# Signal and Systems | Subject Wise

## Signal and Systems | Subject Wise

 Question 1
Consider the signal f(t) = 1 + 2cos (πt) + 3 where t is in seconds. Its fundamental time period, in seconds, is ____________.
 A Fill in the Blank Type Question
Question 1 Explanation:
 Question 2
Let H(z) be the z-transform of a real-valued discrete-time signal h[n]. If P(z) = H(z)  has a zero at  and P(z) has a total of four zeros, which one of the following plots represents all the zeros correctly?
 A B C D
Question 2 Explanation:
 Question 3
A germanium sample of dimensions 1 cm × 1 cm is illuminated with a 20 mW, 600 nm laser light source as shown in the figure. The illuminated sample surface has a 100 nm of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dixodie-Germanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at 600 nm is 3 × 104 cm-1 and the bandgap is 0.66 eV, the thickness of the Germanium layer, rounded off to 3 decimal places, is _________ μm.
 A Fill in the Blank Type Question
Question 3 Explanation:
 Question 4
Let h[n] be a length-7 discrete-time finite impulse response filter, given by

h[0] = 4, h[1] = 3, h[2] = 2, h[3] = 1,

h[-1] = - 3, h[-2] = -2, h[-3] = -1,

and h[n] is zero for [n] ≥ A length-3 finite impulse response approximation g[n] of h[n] has to be obtained such that

is minimized, where H(e) and (e) are the discrete-time Fourier transforms of h[n] and g[n], respectively. For the filter that minimizes E(h, g), the value of
10 g[-1] + g[1], rounded off to 2 decimal places, is ____________.

 A Fill in the Blank Type Question
Question 4 Explanation:

For the minimization of the energy in the error signal there are different approaches like, Prony’s method, Pade approximation. As g(n) has three samples.

Consider them as g(-1) , g(0) , g(1)
E(h,g) can be minimized by making h[n] = g[n] using rectangular window and parsval’s theorem of DTFT.
Now, 10g[–1] + g[1] = 10 x (–3) + 3 = –27

 Question 5
It is desired to find a three-tap causal filter which gives zero signal as an output to an input of the form

where c1 and c2 are arbitrary real numbers. The desired three-tap filter is given by

h[0] = 1, h[1] = a, h[2] = b

and

h[n] = 0 for n < 0 or n > 2.

What are the values of the filter taps a and b if the output is y[n] = 0 for all n, when x[n] is as given above?

 A A = 0, b = -1 B A = 1, b = 1 C A = -1, b = 1 D A = 0, b = 1
Question 5 Explanation:
 Question 6
Consider a six-point decimation-in-time Fast Fourier Transform (FFT) algorithm, for which the signal-flow graph corresponding to X[1] is shown in the figure. Let  In the figure, what should be the values of the coefficients a1, a2, a3 in terms of W6 so that X[1] is obtained correctly?

 A B C D
Question 6 Explanation:

We are obtaining X(1) correctly

k = 1

We know that

comparing with given graph

a1 = 1, a2 = W6,

 Question 7
Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as Which one of the following statements is true about the system?
 A It is causal and stable B It is causal but not stable C It is not causal but stable D It is neither causal nor stable
Question 7 Explanation:
For an input-output relation if the present output depends on present and past input values then the given system is “Causal”.

For the given relation,

For n ranging from 0 to 10 present output depends on present input only.
At all other points present output depends on present and past input values.
Thus the system is “Causal”.

Stability
If x[n] is bounded for the given finite range of n i.e. 0 Similarly x [n] - x [n- 1] is also bounded at all other values of n
Thus the system is “stable”.
 Question 8
The system y(t) = x(2t) + 3 is
 A Linear and Time Invariant B Causal and Linear C Non-Linear and Time Variant D Linear and memoryless
Question 8 Explanation:
We have to determine the characteristics of the system given by the equation in question.
First let us check for Linear/Non-Linear characteristics:
For input x1(t) we have=> y1(t)=x1(2t)+3
For input x2(t) we have=> y2(t)=x2(2t)+3
Now, the weighted sum of outputs can be given as: ay1(t)+by2(t)=a[x1(2t)+3]+b[x2(2t)+3]
The output due to weighted sum of inputs is:
y3(t)=T[ax1(2t)+bx2(2t)]=[ax1(t)+bx2(t)]+3
So, we can see that=> y3(t)ay1(t)+by2(t)
So, the system is non-linear
Next let us check for Time variant/invariant characteristics:
Delay the signal by T=> x(t-T)=X(2t-T)+3
y(t-T)=x(2(t-T))+3
So, from both the equations, we can interpret that: x(t-T)y(t-T)
So, the system is time variant.
 Question 9
Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued
II. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6π rad/s
For the three statements above, which one of the following is correct?
 A only II and III are true B only I and III are true C only III is true D only I is true
Question 9 Explanation:
 Question 10
Two discrete-time signals x[n] and h[n] are both non-zero for n = 0, 1, 2 and are zero otherwise. It is given that X[0] = 1, x[1] =2, x[2]=1,h[0]=1. Let y[n] be the linear convolution od x[n] and h[n]. Given y[1]=3 and y[2]=4, the value of the expression (10y[3]+y[4]) is _________
 A Fill in the Blank Type Question
Question 10 Explanation:
 Question 11
Let h[n] be the impulse response of a discrete-time linear time invariant (LTI) filter. The impulse response is given by h[0]= ; h[1]= ;h[2]= ;and h[n]=0 for n<0 and n>2 Let H(ω)be the discrete-time Fourier system transform (DTFT) of h[n], where ω is the normalized angular frequency in radians. Given that H(ω)=0 and, the value of (in radians) is equal to
 A Fill in the Blank Type Question
Question 11 Explanation:
 Question 12
A discrete-time all-pass system has two of its poles at and Which one of the following statements about the system is TRUE?
 A It has two more poles at and B It is stable only when the impulse response is two-sided. C It has constant phase response over all frequencies. D It has constant phase response over the entire z-plane.
Question 12 Explanation:
The Correct Answer Among All the Options is B
According to data given, we can draw the poles in z-domain as follows,

For the system to be stable, ROC should include the unit circle. From the given pole pattern, it is clear that to make the system stable, the ROC should be two-sided and hence the impulse response of the system should be also two-sided.
For LTI system to be stable ROC of Z transform of unit impulse response must include unity circle: Required ROC for above condition: 0.25 < |z| <2
Since ROC is two sided so unit impulse response must also be two sided.
 Question 13
Let be a periodic function with period The Fourier series coefficients for this series are denoted by that is

The same function can also be considered as a periodic function with period Let be the Fourier series coefficients when period is taken as If then is equal to
 A 256 B 64 C 16 D 4
Question 13 Explanation:
Change in only time period or frequency does not change in the value of Fourier series coefficients
So,

Method 2
 Question 14
The input is fed to a Hilbert transformer to obtain as shown in the figure below:

Here The value (accurate to two decimal places) of is __________.

 A Fill in the Blank Type Question
Question 14 Explanation:
Hilbert transform does not alter the amplitude spectrum of the signal and using CTFT to determine the amplitude,
 Question 15
Let be 8-point DFT of a sequence where The value (correct to two decimal places) of is __________
 A Fill in the Blank Type Question
Question 15 Explanation:
 Question 16
A band limited low-pass signal of bandwidth 5 kHz is sampled at a sampling rate The signal is reconstructed using the reconstruction filter whose magnitude response is shown below:

The minimum sampling rate (in kHz) for perfect reconstruction of is _________.
 A Fill in the Blank Type Question
Question 16 Explanation:
 Question 17
An LTI system with unit sample response is a
 A Low — pass filter B high — pass filter C band — pass filter D band — stop filter
Question 17 Explanation:
 Question 18
The input x(t) and the output y(t) of a continuous-time system are related as  and T is the time period of signal x(t) then the system is
 A Linear and time-variant B Linear and time-invariant C Non-linear and time-variant D Non-linear and time-invariant
Question 18 Explanation:
 Question 19
Consider the parallel combination of two LTI systems shown in the figure.

The impulse responses of the systems are

If the input x(t) is a unit step signal, then the energy of y(t) is ______.
 A Fill in the Blank Type Question
Question 19 Explanation:
 Question 20
The signal x(t) = sin(14000πt) , where ‘t’ is in seconds is sampled at a rate of 9000 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows :
What is the number of sinusoids in the output and their frequencies in kHz?
 A Number = 1, frequency = 7 B Number = 3, frequencies= 2,7,11 C Number = 2, frequencies = 2, 7 D Number = 2, frequencies = 2, 11
Question 20 Explanation:
 Question 21
Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems u(t) denotes the unit-step function)?
 A B C D
Question 21 Explanation:
If the input to a system is its eigen signal, the response has the same form as the eigen signal
 Question 22
A continuous-time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period Ts. In which one of the following cases is the sampled signal periodic?
 A B C Always D Never
Question 22 Explanation:
For periodic signal
T/Ts -> rational number
Here T=1.2 Ts
T/Ts = 12/10
= 6/5 (Which is rational number)
 Question 23
Consider the sequence x[n]=anu[n] + bnu[n] where u[n] denotes the unit-step sequence and.The region of convergence (ROC) of the z-transform of x[n] is
 A B C D
Question 23 Explanation:
 Question 24
A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of 23 Hz. The fundamental frequency (in Hz) of the output is _______.
 A Fill in the Blank Type Question
Question 24 Explanation:
13 Hz. When 33 Hz and 46 Hz are multiplied with each other, we get signals of frequency 13 Hz and 79 Hz so on. Since we are passing the output through low pass filter, it allows only low frequency signals till it’s cut off frequency(23 Hz). So only 13 Hz is passed.
 Question 25
A sequence is specified as
, for
The initial conditions are and for. The value of is_____.
 A Fill in the Blank Type Question
Question 25 Explanation:
 Question 26
The Laplace transform of the causal periodic square wave of period T shown in the figure below is
 A B C D
Question 26 Explanation:
 Question 27
An AC voltage source V = 10 sin(t) volts is applied to the following network. Assume that , and that the diode is ideal. RMS current through the diode is
 A Fill in the Blank Type Question
Question 27 Explanation:

Irms = Imax because it is half wave rectifier.
 Question 28
The result of the convolution x(–t) * δ (–t – t0) is
 A B C D
Question 28 Explanation:
x(-t) is an even function
i.e,.

 Question 29
Two sequences [a, b, c] and [A, B, C] are related as
where
If another sequence [p, q, r] is derived as,

then the relationship between the sequences [p, q, r] and [a, b, c] is
 A [p, q, r] = [b, a, c] B [p, q, r] = [b, c, a] C [p, q, r] = [c, a, b] D [p, q, r] = [c, b, a]
Question 29 Explanation:
 Question 30
For the discrete-time system shown in the figure, the poles of the system transfer function are located at
 A 2, 3 B C D
Question 30 Explanation:
 Question 31
The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[n]. If h [0] = 1, we can conclude
 A h [n] is real for all n B h[n] is purely imaginary for all n C h [n] is real for only even n D h [n] is purely imaginary for only odd n
Question 31 Explanation:
 Question 32
The energy of the signal is_______.
 A Fill in the Blank Type Question
Question 32 Explanation:
 Question 33
A continuous-time filter with transfer function is converted to a discrete time filter with transfer function so that the impulse response of the continuous-time filter, sampled at 2 Hz, is identical at the sampling instants to the impulse response of the discrete time filter. The value of k is______
 A Fill in the Blank Type Question
Question 33 Explanation:
Given
So,
 Question 34
The Discrete Fourier Transform (DFT) of the 4-point sequence

If is the DFT of the 12-point sequence, the value of is_______.
 A Fill in the Blank Type Question
Question 34 Explanation:
Given,
We can directly find the DFT of given sequence

DFT repeats itself 2 times as 2 zeros are added after each sample

DFT repeats itself
2 times as 2 zeros are added after each sample
 Question 35
If the signal denoting the convolution operation, then x(t) is equal to
 A B C D
Question 35 Explanation:
 Question 36
If the signal denoting the convolution operation, then x(t) is equal to
 A B C D
Question 36 Explanation:
 Question 37
A discrete-time signal

has z-transform X(z). If Y(z) = X(-z) is the z-transform of another signal y[n], then
 A Y[n]=x[n] B Y[n]=x[-n] C Y[n] = -x[n] D Y[n] = -x[-n]
Question 37 Explanation:
 Question 38
A signal is the input to an LTI system with the transfer function
H(s) = es + e-s
If Ck denotes the kth coefficient in the exponential Fourier series of the output signal, then C3 is equal to
 A 0 B 1 C 2 D 3
Question 38 Explanation:
 Question 39
The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal
then the ROC of its z-transform
is represented by
 A B C D
Question 39 Explanation:
Thus, Common ROC does not exist for x[n]
 Question 40
A continuous-time speech signal xa(t) is sampled at a rate of 8 kHz and the samples are subsequently grouped in blocks, each of size N. The DFT of each block is to be computed in real time using the radix-2 decimation-in-frequency FFT algorithm. If the processor performs all operations sequentially, and takes 20μs for computing each complex multiplication (including multiplications by 1 and −1) and the time required for addition/subtraction is negligible, then the maximum value of N is _____
 A Fill in the Blank Type Question
Question 40 Explanation:
The number of computations required for each multiplication =
Each computation takes 20μs.

 Question 41
The direct form structure of an FIR (finite impulse response) filter is shown in the figure. The filter can be used to approximate a
 A Low-pass filter B High-pass filter C Band-pass filter D Band-stop filter
Question 41 Explanation:
 Question 42
The impulse response of an LTI system can be obtained by
 A differentiating the unit ramp response B differentiating the unit step response C integrating the unit ramp response D integrating the unit step response
Question 42 Explanation:
For any LTI system,

h(t) = impulse response
s(t) = step response
Hence, the correct option is (B).
 Question 43
Consider a four-point moving average filter defined by the equation y[n] = . The condition on the filter coefficients that results in a null at zero frequency is
 A Α1 = α2 = 0; α0 = –α3 B Α1 = α2 = 1; α0 = –α3 C Α0 = α3 = 0; α1 = α2 D Α1 = α2 = 0; α0 = α3
Question 43 Explanation:
 Question 44
Suppose x[n] is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z = ±2j. Which one of the following statements is TRUE for the signal x[n]?
 A It is a finite duration signal B It is a causal signal C It is a non-causal signal D It is a periodic signal
Question 44 Explanation:
 Question 45
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input x[n], the response y[n] is
 A B C D
Question 45 Explanation:
Let us redraw the given system as

From the circuit, we have

Again,

……(2)
Multiplying equations (1) and (2),

For unit step response,

Hence,
 Question 46
The complex envelope of the bandpass signal , centered about Hz, is
 A B C D
Question 46 Explanation:
Given

Let XC be complex envelope of above signal. So, we have

 Question 47
Let be a periodic signal period 16. Its DFS coefficients are defined by for all k. The value of the coefficient a31 is____________.
 A Fill in the Blank Type Question
Question 47 Explanation:
 Question 48
The characteristic equation of an LTI system is given by F(s) = s5 + 2s4 + 3s3 + 6s2 – 4s – 8= 0. The number of roots that lie strictly in the left half s-plane is _________.
 A Fill in the Blank Type Question
Question 48 Explanation:

Given characteristic equation,

Applying the Routh stability criterion,
s5     1       3         - 4
s4     2       6         - 8
s 3    0       0           0
s2
s1
s0
It contains complete zero row, so we obtain the auxiliary equation as
Put x = s2,
2x2+ 6x − 8 = 0
x = 1, -4
So, s2 = 1 or s = ±1
and
Hence, one root s =− 1 lies on the left side. Taking differential of auxiliary equation,
Now, the Routh array is redrawn as
s5     1           3       -4
s4     2           6       -8
s3     8           12      0
s2     3          -8       0
s1    33.33       0
so     -8
Since, there is only one sign change in the first column of Routh array, so one pole lie in R.H.S and two poles lie on imaginary axis. Hence, the remaining two poles lies in L.H.S.

 Question 49
Two casual discrete – time signal x[n] and y[n] are related as y[n] = is the z-transform of y[n] is , the value of x [2] is___
 A 0 B 1 C 2 D 2.2
Question 49 Explanation:
 Question 50
The bilateral Laplace transform a function
 A B C D
Question 50 Explanation:
 Question 51
The magnitude and phase of the complex Fourier series coefficients ak of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set of purely imaginary numbers.
 A X(t)R B X (t) P C X (t) (C – R) D The information given is not sufficient to draw any conclusion about x(t)
Question 51 Explanation:
only changes the sign of the magnitude |ak|. Since the magnitude spectrum |ak| is even
the corresponding time-domain signal is real.
 Question 52
Consider two real sequences with time-origin marked by the hold value
x1[n] = {1, 2, 3, 0},  x2 [n] = {1, 3, 2, 1}
Let X1 (k) and X2 (k) be 4 –point DFTs of x1 [n] and x2 [n], respectively
Another sequence x3 [n] is derived by taking 4-point inverse DFT of X3(k) = X1 (k) X2 (k).
The value of x3 [2] is_____
 A 35 B 12 C 11 D 14
Question 52 Explanation:
 Question 53
A discrete-time signal x[n]= sin(π2n) , n being an integer, is
 A periodic with period B periodic with period C periodic with period D not periodic
Question 53 Explanation:
 Question 54
Consider two real valued signals, x(t) band-limited to [−500 Hz, 500Hz] and y(t) bandlimited to [−1kHz, 1kHz]. For z (t) = x(t). y(t), the Nyquist sampling frequency (in kHz) is __________
 A 2 B 3 C 4 D 6
Question 54 Explanation:
Given x(t ) is band limited to [−500Hz, 500Hz] and
y(t )is band limited to [−1000Hz, 1000Hz]
z(t ) = x (t ).y(t )

Multiplication in time domain results convolution in frequency domain.
The range of convolution in frequency domain is [−1500Hz, 1500Hz]

So maximum frequency present in z(t) is 1500Hz
Nyquist rate = 3000Hz or 3 kHz
 Question 55
A continuous, linear time-invariant filter has an impulse response h(t) described by

When a constant input of value 5 is applied to this filter, the steady state output is _______.
 A 35 B 40 C 45 D 50
Question 55 Explanation:
 Question 56
 A 0 B -j C D
Question 56 Explanation:
 Question 57
The Region of Convergence (ROC) of the z-transform of x[n]
 A B C D does not exist.
Question 57 Explanation:
 Question 58
Consider a discrete time periodic signal . Let ak be the complex Fourier series coefficients of x[n]. The coefficients ak are non-zero when k = Bm ± 1, where m is any integer. The value of B is_________.
 A 5 B 10 C 15 D 20
Question 58 Explanation:
The Correct Answer Among All the Options is B

Fourier series co-efficients are also periodic with period N =10

Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 59
A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system.

y(t)+5y(t)=u(t)

When y(0) = 1 and u(t) is a unit step function, y(t) is
 A B C D
Question 59 Explanation:
 Question 60
An FIR system is described by the system function The system is
 A maximum phase B minimum phase C mixed phase D zero phase
Question 60 Explanation:
The Correct Answer Among All the Options is C
Minimum phase system has all zeros inside unit circle maximum phase system has all zeros outside unit circle mixed phase system has some zero outside unit circle and some zeros inside unit circle.

H(z)=(2z2 + 7z + 3)/z2
= (2z+1)(z+3)/z2

So zeroes are -1/2 and -3

One zero is inside and one zero outside unit circle hence mixed phase system
Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 61
Let x[n] = x[−n] and X[Z] be the z-transform of If is a zero o X(z), which one of the following must also be a zero of X(z).
 A B C D
Question 61 Explanation:
The Correct Answer Among All the Options is B
Given x[n] = x[−n]

Refer the Topic Wise Question for Z-Transform Signal and Systems
 Question 62
Consider a discrete-time signal

If y[n] is the convolution of x[n] with itself, the value of y[4] is _________.
 A 10 B 15 C 20 D 30
Question 62 Explanation:
The Correct Answer Among All the Options is A

Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 63
The input-output relationship of a causal stable LTI system is given as .
If the impulse response h[n] of this system satisfies the condition the relationship between
 A B C D
Question 63 Explanation:
The Correct Answer Among All the Options is A
Given system equation as

Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 64

In the figure, M(f) is the Fourier transform of the message signal.m(t) where A = 100 Hz and B = 40 Hz. Given

and

The cutoff frequencies of both the filters are fc

The bandwidth of the signal at the output of the modulator (in Hz) is _____.

 A 40 B 60 C 80 D 100
Question 64 Explanation:
The Correct Answer Among All the Options is B
m(t)M(f)

After multiplication with

After high pass filter

After multiplication with and low pass filter of cut off fc

Bandwidth = A – B
= 100 – 40 = 60
Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 65

Let
The quantities p, q, r are real numbers.

Consider

If the zero of H(z) lies on the unit circle, then

 A r =0.5 B r = -0.5 C r= 1 D r= -1
Question 65 Explanation:
The Correct Answer Among All the Options is B

Refer the Topic Wise Question for Z-Transform Signal and Systems
 Question 66
A Fourier transform pair is given by

where u[n] denotes the unit step sequence. The value of A is _________.
 A 2.345 B 2.375 C 3.345 D 3.375
Question 66 Explanation:
The Correct Answer Among All the Options is D

Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 67
The sequence where u[n] is the unit step sequence, is convolved with itself to obtain y[n]. Then
 A 4 B 8 C 7 D 5
Question 67 Explanation:
The Correct Answer Among All the Options is A

Refer the Topic Wise Question for Convolution and Its Properties Signal and Systems
 Question 68
The unilateral Laplace transform of Which one of the following is the unilateral Laplace transform of g(t) = t. f(t)?
 A B C D
Question 68 Explanation:
The Correct Answer Among All the Options is D

Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 69
A stable linear time invariant (LTI) system has a transfer function To make this system causal it needs to be cascaded with another LTI system having a transfer function A correct choice for among the following options is
 A s + 3 B s - 2 C s – 6 D s + 1
Question 69 Explanation:
The Correct Answer Among All the Options is B

It is given that system is stable thus its ROC includes axis. This implies it cannot be causal, because for causal system ROC is right side of the rightmost pole.
Poles at s = 2 must be removes so that it can be become causal and stable simultaneously.

Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 70

A causal LTI system has zero initial conditions and impulses response h (t). Its input x (t) and output y (t) are related through the linear constant-coefficient differential equation

Let another signal g(t) be defined as

If G(s) is the Laplace transform of g(t), then the number of poles of G(s) is _______.

 A 0 B 1 C 2 D 4
Question 70 Explanation:
The Correct Answer Among All the Options is B
Given differential equation

Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 71
The N-point DFT X of a sequence

Denote this relation as X = DFT(x). For N = 4, which one of the following sequences satisfies DFT (DFT (x))=x ?
 A B C D
Question 71 Explanation:
The Correct Answer Among All the Options is B
This can be solve by directly using option and satisfying the condition given in question

DFT of (x) will not result in [1 2 3 4]
Try with DFT of Y 1 2 3 2]

Same as x
Then ‘B’ is right option
Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 72
Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
 A product of h1(t) and h2(t) B sum of h1(t) and h2(t) C convolution of h1(t) and h2(t) D subtraction of h2(t) from hl(t)
Question 72 Explanation:
The Correct Answer Among All the Options is C
If the two systems with impulse response and are connected in cascaded configuration as shown in figure, then the overall response of the system is the convolution of the individual impulse responses.

Hence correct option is C.
Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 73
The impulse response of a system is h(t) = tu(t). Form an input u(t –1), the output is
 A B C D
Question 73 Explanation:
The Correct Answer Among All the Options is C
Given, the input

Its Laplace transform is

The impulse response of system is given

Its Laplace transform is

Hence, the overall response at the output is

Its inverse Laplace transform is

Hence correct option is C.
Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 74
For a periodic signal
, the fundamental frequency in rad/s
 A 100 B 300 C 500 D 1500
Question 74 Explanation:
The Correct Answer Among All the Options is A
Given, the signal

So we have

Therefore, the respective time periods are

So, the fundament time period of the signal is

or,
Hence, the fundamental frequency in rad/sec is

Hence correct option is A.
Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 75
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is
 A 5 kHz B 12 kHz C 15 kHz D 20 kHz
Question 75 Explanation:
The Correct Answer Among All the Options is A
Given, the maximum frequency of the band-limited signal

According to the Nyquist sampling theorem, the sampling frequency must be greater than the Nyquist frequency which is given as

So, the sampling frequency fs must satisfy

Only the option A does’nt satisfy the condition therefore, 5 kHz is not a valid sampling frequency.
Hence correct option is A.
Refer the Topic Wise Question for Sampling Theorem and Applications Signal and Systems
 Question 76

Let and h(t) is a filter matched to g(t) is applied as input to h(t), then the Fourier transform of the output is

 A B C D
Question 76 Explanation:
The Correct Answer Among All the Options is D

The matched filter is characterized by a frequency response that is given as

where
Now, consider a filter matched to a known signal g(t). The fourier transform of the resulting matched filter output go(t) will be

T is duration of
Assume
So,
Since, the given Gaussian function is

Fourier transform of this signal will be

Therefore, output of the matched filter is

Refer the Topic Wise Question for Fouries Series and Its Application Signal and Systems
 Question 77
The impulse response of a continuous time system is given by . The value of the step response at t = 2 is
 A 0 B 1 C 2 D 3
Question 77 Explanation:
The Correct Answer Among All the Options is B
Given, the impulse response of continuous time system

From the convolution property, we know

So, for the input
(Unit step funn)
The output of the system is obtained as

Hence correct option is B.
Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 78
A system is described by the differential equation
Let x(t) be a rectangular pulse given by

Assuming that y(0) = 0 and at t = 0, the Laplace transform of y(t) is
 A B C D
Question 78 Explanation:
The Correct Answer Among All the Options is B
Given, the differential equation

Taking its Laplace transform with zero initial conditions, we have
…(1)
Now, the input signal is

i.e,
Taking its Laplace transform, we obtain

Substituting it in equation (1), we get

Hence correct option is B.
Refer the Topic Wise Question for Convolution and Its Properties Signal and Systems
 Question 79
The DFT of a vector is the vector . Consider the product

The DFT of the vector is a scaled version of
 A B C D
Question 79 Explanation:
The Correct Answer Among All the Options is A
Given, the DFT of vector as
D.F.T.
Also, we have
…(i)
For matrix circular convolution, we know

where are three point signals for and similarly for and are three point signals. Comparing this transformation to Eq(1), we get

Now, we know that

So,

Hence correct option is A.
Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 80
The unilateral Laplace transform of is . The unilateral Laplace transform t f(t) is
 A B C D
Question 80 Explanation:
The Correct Answer Among All the Options is D
If then

In this problem,
Given,

We need

Refer the Topic Wise Question for Convolution and Its Properties Signal and Systems
 Question 81
If , then the region of convergence (ROC) of its Z-transform innthe Z-plane will be
 A B C D
Question 81 Explanation:
The Correct Answer Among All the Options is C

So overall ROC will be intersection of there ROCs i.e

Refer the Topic Wise Question for Z-Transform Signal and Systems
 Question 82
The input x(t) and output y(t) of a system are related as . The system is
 A Time-invariant and stable B Stable and not time-invariant C Time-invariant and not stable D Not time-invariant and not stable
Question 82 Explanation:
The Correct Answer Among All the Options is D

for input is

so system is not time invariant
for input x(τ) = cos (3τ) (bounded i/p)
as
So for bounded i/p, o/p is not bounded therefore system is not stable.
Refer the Topic Wise Question for Sampling Theorem and Applications Signal and Systems
 Question 83
The Fourier transform of a signal h(t) is H(jω) = (2cosω)(sin2ω)/ω. The value of h(0) is
 A 1/4 B 1/2 C 1 D 2
Question 83 Explanation:
The Correct Answer Among All the Options is C
….. (1)

……(2)
Where

So

So h(0) = 1
Refer the Topic Wise Question for Fouries Series and Its Application Signal and Systems
 Question 84
Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)n u[n]  and g[n] is a causal sequence. If y[0] =1 and y [1] = ½, then g[1] equals
 A 0 B 1/2 C 1 D 3/2
Question 84 Explanation:
The Correct Answer Among All the Options is A

will be zero for k > 1 and g[k] will be zero for k = 0 as it is casual sequence.

g[1] = 0
Refer the Topic Wise Question for Convolution and Its Properties Signal and Systems
 Question 85
Consider the following statements regarding a parabolic function:
1) A parabolic function is one degree faster than the ramp function.
2) A unit parabolic function is defined as
3) Laplace transform of unit parabolic function is
Which of the above statements are correct?
 A 1 and 2 only B 1 and 3 only C 2 and 3 only D 1, 2 and 3
Question 85 Explanation:
The Correct Answer Among All the Options is D
Parabolic function is defined as

Laplace transform will be

A parabolic function is degree faster than the ramp function.
Refer the Topic Wise Question for Basic of Signals and Systems Signal and Systems
 Question 86
What is the range of values of a and b for which the linear time-invariant system with impulse response is stable?
 A Both |a| < 1 and |b| > 1 are satisfied B Both |a| > 1 and |b| < 1 are satisfied C Both |a| < 1 and |b| > 1 are satisfied D Both |a| < 1 and |b| < 1 are satisfied
Question 86 Explanation:
The Correct Answer Among All the Options is A

h(n) = anu(n) + bnu(–n–1)

For the system to be stable
| a | < 1 & | b | > 1
Option A
Refer the Topic Wise Question for Z-Transform Signal and Systems
 Question 87
The special case of a finite-duration sequence is given as

The sequence x(n) into a sum of weighted impulse sequences will be
 A 2δ(n + 1) + 4δ(n) + 3δ(n – 2) B 2δ(n) + 4δ(n - 1) + 3δ(n – 3) C 2δ(n) + 4δ(n – 1) + 3δ(n – 2) D 2δ(n + 1) + 4δ(n) + 3δ(n – 1)
Question 87 Explanation:
The Correct Answer Among All the Options is A
Given x(n) =
x(n) = 2(n+1) + 4(n) + 3 (n – 2)
Option A
Refer the Topic Wise Question for Basic of Signals and Systems Signal and Systems
 Question 88
The frequency response and the main lobe width for rectangular window are
 A B C D
Question 88 Explanation:
The Correct Answer Among All the Options is A
Frequency response for rectangular window is
Main lobe width for rectangular window is
Option A
Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 89
Difference in number of complex multiplir rquied for 16 point DFT and 16-point radix-2 FFT is
 A 30 B 63 C 224 D 256
Question 89 Explanation:
The Correct Answer Among All the Options is C
In N-point DFT,
no. of multiplication = 256
in N-point FFT,
no. of multiplication= 32
required difference =256-32=224
Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 90
No of stages(S) in direct FIR filter is given as
S= intger (K*Fs / f)
Where Fs = Sampling Frequency. f= Filter transition band, K=3 (assume)
If x(n) is signal with frequncy rang 0.2.4 MHz and sampled at Fa = 400 MHz and it is filtered by

Assumptions :
Passband Frequency LPF(1): 1.8 MHz, Stopband Frequency LPF(1): 4MHz
Passband Frequency LPF(2): 1.8 MHz, Stopband Frequency LPF(2): 2 MHz
Both filters are having flat passbands and stopbands
Passband attenuation of both filters = 0 dB and stop band attenustion of both filters is infinity.
Calculate total no. stages SLPF1 + SLPF2
 A 120 B 545 C 555 D 665
Question 90 Explanation:
The Correct Answer Among All the Options is D
Formula for calculating no. of stages (S)=integer
Given
For LPF1 :
Transition band() = |passband frequency-stopband frequency|
= |4-1.8|
=2.2MHz

For LPF2:
input x(n) is fed after decimation by 50. So,
x() x()
therefore ,
now, Transition band()=|2-0.8| =0.2MHz
= 120
+= 545+120 => 665
Refer the Topic Wise Question for DFT and Its Applications Signal and Systems
 Question 91

If System 1 and 2 are Linear Time Invariant systems and same input x(n) is provided both configuration
Statement 1:
Statement 2: f(n)=g(n)
 A Statement 1 is always true B Statement 2 is always true C Both Statement 1 and Statement 2 are always true D Both Statement 1 and Statement 2 are not true
Question 91 Explanation:
The Correct Answer Among All the Options is A
For given LTI system,
f(n)=x(n) and
in frequency domain,
F(w)=X(w). and

Similarly for the other LTI system,

f(n)= I.F [X(w).]
g(n)=I.F[X(w).]
f(n) g(n) because ], so statement 2 is not true.
Refer the Topic Wise Question for Basic of Signals and Systems Signal and Systems
 Question 92
Benefit(s) of Bandpass sampling over low pass sampling
 A It reduces speed requirement of A/D convertor B Increase the amount of digital memory necessary to capture a given interval of signal C Both (A) and (B) are correct D Both (A) and (B) are incorrect
Question 92 Explanation:
The Correct Answer Among All the Options is A
Bandpass sampling require less bandwidth to reconstruct the signal compare to low pass sampling. Bandpass sampling time is more i.e. speed requirement is less because it will store less sample compared to low pass sampling . it will decrease the memory requirement , because it store less sample when compared to low pass sampling
Refer the Topic Wise Question for Sampling Theorem and Applications Signal and Systems
 Question 93
For a signal with FC (Centre Frequency) = 1200 MHz and BW = 100 MHz which of the following Sampling frequency(Fs) will cause spectrum inversion:
 A 287.5 MHz B 575 MHz C 1150 MHz D 1600MHz
Question 93 Explanation:
The Correct Answer Among All the Options is D
, m is an even integer.

For minimum sampling frequency ,

Therefore , from the given option spectrum inversion occurs at 1600MHz.
Refer the Topic Wise Question for Sampling Theorem and Applications Signal and Systems
 Question 94
If is sampled with Fs = 16000Hz calculate X(0) if X(m)= When N=8, where
 A 0.0-j 4.0 B 0.0 – j 0.0 C 1.414 + j 1.414 D 0.0 + j 4.0
Question 94 Explanation:
The Correct Answer Among All the Options is B

Given ,

………………..(1)
We have , X(m)=
X(0)=
=
As N=8, therefore , n=0,1,2,3,4,5,6,7
X(0)=x(0)+x(1)+……..x(7)
On putting different values of n in (1) we get values of x(0)….x(7). But as equation (1) is sum of sinusoidal function , sinusoidal has real values lies in[-1,1]. So all values of x(n) will also be real.
Refer the Topic Wise Question for Sampling Theorem and Applications Signal and Systems
 Question 95
Fourier transform of te-at u(t), (where, a>0, u(t) is the Unit step function) is:
 A B C D
Question 95 Explanation:
The Correct Answer Among All the Options is B
X(w)=
As we know the properties of F.T
(-jt)x(t)

(-jt)
t
=
Refer the Topic Wise Question for Fouries Series and Its Application Signal and Systems
 Question 96
Let and . If
What is x[n] in terms of unit discrete step function u(n)?
 A 2(0.2)nu(n)-(0.1)nu(n) B 2(0.1)nu(n)-(0.2)nu(n) C (0.2)nu(n)-(0.1)nu(n) D (0.1)nu(n)-(0.2)nu(n)
Question 96 Explanation:
The Correct Answer Among All the Options is A
expression for DTFT is :
X[] =
x[n] =.dw

DTFT of , when |a|<1
Therefore,
X[] =
Using partial fraction,

On solving we get, A=2,B=-1

Now taking inverse DTFT of we get ,
. 2(0.2)nu(n)-(0.1)nu(n)
Refer the Topic Wise Question for Z-Transform Signal and Systems
 Question 97
What is the peak to average power ratio for the signal x(t) = A sin (wt) with 50% duty cycle?
 A 0 dB B 1 dB C 3 dB D 6 dB
Question 97 Explanation:
The Correct Answer Among All the Options is D
x(t)=A sin (wt)

=
Given, Duty cycle =

Therefore,
=
Peak power =
=

10
Refer the Topic Wise Question for Basic of Signals and Systems Signal and Systems
 Question 98
x(t) = {
1, 0tT
0, otherwise
}
h(t) = {
t, 0t2T
0, otherwise
}
Calculate y(t) =x(t) * y(t), where * denotes convolution for interval T t 2T
 A 0 B 0.5t2 C Tt – 0.5T2 D -0.5t2 + Tt +2.5T2
Question 98 Explanation:
The Correct Answer Among All the Options is C
y(t) = x(t) * y(t) .

y(t)=
= [T() - ] +0
= T
Refer the Topic Wise Question for Convolution and Its Properties Signal and Systems
 Question 99
The It R= 1/3 convolution encoder defined by transfer functions H1(z)=1+z-1
H2(z)=1+z-2
H3(z)=1+z-1+z-2is
 A recursive and K = 3 B systematic and K = 2 C non recursive and k=3 D non recursive and K = 2
Question 99 Explanation:
The Correct Answer Among All the Options is C
In a convolution encoder, convolution of the input signal and impulse response is done. A convolution encoder is a time invariant system, and non-recursive codes are simply non-systematic codes. The given transfer functions clearly represents a non-recursive encoder(first), and z transform is what connects a transfer function with impulse response. Also, the constraint length of the given encoder is 3.
Refer the Topic Wise Question for Convolution and Its Properties Signal and Systems
 Question 100
The match filter response for given signal sampled at t =T is
 A B C D
Question 100 Explanation:
The Correct Answer Among All the Options is B
We have to find the response of a matched filter at t=T.
Now, matched filter response is given as: h(T-t)
Let us first draw h(t)

Now, h(t+T)='+' left shift by 'T'

Next: h(-t+T)=> h(T-t)
So, now it can be drawn as:

Refer the Topic Wise Question for Responses and Stability Signals and Systems
 Question 101
Which of the following statement is not true
 A Autocorrelation function and energy spectral density forms a Fourier transform pair B Autocorrelation function of a real valued energy signal is a real valued odd function C The value of autocorrelation function of a power signal at the origin is equal to the average power of the signal D Autocorrelation function is the inverse Fourier transform of power spectral density
Question 101 Explanation:
The Correct Answer Among All the Options is B
Auto-correlation function is also called as serial correlation.
For auto-correlation function, following property exist:
Rxx(т)= F.T(Sxx(f))
And, Rxx(т)= dт and
Sxx(f)=
Refer the Topic Wise Question for Convolution and Its Properties Signal and Systems
There are 101 questions to complete.