Fourier series AM
Laplace And Fourier Transform objective questions (mcq) and answers - MechanicalTutorial 6. For the given periodic function ≤ ≤ ≤ ≤ = 4 for 2 6 2 for 0 2 ( ) t t t f t with a period T = 6 as shown in Problem 5. The complex form of the Fourier series can be expressed as ∑ ∞ =−∞ = k ikw t k f t C e 0 ~ ( ) . The complex coefficient 1 ~ C can be expressed as (A) 0.4560 + 0.3734i (B) 0.4560 − 0.3734i (C) − 0.4560 + 0.3734i (D) 0.3734 − 0.4560i Solution The correct answer is (C). 1. In Fourier transform f ( p ) = ∫ ∞ − ∞ e ( i p x ) F ( x ) d x , e ( i p x ) is said to be Kernel function. a) True b) False View Answer Answer: a Explanation: In any transform, apart from function given, the other function is said to be Kernel function. So, here in Fourier transform, e (ipx) is said to be the Kernel function. 2. Fourier Transform of e − | x | i s 2 1 + p 2 . Then what is the fourier transform of e − 2 | x | ? a) 4 ( 4 + p 2 ) b) 2 ( 4 + p 2 ) c) 2 ( 2 + p 2 ) d) 4 ( 2 + p 2 )