QUESTION 2 Given two periodic functions, f(t) and g(t) is defined by and f (t) =...
HW 11.5 Consider the periodic "square wave" signal defined by x(t)- u(t - 4k) - u(t - 2-4k) (a) Sketch x(t) (b) Sketch g(t) = x(t)-0.5 (c) Sketch |x(jw)|. Hint: First determine the Fourier series expansion of x() (d) Sketch IG(Go) HW 11.5 Consider the periodic "square wave" signal defined by x(t)- u(t - 4k) - u(t - 2-4k) (a) Sketch x(t) (b) Sketch g(t) = x(t)-0.5 (c) Sketch |x(jw)|. Hint: First determine the Fourier series expansion of x() (d)...
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao Consider the periodic function defined by 1
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch the function over the interval -3m<<3x. [3] (b) Find the cireular frequency a and the symmetry of the function (odd, even or neither). 21 (e) Determine the trigonometric Fourier coefficients for the function f) [10] (d) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number. [5] (e) Determine the Fourier series for the function g(t)-2r-1 over the...
(a) Determine algebraically whether the functions below are even, odd or neither. i. r+6 f(x)=- r-r? (2 marks) ii. f(x) = 2x sinx (2 marks) (b) A periodic function is defined by: f(x) = 4-x?, -25x52, f(x+4)= f(x) i. Sketch the graph of the function over -10<x<10. (4 marks) ii. Based on result in (i), identify whether the function is even or odd. Give your reason. (2 marks) ii. Calculate the Fourier series expansion of f(x). (12 marks) (c) An...
Find a Fourier series expansion of the periodic function 0 -T -asts 2 - f(t) = 6 cost T <<- 2 2 0 I SISE 2 f(t) = f (t +21) Select one: a f(t)= 12 12 5 (-1)** cos nt 1 2n-1 b. f(t) = 12.12 F(-1)** cos 2nt T 4n-1 C 6 12 =+ 125 (-1) C05 211 472-1 6 12 (-1) * cosm d
Find a Fourier series expansion of the periodic function 0 - Sts- 2 f(t) = 4x2 cost VI VI st 2 0 .sta 2 f(t)= f (t+2A) Select one: 1 (-1)** cos 2n a. f (0) = 87 +87 4n2 -1 12 12 * (-1) "*l cosnt b. f(t) 2n-1 =+ 7 77 c. f(t) 6 12 - (-1)' cosnt 2n-1 =1 00 d. f(t) = 4A+87 .(-1) "* cos ant 4n2-1
Find the Fourier series for f(t) which is defined as f(t) = t for LtSLWI f(t) = f(t+ 2L) as periodic function. (20 m I T Find the Fourier series for f(t) which is defined as f(t) = t for LtSLWI f(t) = f(t+ 2L) as periodic function. (20 m I T
MECH2407: Multivariable Calculus and Partial Differential Equations 4. (a) Given two periodic functions as below in part (0) and part (iã) i) f2 1 -1st< (ii) f)-1/2 State the period of the two periodic functions respectively. Hence, sketch the two given perodic functions for 3 periods. Find the Fourier series for the two given perodic functions over the given interval and expand the series to give the partial sum up to the first three non-zero terms respectively. (16 marks) Use...
Consider f(x), a 27 periodic function defined by: f(x) = 1o, 1 if if -T <I< 0 0 < < Calculate the DC component of the Fourier series of f(x):
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...