Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
Hindi
English

Question

Download Solution PDF

फलन f(t) आवर्तकाल 2π का आवर्ती फलन है । ( -π, π) परिसर में, यह e-t के बराबर है। यदि f(t) = \(\sum\nolimits_{ - \infty }^\infty {{c_n}{e^{{\mathop{\rm int}} }}} \) इसका फूरिये श्रेणी विस्तार हो, तो योग \({\sum\nolimits_{ - \infty }^\infty {\left| {{c_n}} \right|} ^2}\) है

  1. 1
  2. \(\frac{1}{{2{\rm{\pi }}}}\)
  3. \(\frac{1}{{2{\rm{\pi }}}}\) cosh (2π)
  4. \(\frac{1}{{2{\rm{\pi }}}}\) sinh (2π)

Answer (Detailed Solution Below)

Option 4 : \(\frac{1}{{2{\rm{\pi }}}}\) sinh (2π)

Detailed Solution

Download Solution PDF
Download Solution PDF
‹‹ Previous Ques
Next Ques ››

More Fourier Transform Questions

Q1.फलन f(t) आवर्तकाल 2π का आवर्ती फलन है । ( -π, π) परिसर में, यह e-t के बराबर है। यदि f(t) = \(\sum\nolimits_{ - \infty }^\infty {{c_n}{e^{{\mathop{\rm int}} }}} \) इसका फूरिये श्रेणी विस्तार हो, तो योग \({\sum\nolimits_{ - \infty }^\infty {\left| {{c_n}} \right|} ^2}\) है
Q2.The region of convergence (ROC) of the z-transform of discrete time Dicae delta function δ(n) is 
Q3.δ(ω) का व्युत्क्रम फूरिये रूपांतरण क्या है?
Q4.If f(x) represented by Fourier integral  \(f(x)=\int_0^{\infty} [A(ω) cos~ω x + B(ω) sin~ω x]dω \) then A(ω) is defined as
Q5.फलन f(t) का लाप्लास रूपांतरण L(t) \( = \frac{1}{{\left( {{s^2} + {\omega ^2}} \right)}}\) है। तो f(t) का मान क्या है?
Q6.The Fourier transform of \({e^{ - \frac{{{x^2}}}{2}}}\) is
Q7.The Fourier cosine series for an even function f(x) is given by \(f(x) = {a_0} + \sum\limits_{n = 1}^\infty {{a_n}\cos (nx)} \) The value of the coefficient a2 for the function f(x) = cos2(x) in [0,π] is
Q8.The Fourier transform of a continuous-time signal x(t) is given by \(X\left( \omega \right) = \frac{1}{{{{\left( {10 + j\omega } \right)}^2}}}, - \infty < \omega < \infty ,\) where \(j = \sqrt { - 1} \) and ω denotes frequency. Then the value of |ln x(t)| at t = 1 is _____ (up to 1 decimal place). (In denotes the logarithm to base e)
Q9.The Fourier sin transform of xm-1 is defined by

More Transform Theory Questions

Q1.If f(t) = eat, its Laplace Transform (for s > a) is given by
Q2.\(\rm\frac{6s−4}{s^2−4s+20}\) का विपरीत लाप्लास रूपांतरण ज्ञात कीजिए, जहाँ प्राचल s वास्तविक होता है।
Q3.फलन f(t) आवर्तकाल 2π का आवर्ती फलन है । ( -π, π) परिसर में, यह e-t के बराबर है। यदि f(t) = \(\sum\nolimits_{ - \infty }^\infty {{c_n}{e^{{\mathop{\rm int}} }}} \) इसका फूरिये श्रेणी विस्तार हो, तो योग \({\sum\nolimits_{ - \infty }^\infty {\left| {{c_n}} \right|} ^2}\) है
Q4.दो असतत फूरियर रूपांतरणाें (DFT) का गुणन, काल क्षेत्र (टाइम-डोमेन) में दो क्रमों के ______ के बराबर होता है।
Q5.A particle moves along the x-axis according to the law \(\frac{{{d^2}x}}{{d{t^2}}} + 6\frac{{dx}}{{dt}} + 25x = 0.\) If the particle is started at x = 0 with an initial velocity of 12 ft/s to the left, determine x in terms of t.
Q6.The system function of an LTI system is given by \(H(z) = \frac{1 - \frac{1}{3}Z^{-1}}{1- \frac{1}{4} Z^{-1}}\) The above system can have stable inverse if the region of convergence of H(z) is defined as
Q7.The question consists of two statements, one labeled as ‘Statement (I)’ and the other labeled as ‘Statement (II)’. You are to examine these two statements carefully and select the answers to these items using the codes given below: Statement (I): ROC of the z-transform of the signal x(n)= an u(n) + bn u(-n-1) is  |a| < |z| < |b| Statement (II): ROC of a causal infinite length sequence is |z| < r1
Q8.Find the Inverse Laplace transform of \({\rm{F}}\left( {\rm{s}} \right) = \frac{1}{{{\rm{s}} - 1}}\)
Q9.The Inverse Laplace transform of \(\left(\frac{s}{s^2+\alpha^2}\right)\) is:
Q10.Let f(t) = sin2 t, find the Laplace transform of f(t)

More Engineering Mathematics Questions

Q1.यदि L = {1, 2, 3, 4, 6, 9, 36} जालक है, तो नीचे दिए गए हैस आरेख में 9 के पूरकों की संख्या ज्ञात कीजिए।
Q2.अनिर्देशित आलेख के लिए निम्नलिखित में से कौन सा/से कथन सत्य है?
Q3.\(\iint \frac{x y}{\sqrt{1-y^{2}}} d x d y\) Over the positive quadrant of the circle x2 + y2 = 1 is __________.
Q4.The real root of the equation x3 − x − 5 = 0 lying between 1 and 2 after first iteration by Newton-Raphson method is ________, if initial approximation is taken as x0 = 2 ∈ [1, 2] : 
Q5.Let X be uniform random variable on [0, 4] and Y be uniform random variable on [0, 1]. If X and Y are independent, then P(max {X, Y} > 3) is equal to : 
Q6.If R and D are the radius and diameter of the graph K4,7, then the ordered pair (R, D) is equal to : 
Q7.The largest number of faces in a simple connected maximal planar graph with 100 vertices is :
Q8.If for the matrix A, A3 = I then A−1 = __________. 
Q9.Energy of power signal is : 
Q10.With usual notations, the properties of maxima and minima under various conditions are __________. I II (P) Maxima (i) r t− s2 = 0 (Q) Minima (ii) rt − s2 < 0 (R) Saddle Point (iii) rt − s2 > 0, r > 0 (S)  Case of failure (iv) rt − s2 > 0, r < 0
Exams
Test Series
SuperCoaching
Previous Year Papers
Latest Updates
MCQ Questions
Testbook Products & Resources for Students
Testbook USA
Books
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 master list teen patti real teen patti 50 bonus teen patti 500 bonus teen patti master downloadable content