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GATE EC Discrete-time Signals questions

Practise Discrete-time Signals questions for GATE EC. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify whether the signal and system are continuous-time or discrete-time. Check linearity, time invariance and stability before selecting a transform or response method.

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Official PYQ2015Networks, Signals and SystemsDiscrete-time SignalsMCQ · 2 marks
Suppose x[n]x[n] is an absolutely summable discrete-time signal. Its zz-transform is a rational function with two poles and two zeroes. The poles are at z=±2j.z = \pm 2j. Which one of the following statements is TRUE for the signal x[n]x[n]?
Official PYQ2015Networks, Signals and SystemsDiscrete-time SignalsMCQ · 2 marks
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],x[n ], the response y[n]y[n ] is
Official PYQ2015Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
Let x~[n]=1+cos⁡(πn8)\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right) be a periodic signal with period 16.16. Its DFS coefficients are defined by ak=116∑n=015x~[n]exp(−jπ8kn)a_{k} = \displaystyle{}\dfrac{1}{16}\sum_{n=0}^{15}\widetilde{x}[n] \text{exp}\big(-j\dfrac{\pi}{8} kn\big) for all k.k . The value of the coefficient ܽa31a_{31} is _______.
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
Consider a discrete time periodic signal x[n]=sin⁡(πns).x[n] = \sin(\frac{\pi n}{s}). Let aka_{k} be the complex Fourier series coefficients of x[n].x[n]. The coefficients {ak}\{a_{k}\} are non-zero when k=Bm ±1,k = Bm\: \pm 1, where mm is any integer. The value of BB is ______.
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
Let x[n]=x[−n]x[n] = x[-n]. Let X(z)X(z) be the zz-transform of x[n]x[n]. If 0.5+j0.250.5 + j 0.25 is a zero of X(z)X(z), which one of the following must also be a zero of x(z)x(z)
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
For an all-pass system H(z)=(z−1−b)(1−az−1)H(z)= \frac{(z^{-1}-b)}{(1-az^{-1})}, where ∣H(e−jω)∣=1,\mid H(e^{-j\omega }) \mid= 1, for all ω\omega. If Re(a)≠0, Im(a)≠0,\text{Re}(a)\neq 0, \: \text{Im}(a)\neq 0,then bb equals
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
The zz-transform of the sequence x[n]x[n] is given by X(z)=1(1−2z−1)2,X(z)=\frac{1}{(1-2z^{-1})^{2}}, with the region of convergence ∣z∣>2\mid z \mid >2. Then, x[2]x[2] is _________.
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsNAT · 1 mark
A Fourier transform pair is given by (23) u[n+3]⇔FTAe−j6πf1−(23)e−j2πf\left ( \frac{2}{3} \right ) \: u[n+3] \overset{FT}{\Leftrightarrow} \frac{Ae^{-j6 \pi f}}{1- (\frac{2}{3} ) e^{-j2 \pi f}} where u[n]u[n] denotes the unit step sequence. The values of AA is ____________
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsMCQ · 2 marks
The NN-point DFT XX of a sequence x[n]x[n], 0≤n≤N−10 \leq n \leq N-1 is given by X[k]=1NΣn=0N−1x[n]e−j2πNnk,   0≤k≤N−1.X[k] = \frac{1}{\sqrt{N}} \Sigma_{n=0}^{N-1} x[n] e^{-j \frac{2\pi}{N}nk}, \: \: \: 0 \leq k \leq N-1. Denote this relation as X=DFT(x)X=DFT(x). For N=4N=4, which one of the following sequences satisfies DFT(DFT(x))=xDFT(DFT(x))=x?
Official PYQ2006Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
If the region of convergence of x1[n]+x2[n]x_1[n]+x_2[n] is 13<∣z∣<23\frac{1}{3}<|z|<\frac{2}{3}, then the region of convergence of x1[n]−x2[n]x_1[n]-x_2[n] includes
Official PYQ2005Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
The region of convergence of ZZ-transform of the sequence (56)nu(n)−(65)nu(−n−1)\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1) must be
Official PYQ2005Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
Let x(n)=(12)nu(n),y(n)=x2(n)x(n)=\left(\frac{1}{2}\right)^{n} u(n), y(n)=x^{2}(n) and Y(ejie)\mathrm{Y}\left(e^{j i e}\right) be the Fourier transform of y(n)y(n). Then Y(ejie)Y\left(e^{j i e}\right) is
Official PYQ2004Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
The zz-transform of a system is H(z)=zz−0.2.H(z)=\frac{z}{z-0.2}. If the ROC is ∣z∣<0.2|z|<0.2, then the impulse response of the system is
Official PYQ2003Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
A sequence x(n)x(n) with the z-transform X(z)=z4+z2−2z+2−3z−4X(z)=z^4+z^2-2 z+2-3 z-4 is applied as an input to a linear, time-invariant system with the impulse response h(n)=2δ(n−3)h(n)=2 \delta(n-3) where δ(n)={1,n=00, otherwise \delta(n)= \begin{cases}1, & n=0 \\ 0, & \text{ otherwise }\end{cases} The output at n=4n=4 is
Official PYQ2002Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
If the impulse response of a discrete-time system is h[n]=−5nu[−n−1]h[n]=-5^{n} u[-n-1], then the system function H(z)\mathrm{H}(z) is equal to
Official PYQ2001Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
The region of convergence of the zz-transform of a unit step function is
Official PYQ1999Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
The zz-transform F(z)\mathrm{F}(z) of the function f(nT)=a′′Tf(n \mathrm{T})=a^{\prime \prime T} is
Official PYQ1999Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
The zz-transform of a signal is given by C(z)=1z−1(1−z−4)4(1−z−1)2C(z)=\frac{1 z^{-1}\left(1-z^{-4}\right)}{4\left(1-z^{-1}\right)^{2}} Its final value is
Official PYQ1998Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
The transfer function of a zero-order-hold system is
Official PYQ1998Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
The ZZ-transform of the time function ∑k=0∞δ(n−k)\sum_{k=0}^{\infty} \delta(n-k) is