Question

Download Solution PDF

Consider a complex exponential sequence  with frequency ω0. Suppose ω0 = 1, then 

This question was previously asked in
ESE Electronics 2015 Paper 1: Official Paper
Attempt in App
View all UPSC IES Papers >
  1. Such a sequence is periodic
  2. Such a sequence is not periodic at all
  3. Periodic for some value of period ‘N’
  4. Some definite range N0 < n < N exists for a periodic sequence

Answer (Detailed Solution Below)

Option 2 : Such a sequence is not periodic at all
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

Any discrete signal is said to be periodic if:

 is a rational number 

Calculation:

Given signal is , ω0 = 1 rad / sec

 

Since this is not a rational number, so it is not periodic at all.

Note:

Continuous sinusoidal and complex sinusoids are periodic for every value of ‘ω0’, but discrete-time signals are periodic only if  is a rational number .

Download Solution PDF
Latest UPSC IES Updates

Last updated on May 28, 2025

->  UPSC ESE admit card 2025 for the prelims exam has been released. 

-> The UPSC IES Prelims 2025 will be held on 8th June 2025.

-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.

-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.

Exams Tests Super Practice

More Properties of DTFT Questions

Q1.Consider a complex exponential sequence \({e^{j{\omega _0}n}}\) with frequency ω0. Suppose ω0 = 1, then 
Q2.A Fourier transform pair is given by: \({\left( {\frac{2}{3}} \right)^n}u\left[ {n + 3} \right]\mathop \Leftrightarrow \limits^{FT} \frac{{A{e^{ j6\pi f}}}}{{1 - \left( {\frac{2}{3}} \right){e^{ - j2\pi f}}}}\) where u[n] denotes the unit step sequence. The values of A is _______.

More Discrete Time Fourier Transform (DTFT) Questions

Q1.Let an input π‘₯[𝑛] having discrete time Fourier transform 𝑋(𝑒𝑗𝛺) = 1 − 𝑒−𝑗𝛺 + 2𝑒−3𝑗𝛺 be passed through an LTI system. The frequency response of the LTI system is \(\rm H(e^{j\Omega)}=1-\frac{1}{2}e^{-j2\Omega}\). The output 𝑦[𝑛] of the system is
Q2.discrete time signal x[n] = {1, 2, 3, 0, −3, −2, −1} is having a discrete-time Fourier transform X(ejΩ). The value of \(\int_{βˆ’\pi}^{\pi}\)|X(ejΩ)|2 dΩ is:
Q3.Let x[n] be a discrete time sequence given by x[n] = {1, 2, 3, 0, −3, −2, −1}, where x[0] is 1. The value of X(ejπ) is:
Q4.Consider the signals x[n] = 2n-1 u[-n + 2] and y[n] = 2-n+2 u[n + 1], where u[n] is the unit step sequence. Let X(ejω) and Y(ejω) be the discrete-time Fourier transform of x[n] and y[n], respectively. The value of the integral \(\dfrac{1}{2\pi}\displaystyle\int_0^{2\pi} X(e^{j\omega}) Y(e^{-j\omega})d\omega\) (rounded off to one decimal place) is _____  
Q5.H(ejω) is the frequency response of a discrete time LTI system and H1(ejω) is the frequency response of its inverse function. Then
Q6.Consider a complex exponential sequence \({e^{j{\omega _0}n}}\) with frequency ω0. Suppose ω0 = 1, then 
Q7.In inverse DTFT, the limits of the integral is defined between -π to π because of the property
Q8.A Fourier transform pair is given by: \({\left( {\frac{2}{3}} \right)^n}u\left[ {n + 3} \right]\mathop \Leftrightarrow \limits^{FT} \frac{{A{e^{ j6\pi f}}}}{{1 - \left( {\frac{2}{3}} \right){e^{ - j2\pi f}}}}\) where u[n] denotes the unit step sequence. The values of A is _______.
Q9.The frequency response and the main lobe width for rectangular window are
Suggested Test Series
View All >
UPSC ESE (IES) Civil Mock Test Series
116 Total Tests with 1 Free Tests
Start Free Test
UPSC ESE (IES) Prelims Paper 1 Mock Test Series
54 Total Tests with   1 Free Tests
Start Free Test

GATE EE Important Links

Paper AnalysisBooksPreparation TipsSyllabusCut OffPrevious Year Paper

More Signals and Systems Questions

Q1.The Fourier Transform of an real and even function results in:
Q2.Sinc pulse shaping is derived from the Fourier Transform of a _______ function.
Q3.What type of distortion occurs if a signal that contains frequency components up to 15 kHz is sampled using 20 kHz?
Q4.Which one of the following systems described by the following input-output relations is time invariant ? 
Q5.The equation for voltage waveform v(t) shown below is (where u(t) is unit step input) :
Q6.A continuous-time signal x(t) is defined as : \(x(\mathrm{t})=\left\{\begin{array}{cc} 5 & -2 \leq \mathrm{t} \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\) The energy of signal x(t) is : 
Q7.If Z(un) = f(z), then Z(a − nun) (where Z denotes z-transform) equals to :
Q8.The Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\).  Then Laplace transform of e−6tx(t) is :
Q9.Which one of the following is the correct relation ? (a > 0) 
Q10.What is the formula of finding the final value of any time varying function f(t)?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright Β© 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti lucky teen patti sweet teen patti joy 51 bonus