English
Hindi

Question

Download Solution PDF

What is the inverse discrete-time Fourier transform of the frequency domain representation shown in the figure?

This question was previously asked in
UPSC IES Electrical 2022 Prelims Official Paper
Download PDF Attempt in App
View all UPSC IES Papers >

Answer (Detailed Solution Below)

Option 4 :
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:

The inverse discrete-time Fourier transform is given by:

where, N = Time period of one complete cycle

Calculation:

In the given figure, -π to +π makes one complete cycle. So, the time period is 2π.

Multiplying the numerator and denominator by 2j, we get:

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 Inverse Discrete Fourier Transform Questions

Q1.The inverse Fourier Transform of \(\frac{e^{-j\omega}}{2+j \omega}\) is -
Q2.For discrete- -time sinc function, what is the inverse discrete-time Fourier transform of the function as shown in the figure?
Q3.What is the inverse discrete-time Fourier transform of the frequency domain representation shown in the figure?
Q4.Inverse discrete Fourier transform of Y(k) = {1, 0, 1, 0} is
Q5.Consider the finite sequence X = (1, 1, 1). The Inverse Discrete Fourier Transform (IDFT) of X is given as (x(0), x(2)). The value of x(2) is
Q6.Consider the system \(R\left[ m \right] =\mathop{\mathop \sum \limits^{N - 1} }\limits_{n = 0} {\mkern 1mu} y\left[ n \right]x\left[ {n - m} \right]\) ,where y[n] and x[n] are real periodic signals with period N. The above output can be obtained using:
Q7.Let the finite length signal x(n) = {x(0), x(1), x(2), (3)} = {j, -2, -j, 1}. The DFT of x(n) is

More Discrete Fourier Transform (DFT) and Discrete Fourier Series (DFS) Questions

Q1.Let xa(t) be an analog signal with bandwidth B = 6 kHz. We wish to use an N = 2m point DFT to compute the spectrum of the signal with resolution less than or equal to 200 Hz. What is the minimum length of the analog signal recorded?
Q2.The Fourier transform 𝑋(𝜔) of the signal 𝑥(𝑡) is given by 𝑋(𝜔) = 1, for |𝜔| < 𝑊0 = 0, for |𝜔| > 𝑊0
Q3.Consider a discrete-time periodic signal with period 𝑁 = 5. Let the discrete-time Fourier series (DTFS) representation be \(\rm x[n]=\Sigma_{k=0}^4a_ke^{\frac{jk2\pi n}{s}}\), where 𝑎0 = 1, 𝑎1 = 3𝑗, 𝑎2 = 2𝑗, 𝑎3 = −2𝑗 and 𝑎4 = −3𝑗. The value of the sum \(\rm \Sigma_{n=0}^4x[n]\sin\frac{4\pi n}{5}\) is
Q4.Two point DFT of a sequence x[n] is X[k] = [6, 2], compute its inverse.
Q5.The inverse Fourier Transform of \(\frac{e^{-j\omega}}{2+j \omega}\) is -
Q6.For discrete- -time sinc function, what is the inverse discrete-time Fourier transform of the function as shown in the figure?
Q7.What is the inverse discrete-time Fourier transform of the frequency domain representation shown in the figure?
Q8.Consider the following statements for quarter-wave symmetry : A periodic function possesses a quarter-wave symmetry, if 1. it has either odd or even symmetry 2. it has half-wave symmetry Which of the above statements is/are correct?
Q9.For a vector x̅ = [x[0], x[1],......x[7]] the 8-point discrete Fourier transform (DFT) is denoted by X̅ = DFT (x̅) = X[0], X[1], ...., X[7]], where \(\rm X[k]=\sum_{n=0}^{7}x[n]\ exp\left(-j\frac{2\pi}{8}nk\right) \space \) Here j = √-1, if X̅ = [1, 0, 0, 0, 2, 0, 0, 0] and y̅ = (DFT (x̅)), then the value of y[0] is ________ (rounded off to one decimal place).
Q10.𝑋(𝑘)is the Discrete Fourier Transform of a 6-point real sequence 𝑥(𝑛). If 𝑋(0) = 9 + 𝑗0, 𝑋(2) = 2 + 𝑗2, 𝑋(3) = 3 – 𝑗0, 𝑋(5) = 1 – 𝑗1, 𝑥(0) is
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

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 © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti royal - 3 patti teen patti app teen patti win lucky teen patti teen patti master new version