h2(t))
Explanation: the equivalent impulse response of two systems connected in parallel is the sum of individual impulse responses. it is represented as
73.

## When two LTI systems with impulse responses ha (t) and hb (t) are cascaded then equivalent response is given by

A. h(t) = ha(t) + hb(t)
B. h(t) = ha(t) – hb(t)
C. h(t) = ha(t) hb(t)
D. h(t) = ha(t) * hb(t)
Answer» D. h(t) = ha(t) * hb(t)
Explanation: the equivalent impulse response of two systems connected in series (cascaded) is given by convolution of individual impulse responses.
74.

## The condition for memory-less system is given by

A. h[k] = cδ[k]
B. h[k] = cδ[n-k]
C. h[k] = ch[k]δ[k]
D. h[k] = ch[n-k]δ[k]
Explanation: the lti discrete-time system is
75.

## The causal continuous system with impulse response should satisfy          equation.

A. h(t)=0,t<0
B. h(t)=0,t>0
C. h(t)≠0,t<0
D. h(t)≠0,t≤0
Explanation: to the continuous system to be causal, the impulse response should satisfy the equation h(t)=0,t<0 and convolution
76.

## Causal systems are

A. anticipative
B. non anticipative
C. for certain cases anticipative
D. for certain cases anticipative and non anticipative
Explanation: causal systems are non anticipative. they cannot generate an output before the input is applied. which indicates the impulse response is zero for negative time.
77.

## The impulse response of discrete-time signal is given by h [n] = u [n+3]. Whether the system is causal or not?

A. causal
B. non-causal
C. insufficient information
D. the system cannot be classified