5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series o...
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0< x < X f(x) = -< x< 2 2 Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0
Consider the function 0<x<π/2. z, f(x) = (a) Sketch the odd and even periodic extension of f(x) for-3π 〈 x 〈 3π. (b) Find the Fourier cosine series of the even periodic extension of f(x) Consider the function 0
Fourier Series for Odd Functions Recall that if f is an odd function, f(-x)f(x). An odd Fourier series has only the sine terms, and can be approximate an odd function, so Fo(x) b sinx)+b2 sin(2x)+ b, sin(3x)+. Why is there no b, term in the series F, (x)? 1. 2. Using steps similar to those outlined for even functions, develop a rule for finding the coefficients to approximate any odd function on the interval [-π, π]. 3. If f (x)sin...
Consider a periodic function f(x) defines as follows: 4. f(x)-0 f(x)-0 The function is periodic every 2π Find the first four non-zero terms in the Fourier series of this function for the interval [-π, π] or equivalently for the interval [0, 2자 Note that depending if the function is odd or even, the first four terms do not necessarily correspond to h = 1, 2, 3, and 4. Consider a periodic function f(x) defines as follows: 4. f(x)-0 f(x)-0 The...
2. [10]For the function, f(x), given on the interval 0 <x<L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods (b)[6] Find the Fourier cosine and sine series of f(x) f(x) = 3 - x, 0<x<3
2.[10]For the function, f(x), given on the interval 0 < x <L (a)[4] Sketch the graphs of the even extension g(x) and odd extension h(x) of the function of period 2L over three periods (b) [6] Find the Fourier cosine and sine series of f(x) f(x) = 3 - x 0<x<3
Q8*. (15 marks) The following f(t) is a periodic function of period 2π defined over the domain when 0 < t < t π f (t) When π Express f(t) as a Fourier series expansion Q8*. (15 marks) The following f(t) is a periodic function of period 2π defined over the domain when 0
Consider a periodic function f(x) defines as follows: -π < x < -π/2, f(x) = 0 -π/2 < x < π/2, f(x) = 1 π/2 < x < π, f(x) = 0 The function is periodic every 2π. Find the first four non-zero terms in the Fourier series of this function for the interval [-π, π] or equivalently for the interval [0, 2π]. Note that depending if the function is odd or even, the first four terms do not necessarily...
(2) Consider the function f(x)- 1 (a) Find the Fourier sine series of f (b) Find the Fourier cosine series of f. (c) Find the odd extension fodd of f. (d) Find the even extension feven of f. (e) Find the Fourier series of fod and compare it with your result -x on 0<a < 1. in (a) (f) Find the Fourier series of feven and compare it with your result in (b)
Let be a function defined by: We define by extension the odd, periodic function of period p = 2 which coincides with the function f (x) on the interval [0, 1]. Draw over the interval [−1, 3] the graph of the function towards which the Fourier series of the odd continuation of the function f (x) converges. f(x) = 1 + x2 pour 0 < x < 1.