Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

The Fourier Transform of an real and even function results in:

This question was previously asked in
RRB JE ECE 22 Apr 2025 Shift 2 CBT 2 Official Paper
Download PDF Attempt Online
View all RRB JE Papers >
  1. a purely real and odd function
  2. a purely imaginary and even function
  3. an imaginary and odd function
  4. a purely real and even function

Answer (Detailed Solution Below)

Option 4 : a purely real and even function
Free Tests
View all Free tests >
Free
General Science for All Railway Exams Mock Test
2.1 Lakh Users
20 Questions 20 Marks 15 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept: Fourier Transform Symmetry Property

If a time-domain function is:

  • Real: It has no imaginary part

  • Even: f(t) = f(-t)

Then it's  Fourier Transform will be:

  • Purely real

  • Even: F(ω)=F(−ω)

🔍 Example: Cosine Wave

Let’s take: f(t) = cos(ω0​t)

  • It is real.

  • It is even, because

Fourier Transform of is: F(ω)=π [δ(ω−ω0​)+δ(ω+ω0​)]

This result is:

  • Purely real (involves delta functions, no imaginary component)

  • Even since it's symmetric around

Download Solution PDF
Latest RRB JE Updates

Last updated on Jun 7, 2025

-> RRB JE CBT 2 answer key 2025 for June 4 exam has been released at the official website.

-> Check Your Marks via RRB JE CBT 2 Rank Calculator 2025

-> RRB JE CBT 2 admit card 2025 has been released. 

-> RRB JE CBT 2 city intimation slip 2025 for June 4 exam has been released at the official website.

-> RRB JE CBT 2 Cancelled Shift Exam 2025 will be conducted on June 4, 2025 in offline mode. 

-> RRB JE CBT 2 Exam Analysis 2025 is Out, Candidates analysis their exam according to Shift 1 and 2 Questions and Answers.

-> The RRB JE Notification 2024 was released for 7951 vacancies for various posts of Junior Engineer, Depot Material Superintendent, Chemical & Metallurgical Assistant, Chemical Supervisor (Research) and Metallurgical Supervisor (Research). 

-> The selection process includes CBT 1, CBT 2, and Document Verification & Medical Test.

-> The candidates who will be selected will get an approximate salary range between Rs. 13,500 to Rs. 38,425.

-> Attempt RRB JE Free Current Affairs Mock Test here

-> Enhance your preparation with the RRB JE Previous Year Papers. 

‹‹ Previous Ques
Next Ques ››

More Fourier Transform 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.The Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\).  Then Laplace transform of e−6tx(t) is :
Q4.Which one of the following is the correct relation ? (a > 0) 
Q5.Which type of property is shown by the following function. L{K f(t)} = K F(s)
Q6.In the table shown below, match the signal type with its spectral characteristics. Signal type Spectral characteristics I. Continuous, aperiodic a. Continuous, aperiodic II. Continuous, periodic b. Continuous, periodic III. Discrete, aperiodic c. Discrete, aperiodic IV. Discrete, periodic d. Discrete, periodic
Q7.The Fourier transform 𝑋(𝜔) of \(\rm x(t)=e^{-t^2}\) is Note: \(\rm \int_{-\infty}^{\infty}e^{-y^2}dy=\sqrt{\pi}\)
Q8.Let 𝑚(𝑡) be a strictly band-limited signal with bandwidth 𝐵 and energy 𝐸. Assuming 𝜔0 = 10𝐵, the energy in the signal 𝑚(𝑡) cos 𝜔0𝑡 is 
Q9.A signal 𝑥(𝑡) is band-limited between 100 Hz and 200 Hz. A signal 𝑦(𝑡) is related to 𝑥(𝑡) as follows: 𝑦(𝑡) = 𝑥(2𝑡 − 5) The statement that is always true is______

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)?
Exams
Cut Off
Eligibility
Coaching
Previous Year Papers
Syllabus
Test Series
Important Exams
Super Coaching
Testbook USA SAT Exam
Testbook USA ACT Exam
US College Admissions Guide
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
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
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti real cash teen patti master 51 bonus real cash teen patti teen patti glory teen patti casino download