Fourier Series Questions PDF

UNIT II Foutier Series S.NO Questions opt 1. 1 Which of the following functions has the period 2π? cos x 2 1/π ∫ f(x) sinnx dx between...

UNIT II Foutier Series S.NO Questions opt 1. 1 Which of the following functions has the period 2π? cos x 2 1/π ∫ f(x) sinnx dx between the limits c to c+2π gives the Fourier a_0 coefficient 3 If f(x) = -x for -π< x< 0 then its Fourier coefficient a0 is - (π^2)/2 4 If a function satisfies the condition f(-x) = f(x) then which is true? a_0 = 0 5 If a function satisfies the condition f(-x) = -f(x) then which is true? a0 = 0 6 Which of the following is an odd function? sin x 7 Which of the following is an even function? x^3 8 The function f(x) is said to be an odd function of x if f(-x) = f( x) 9 The function f(x) is said to be an even function of x if f(-x) = f( x) 10 ∫f(x) dx = 2∫f(x) dx between the limits -a to a if f(x) is even ------ 11 ∫f(x) dx = 0 between the limits -a to a if f(x) is ------ even 12 If a periodic function f(x) is odd, it’s Fourier expansion contains no coefficient an terms. 13 If a periodic function f(x) is even, it’s Fourier expansion contains no cosine terms. 14 In dirichlet condition, the function f(x) has only a ----- uncountab le number of maxima and minima. 15 In Fourier series, the function f(x) has only a finite number of maxima Dirichlet and minima. This condition is known as ------- 16 In dirichlet condition, the function f(x) has only a ----- uncountab le number of discontinuities. 17 a 0 /2 + ∑ (an cosnx+ bn sin The Fourier series of f(x) is given by ---- nx ) 18 In Fourier series, the expansion f(x) = a 0 /2 + ∑ (an cos nx + bn sin nx kuhn- Tucker ) is possible only if in the interval c1≤ x≤ c2 the function f(x) satisfies - --condition. 19 If the periodic function f(x) is even, then the Fourier expansion is of the a 0 /2 + form --- ∑an sin( nπx/ l ) 20 If the periodic function f(x) is even, then it’s Fourier co- efficient an is 2/ l ∫f(x) sin( of the form --- nπx/ l ) dx 21 If the periodic function f(x) is even, then it’s Fourier co- efficient a0 is 2/ l ∫f(x) dx of the form --- 22 If the periodic function f(x) is odd, then it’s Fourier co- efficient bn is 2/ l ∫f(x) cos of the form --- (nπx/ l ) dx 23 If the periodic function f(x) is even, then it’s Fourier co- efficient a0 is zero. 24 If the periodic function f(x) is odd, then it’s Fourier co- efficient a_0 & a_n is zero. 25 If the periodic function f(x) is even, then the Fourier expansion is of the ∑b_n sin nπx/ l form --- 26 If the periodic function f(x) is odd, then the Fourier expansion is of the ∑bn sin nπx/ l form --- 27 1/π∫f(x) cos nx dx gives the Fouier coefficient ----------- a_0 28 1/π∫f(x) dx gives the Fourier coefficient a_0 29 1/π∫f(x)sin nx dx gives the Fouier coefficient ----------- a_0 30 The period of cos nx where n is the positive integer is 2π/n 31 The Fourier co efficient a0 for the function defined by f(x) = x for 0< π x< π is 32 If the function f (x) = -π in the interval –π< x< 0, the coefficient a0 is π^2/3 33 If the function f(x) = x sin x, in –π< x< π then Fourier coefficient bn = 0 34 For the cosine series, which of the Fourier coefficient will vanish? a_n 35 For the sine series, which of the Fourier coefficient variables will be b_n vanish? 36 For a function f(x) = x^3, in –π< x< π the Fourier coefficient bn = 0 37 F(x)=x cos x is an function. an odd function 38 If f(x) = x, in –π< x< π then Fourier co efficient b_n = 0 39 F(x)=e^x is in –π< x< π. an odd function 40 Which of the coefficients in the Fourier series of the function f(x) = x2 a0 in -π < x< π will vanish 41 If f(-x) = -f(x), then the function f(x) is said to be ----- odd 42 If f(-x) = f(x), then the function f(x) is said to be ----- odd 43 The function x sin x is a ------- function in –π< x< π. even 44 The function x cos x is a ------- function in –π< x< π. even 45 The formula for finding the fourier coefficient a_0 in Harmonic (2/N)Σ y analysis is ---- cos nx 46 The formula for finding the fourier coefficient a_n in Harmonic (2/N)Σ y analysis is ---- cos nx 47 The formula for finding the fourier coefficient bn in Harmonic analysis is ---- ( 2/N)Σ y 48 The term a1cos x+ b1 sin x is called the harmonic. second 49 The term ------------- is called the first harmonic in Furier Series a1cosn x+ b1 expansion. sin x 50 If f(x)= x in 0