Back to Sections

Type:ALLMCQNATMSQ

Circuit Analysis(14)Time and Frequency Domain Analysis of Linear Circuits(9)LTI Systems(5)Continuous-time Signals(17)Discrete-time Signals(7)

Circuit Analysis

14 Questions

GATE→2026→Networks, Signals and Systems→Circuit Analysis

Q1

NAT[1 Mark]

The output voltage $V_{o}$ (in Volt) for the network given in the Figure is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Networks, Signals and Systems→Circuit Analysis

Q2

MCQ[2 Marks]

In the given circuit, $L=1\mu H$ and $C=1~\mu F$. The phasor diagram for Ic and IL is also shown. Assume that the phase $(\theta_{1}+\theta_{2})$ is $90^{\circ}$ at a frequency of 159.15 kHz. Among the following options, what is the nearest integer value of $R_{C}\times R_{L};$

(A)

0

(B)

1

(C)

2

(D)

10

Explanation

GATE→2025→Networks, Signals and Systems→Circuit Analysis

Q3

MCQ[1 Mark]

Consider a part of an electrical network as shown below. Some node voltages, and the current flowing through the $3\Omega$ resistor are as indicated. The voltage (in Volts) at node X is ______

(A)

20/3

(B)

32/3

(C)

22/3

(D)

2/3

Explanation

GATE→2025→Networks, Signals and Systems→Circuit Analysis

Q4

MCQ[1 Mark]

Let $i_c$, $i_L$ and $i_R$ be the currents flowing through the capacitor, inductor, and resistor, respectively, in the circuit given below. The AC admittances are given in Siemens (S). Which one of the following is TRUE?

(A)

$i_C = 0.25\angle 180^{\circ}$ A, $i_L = 0.1\angle 0^{\circ}$ A, $i_R = 0.2\angle 90^{\circ}$ A

(B)

$i_C = 4\angle 180^{\circ}$ A, $i_L = 10\angle 0^{\circ}$ A, $i_R = 5\angle 90^{\circ}$ A

(C)

$i_C = 0.25\angle 270^{\circ}$ A, $i_L = 0.1\angle 90^{\circ}$ A, $i_R = 0.2\angle 90^{\circ}$ A

(D)

$i_C = 4\angle 90^{\circ}$ A, $i_L = 10\angle 270^{\circ}$ A, $i_R = 5\angle 0^{\circ}$ A

Explanation

GATE→2025→Networks, Signals and Systems→Circuit Analysis

Q5

MCQ[2 Marks]

In the circuit below, $M_1$ is an ideal AC voltmeter and $M_2$ is an ideal AC ammeter. The source voltage (in Volts) is $v_s(t) = 100 \cos(200 t)$. What should be the value of the variable capacitor C such that the RMS readings on $M_1$ and $M_2$ are 25 V and 5 A, respectively?

(A)

25 $\mu F$

(B)

4 $\mu F$

(C)

0.25 $\mu F$

(D)

Insufficient information to find C

Explanation

GATE→2024→Networks, Signals and Systems→Circuit Analysis

Q6

NAT[1 Mark]

In the given circuit, the current $I_x$ (in mA) is

Explanation

GATE→2024→Networks, Signals and Systems→Circuit Analysis

Q7

NAT[2 Marks]

In the network shown below, maximum power is to be transferred to the load $R_L$. The value of $R_L$ (in $\Omega$) is

Explanation

GATE→2023→Networks, Signals and Systems→Circuit Analysis

Q8

NAT[1 Mark]

In the circuit shown below, the current i flowing through $200~\Omega$ resistor is _______ mA (rounded off to two decimal places).

Explanation

GATE→2023→Networks, Signals and Systems→Circuit Analysis

Q9

NAT[1 Mark]

For the two port network shown below, the [Y]-parameters is given as $[Y] = \frac{1}{100} \begin{bmatrix} 2 & -1 \\ -1 & 4/3 \end{bmatrix}$ S. The value of load impedance $Z_L$ in $\Omega$, for maximum power transfer will be

Explanation

GATE→2023→Networks, Signals and Systems→Circuit Analysis

Q10

NAT[2 Marks]

A sample and hold circuit is implemented using a resistive switch and a capacitor with a time constant of 1 $\mu$s. The time for the sampling switch to stay closed to charge a capacitor adequately to a full scale voltage of 1 V with 12-bit accuracy is _______ $\mu$s (rounded off to two decimal places).

Explanation

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q11

MCQ[1 Mark]

The current I in the circuit shown is

(A)

$10^{-3}$ A

(B)

$1.25 \times 10^{-3}$ A

(C)

$0.75 \times 10^{-3}$ A

(D)

$-0.5 \times 10^{-3}$ A

Explanation

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q12

MCQ[1 Mark]

Consider the circuit shown in the figure. The current I flowing through the $10~\Omega$ resistor is

(A)

1 A

(B)

0 A

(C)

0.1 A

(D)

-0.1 A

Explanation

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q13

MCQ[2 Marks]

Consider the circuit shown in the figure with input $V(t)$ in volts. The sinusoidal steady state current $I(t)$ flowing through the circuit is shown graphically... The circuit element Z can be

(A)

a capacitor of 1 F

(B)

an inductor of 1 H

(C)

a capacitor of $\sqrt{3}$ F

(D)

an inductor of $\sqrt{3}$ H

Explanation

GATE→2022→Networks, Signals and Systems→Circuit Analysis

Q14

NAT[2 Marks]

A linear 2-port network is shown in Fig. (a)... When the variable resistance R at Port 2 is replaced by the load shown in Fig. (c), the current $I_2$ is _______ mA (rounded off to one decimal place).

Explanation

Time and Frequency Domain Analysis of Linear Circuits

9 Questions

GATE→2026→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q15

MCQ[1 Mark]

The relation between the input current ($I$) and the output voltage $(V)$ of a circuit is governed by the equation: $C\frac{dV}{dt}=I(t)-m(t)$ . The circuit is excited by $I(t)=q\delta(t)$, where q is a real valued constant. V at $t=0^{-}$ is $V_{0}.$ Which of the following is an equivalent representation of the above case?

(A)

$C\frac{dV}{dt}=-m(t)$ , with $V(t=0^{-})=V_{0}+q/C$

(B)

$C\frac{dV}{dt}=-m(t)$ , with $V(t=0^{-})=V_{0}+q/C+m(t=0^{-})$

(C)

$C\frac{dv}{dt}=-m(t)$ with $V(t=0^{-})=V_{0}-q/C+m(t=0^{-})$

(D)

$C\frac{dv}{dt}=-m(t)$ with $V(t=0^{-})=q/C$

Explanation

GATE→2026→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q16

NAT[1 Mark]

Consider the circuit shown in the Figure, where the input $v_{i}(t)$ is in Volt. The average power (in mW) dissipated in the load resistance of $1~k\Omega$ at the resonant frequency is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q17

MCQ[2 Marks]

Consider the two-port network as shown in the Figure. Which of the following options provides the correct set of values of A, B, C and D parameters?

(A)

$A=1/2$, $B=3\times10^{3}S$, $C=10^{-3}\Omega^{-1}$, $D=1/2$

(B)

$A=2$, $B=3~\Omega$ $C=1~\Omega^{-1}$ $D=2$

(C)

$A=2$, $B=6\times10^{3}\Omega$ $C=2\times10^{-3}\Omega^{-1}$ $D=2$

(D)

$B=3\times10^{3}$ Ω, $C=10^{-3}\Omega^{-1}$, $D=2$ $A=2$

Explanation

GATE→2025→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q18

MCQ[2 Marks]

The Z-parameter matrix of a two port network relates the port voltages and port currents as follows: $\begin{bmatrix} V_1 \\ V_2 \end{bmatrix} = Z \begin{bmatrix} I_1 \\ I_2 \end{bmatrix}$ The Z-parameter matrix (with each entry in Ohms) of the network shown below is:

(A)

$\begin{bmatrix} 10/3 & 2/3 \\ 2/3 & 10/3 \end{bmatrix}$

(B)

$\begin{bmatrix} 10 & 2 \\ 2 & 10 \end{bmatrix}$

(C)

$\begin{bmatrix} 10/3 & 1/3 \\ 1/3 & 10/3 \end{bmatrix}$

(D)

[Option D]

Explanation

GATE→2024→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q19

NAT[1 Mark]

In the circuit given below, the switch has been open for a long time and is closed at time $t = 0$. The time constant (in seconds) of the circuit for $t > 0$ is

Explanation

GATE→2023→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q20

MCQ[1 Mark]

A series RLC circuit has a quality factor Q of 1000 at a center frequency of $10^6$ rad/s. The possible values of R, L and C are

(A)

$R = 1~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

(B)

$R = 0.1~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

(C)

$R = 0.01~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

(D)

$R = 0.001~\Omega$, $L = 1~\mu\text{H}$ and $C = 1~\mu\text{F}$

Explanation

GATE→2023→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q21

NAT[1 Mark]

In the circuit shown below, switch S was closed for a long time. If the switch is opened at $t = 0$, the maximum magnitude of the voltage $V_R$ in volts, is

Explanation

GATE→2023→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q22

MCQ[2 Marks]

The switch $S_1$ was closed and $S_2$ was open for a long time. At $t = 0$, switch $S_1$ is opened and $S_2$ is closed, simultaneously. The value of $i_c(0^+)$, in amperes, is

(A)

-0.8

(B)

-1

(C)

0.2

(D)

0.8

Explanation

GATE→2022→Networks, Signals and Systems→Time and Frequency Domain Analysis of Linear Circuits

Q23

MCQ[2 Marks]

For the circuit shown, the locus of the impedance $Z(j\omega)$ is plotted as $\omega$ increases from zero to infinity. The values of $R_1$ and $R_2$ are:

(A)

$R_1 = 2~\text{k}\Omega, R_2 = 3~\text{k}\Omega$

(B)

$R_1 = 5~\text{k}\Omega, R_2 = 2~\text{k}\Omega$

(C)

$R_1 = 5~\text{k}\Omega, R_2 = 2.5~\text{k}\Omega$

(D)

$R_1 = 2~\text{k}\Omega, R_2 = 5~\text{k}\Omega$

Explanation

LTI Systems

5 Questions

GATE→2026→Networks, Signals and Systems→LTI Systems

Q24

MCQ[2 Marks]

Consider the discrete time system (S) with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_{1}[n]$ and $h_{2}[n]$ are linear and time invariant. Which of the following statements is necessarily TRUE?

(A)

S is causal.

(B)

S is linear and time invariant.

(C)

S is linear and time varying.

(D)

S is non-linear.

Explanation

GATE→2025→Networks, Signals and Systems→LTI Systems

Q25

MCQ[1 Mark]

Consider the discrete-time system below with input $x[n]$ and output $y[n]$. In the figure, $h_1[n]$ and $h_2[n]$ denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also, $\delta[n]$ is the unit impulse, and $b > 0$. Assuming $h_2[n] \neq \delta[n]$ the overall system (denoted by the dashed box) is

(A)

linear and time invariant

(B)

linear and time variant

(C)

nonlinear and time invariant

(D)

nonlinear and time variant

Explanation

GATE→2024→Networks, Signals and Systems→LTI Systems

Q26

MCQ[1 Mark]

A causal and stable LTI system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5t)$ is applied to another causal and stable LTI system with impulse response $h(0.5t)$. The resulting output is

(A)

$2y(0.5t)$

(B)

$4y(0.5t)$

(C)

$0.25y(2t)$

(D)

$0.25y(0.25t)$

Explanation

GATE→2023→Networks, Signals and Systems→LTI Systems

Q27

MCQ[1 Mark]

Consider a system with input $x(t)$ and output $y(t) = x(e^t)$. The system is

(A)

Causal and time invariant.

(B)

Non-causal and time varying.

(C)

Causal and time varying.

(D)

Non-causal and time invariant.

Explanation

GATE→2022→Networks, Signals and Systems→LTI Systems

Q28

MSQ[2 Marks]

The outputs of four systems ($S_1, S_2, S_3,$ and $S_4$) corresponding to the input signal $\sin(t)$, for all time t, are shown in the figure. Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?

(A)

$S_1$

(B)

$S_2$

(C)

$S_3$

(D)

$S_4$

Explanation

Continuous-time Signals

17 Questions

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q29

MCQ[1 Mark]

The Laplace Transform of the signal $x(t)=u(t-2)*(tu(t))$ is given by which of the following expressions? ["*" represents convolution operator]

(A)

$\frac{e^{-2s}}{s^{2}(s-2)}$

(B)

$\frac{e^{-2(s-2)}}{s^{3}}$

(C)

$\frac{se^{-2s}}{(s-2)^{2}}$

(D)

$\frac{e^{-2s}}{s^{3}}$

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q30

MCQ[1 Mark]

Two analog signals $x_{1}(t)$ and $x_{2}(t)$ (t in second), are sampled at a rate $F_{s}=40~Hz,$ where $x_{1}(t)=cos(20\pi t)$, $t\ge0$ and $x_{2}(t)=cos(100\pi t)$, $t\ge0$. The first ten samples (starting from $t=0$) are considered for the analysis. Which of the following statements is TRUE?

(A)

All of the first three samples of $x_{1}(t)$ are greater than the corresponding samples of $x_{2}(t)$.

(B)

All of the last three samples of $x_{1}(t)$ are greater than the corresponding samples of $x_{2}(t)

(C)

All of the samples of $x_{2}(t)$ are greater than the corresponding samples of $x_{1}(t).$

(D)

All of the fourth to seventh samples of $x_{1}(t)$ are equal to the corresponding samples of $x_{2}(t).

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q31

MCQ[2 Marks]

The continuous time signal $x(t)$ is real, periodic with period T and satisfies the Dirichlet conditions. The Fourier series representation of $x(t)=\Sigma_{-\infty}^{\infty}a_{n}e^{j(\frac{2\pi nt}{T})}$ and $x(t)$ satisfies the following: $x(t-\frac{T}{2})=-x(t).$ For any integer m, which of the following options is correct?

(A)

$a_{2m}=0$

(B)

$a_{2m}=1$

(C)

$a_{2m}=a_{2m+1}$

(D)

$a_{2m}=-1$

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q32

MCQ[2 Marks]

Consider a real signal $x(t)$, $-\infty<t<\infty$, such that $x(t)=0$ for $t<0$ $x(t)=2$ for $0\le t<1$ and $x(t)=0$ for $t\ge1$. Let $E[x(t)]=\int_{-\infty}^{\infty}[x(t)]^{2}dt$. Which of the following options correctly represents the ratio, $E[x(t)]/E[3~x(-3t+5)]$?

(A)

3

(B)

1

(C)

$1/3$

(D)

$1/9$

Explanation

GATE→2026→Networks, Signals and Systems→Continuous-time Signals

Q33

MSQ[2 Marks]

Let $x_{1}(t)=cos(2\pi nt)$ and $x_{2}(t)=2~sin(4\pi nt)$ represent two sinusoids for a positive integer n and $-\infty<t<\infty$. Which of the following statements about $x_{1}(t)$ and $x_{2}(t)$ is/are valid?

(A)

$x_{1}(t)$ and $x_{2}(t)$ are orthogonal to each other over $0\le t<1/n$.

(B)

$x_{1}(t)$ and $x_{2}(t)$ are orthonormal to each other over $0\le t<1/n$.

(C)

$x_{2}(t)$ is a harmonic of $x_{1}(t).$

(D)

$x_{1}(t)$ and $x_{2}(t)$ are non-orthogonal to each other over $0\le t<1/(2n)$.

Explanation

GATE→2025→Networks, Signals and Systems→Continuous-time Signals

Q34

MCQ[1 Mark]

Consider a continuous-time, real-valued signal $f(t)$ whose Fourier transform $F(\omega) = \int_{-\infty}^{\infty} f(t) \exp(-j \omega t) dt$ exists. Which one of the following statements is always TRUE?

(A)

$|F(\omega)| \le \int_{-\infty}^{\infty} |f(t)| dt$

(B)

$|F(\omega)| > \int_{-\infty}^{\infty} |f(t)| dt$

(C)

$|F(\omega)| \le \int_{-\infty}^{\infty} f(t) dt$

(D)

$|F(\omega)| \ge \int_{-\infty}^{\infty} f(t) dt$

Explanation

GATE→2025→Networks, Signals and Systems→Continuous-time Signals

Q35

MCQ[2 Marks]

Consider a continuous-time finite-energy signal $f(t)$ whose Fourier transform vanishes outside the frequency interval $[-\omega_c, \omega_c]$, where $\omega_c$ is in rad/sec. The signal $f(t)$ is uniformly sampled to obtain $y(t) = f(t)p(t)$. Here, $p(t) = \sum_{n=-\infty}^{\infty} \delta(t - \tau - nT_s)$, with $\delta(t)$ being the Dirac impulse, $T_s > 0$, and $\tau > 0$. The sampled signal $y(t)$ is passed through an ideal lowpass filter $h(t) = \omega_c T_s \frac{\sin(\omega_c t)}{\pi \omega_c t}$ with cutoff frequency $\omega_c$ and passband gain $T_s$. The output of the filter is given by

(A)

$f(t)$ if $T_s < \pi / \omega_c$

(B)

$f(t-\tau)$ if $T_s < \pi / \omega_c$

(C)

$f(t-\tau)$ if $T_s < 2\pi / \omega_c$

(D)

$T_s f(t)$ if $T_s < 2\pi / \omega_c$

Explanation

GATE→2025→Networks, Signals and Systems→Continuous-time Signals

Q36

MSQ[2 Marks]

Let $f(t)$ be a periodic signal with fundamental period $T_0 > 0$. Consider the signal $y(t) = f(\alpha t)$, where $\alpha > 1$. The Fourier series expansions of $f(t)$ and $y(t)$ are given by $f(t) = \sum_{k=-\infty}^{\infty} c_k e^{j \frac{2\pi}{T_0} k t}$ and $y(t) = \sum_{k=-\infty}^{\infty} d_k e^{j \frac{2\pi \alpha}{T_0} k t}$. Which of the following statements is/are TRUE?

(A)

$c_k = d_k$ for all k

(B)

$y(t)$ is periodic with a fundamental period $\alpha T_0$

(C)

$c_k = d_k / \alpha$ for all k

(D)

$y(t)$ is periodic with a fundamental period $T_0 / \alpha$

Explanation

GATE→2024→Networks, Signals and Systems→Continuous-time Signals

Q37

MCQ[2 Marks]

Consider two continuous time signals $x(t)$ and $y(t)$ as shown below. If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Networks, Signals and Systems→Continuous-time Signals

Q38

MCQ[2 Marks]

A continuous time signal $x(t) = 2 \cos(8\pi t + \pi/3)$ is sampled at a rate of 15 Hz. The sampled signal $x_s(t)$ when passed through an LTI system with impulse response $h(t) = \left(\frac{\sin 2\pi t}{\pi t}\right) \cos(38\pi t - \pi/2)$ produces $x_o(t)$.

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Networks, Signals and Systems→Continuous-time Signals

Q39

MSQ[2 Marks]

The radian frequency value(s) for which the discrete time sinusoidal signal $x[n] = A \cos(\Omega n + \pi/3)$ has a period of 40 is/are

(A)

$0.05\pi$

(B)

Option B

(C)

$0.3\pi$

(D)

$0.45\pi$

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q40

MCQ[1 Mark]

The Fourier transform $X(\omega)$ of $x(t) = e^{-t^2}$ is Note: $\int_{-\infty}^{\infty} e^{-y^2} dy = \sqrt{\pi}$

(A)

$\sqrt{\pi} e^{\frac{\omega^2}{2}}$

(B)

$\frac{e^{-\frac{\omega^2}{4}}}{2\sqrt{\pi}}$

(C)

$\sqrt{\pi} e^{-\frac{\omega^2}{4}}$

(D)

$\sqrt{\pi} e^{-\frac{\omega^2}{2}}$

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q41

MCQ[1 Mark]

In the table shown below, match the signal type with its spectral characteristics.

(A)

(A) (i)->(a), (ii)->(b), (iii)->(c), (iv)->(d)

(B)

(B) (i)->(a), (ii)->(c), (iii)->(b), (iv)->(d)

(C)

(C) (i)->(d), (ii)->(b), (iii)->(c), (iv)->(a)

(D)

(D) (i)->(a), (ii)->(c), (iii)->(d), (iv)->(b)

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q42

MCQ[2 Marks]

Let $x(t) = 10 \cos(10.5Wt)$ be passed through an LTI system having impulse response $h(t) = \pi \left(\frac{\sin Wt}{\pi t}\right)^2 \cos 10Wt$. The output of the system is

(A)

$(\frac{15W}{4}) \cos(10.5Wt)$

(B)

$(\frac{15W}{2}) \cos(10.5Wt)$

(C)

$(\frac{15W}{8}) \cos(10.5Wt)$

(D)

$(15W) \cos(10.5Wt)$

Explanation

GATE→2023→Networks, Signals and Systems→Continuous-time Signals

Q43

NAT[2 Marks]

Let $x_1(t) = u(t+1.5) - u(t-1.5)$ and $x_2(t)$ is shown in the figure below. For $y(t) = x_1(t) * x_2(t)$, the $\int_{-\infty}^{\infty} y(t) dt$ is _______ (rounded off to the nearest integer).

Explanation

GATE→2022→Networks, Signals and Systems→Continuous-time Signals

Q44

MCQ[1 Mark]

The Fourier transform $X(j\omega)$ of the signal $x(t) = \frac{t}{(1+t^2)^2}$ is

(A)

$\frac{\pi}{2j} \omega e^{-|\omega|}$

(B)

$\frac{\pi}{2} \omega e^{-|\omega|}$

(C)

$\frac{\pi}{2j} e^{-|\omega|}$

(D)

$\frac{\pi}{2} e^{-|\omega|}$

Explanation

GATE→2022→Networks, Signals and Systems→Continuous-time Signals

Q45

NAT[1 Mark]

Let $x_1(t) = e^{-t} u(t)$ and $x_2(t) = u(t) - u(t-2)$ where $u(\cdot)$ denotes the unit step function. If $y(t)$ denotes the convolution of $x_1(t)$ and $x_2(t)$, then $\lim_{t \to \infty} y(t) =$

Explanation

Discrete-time Signals

7 Questions

GATE→2026→Networks, Signals and Systems→Discrete-time Signals

Q46

MCQ[1 Mark]

The response of a discrete time system $y[n]$ obeys the following relation: $y[n]=\frac{5}{6}y[n-1]-\frac{1}{6}y[n-2]+x[n].$ The input to the system is $x[n]=\delta[n]-\frac{1}{3}\delta[n-1]$ Which of the following options is TRUE for $y[n]$?

(A)

Stable and causal response

(B)

Stable and non-causal response

(C)

Unstable and causal response

(D)

Unstable and non-causal response

Explanation

GATE→2025→Networks, Signals and Systems→Discrete-time Signals

Q47

MSQ[1 Mark]

Let $x[n]$ be a discrete-time signal whose Z-transform is $X(z)$. Which of the following statements is/are TRUE?

(A)

The discrete-time Fourier transform (DTFT) of $x[n]$ always exists

(B)

The region of convergence (ROC) of $X(z)$ contains neither poles nor zeros

(C)

The discrete-time Fourier transform (DTFT) exists if the region of convergence (ROC) contains the unit circle

(D)

If $x[n] = \alpha\delta[n]$, where $\delta[n]$ is the unit impulse and a is a scalar, then the region of convergence (ROC) is the entire Z-plane

Explanation

GATE→2024→Networks, Signals and Systems→Discrete-time Signals

Q48

MSQ[1 Mark]

For a causal discrete-time LTI system with transfer function $H(z) = \frac{2z^2 + 3}{(z + 1/3)(z - 1/3)}$, which of the following statements is/are true?

(A)

The system is stable.

(B)

The system is a minimum phase system.

(C)

The initial value of the impulse response is 2.

(D)

The final value of the impulse response is 0.

Explanation

GATE→2024→Networks, Signals and Systems→Discrete-time Signals

Q49

NAT[2 Marks]

Another sequence $y[n]$ is formed as below $y[n] = \mathcal{F}\{\mathcal{F}\{\mathcal{F}\{\mathcal{F}\{x[n]\}\}\}\}$. For the sequence $x[n] = \{1, 2, 1, 3\}$, the value of $Y[0]$ is

Explanation

GATE→2023→Networks, Signals and Systems→Discrete-time Signals

Q50

MCQ[2 Marks]

Consider a discrete-time periodic signal with period $N = 5$. Let the discrete-time Fourier series (DTFS) representation be $x[n] = \sum_{k=0}^4 a_k e^{j \frac{k 2\pi n}{5}}$, where $a_0 = 1$, $a_1 = 3j$, $a_2 = 2j$, $a_3 = -2j$ and $a_4 = -3j$. The value of the sum $\sum_{n=0}^4 x[n] \sin \frac{4\pi n}{5}$ is

(A)

-10

(B)

10

(C)

-2

(D)

2

Explanation

GATE→2023→Networks, Signals and Systems→Discrete-time Signals

Q51

MCQ[2 Marks]

Let an input $x[n]$ having discrete time Fourier transform $X(e^{j\Omega}) = 1 - e^{-j\Omega} + 2e^{-3j\Omega}$ be passed through an LTI system. The frequency response of the LTI system is $H(e^{j\Omega}) = 1 - \frac{1}{2}e^{-j2\Omega}$. The output $y[n]$ of the system is

(A)

Option A

(B)

Option B

(C)

$\delta[n] - \delta[n-1] - \frac{1}{2}\delta[n-2] + \frac{5}{2}\delta[n-3] - \delta[n-5]$

(D)

Option D

Explanation

GATE→2022→Networks, Signals and Systems→Discrete-time Signals

Q52

NAT[2 Marks]

For a vector $\bar{x} = [x[0], x[1], \dots, x[7]]$ the 8-point discrete Fourier transform (DFT)... If $\bar{x} = [1, 0, 0, 0, 2, 0, 0, 0]$ and $\bar{y} = \text{DFT}(\text{DFT}(\bar{x}))$, then the value of $y[0]$ is _______ (rounded off to one decimal place).

Explanation