Advanced engineering mathimatics
Advanced engineering mathimatics is a f(3) = cosh²(z) Periodic function? what is the fundamental period (T)...
Q2. The following function f(t) is periodic with fundamental period To Sketch f(t) for at least 2 full cycles and obtain an expression for the Fourier series. Ensure that you calculate all coefficients and check your answer with the knowledge of odd or even functions. (0 – T. /251<-To 14, f(t) = {2A, - T./451< +T./4, 0, +T, / 4<t<+T72.
Given a continuous periodic function f ( t ) with period 3 T,
let F ( s ) be the Laplace transform of f ( t ). Identify the
correct expressions for A and B which make the formula for the
Laplace transform of f ( t ) correct:
F ( s ) = ∫ 0 A f ( t ) e − s t d t 1 − e B
Group of answer choices
Given a continuous periodic function...
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the exponential Fourier series representation f(t) = Σ Dnejuont . where wo 2T/To and 1. (2 points) When f(t) is a real-valued, show that DD This is known as the complex conjugate symmetry property or the Hermitian property of real signals. 2. (2 points) Show that when f(t) is an even function of time that Dn is an even function of n 3. (2 points)...
11. Show that following are an entire function. f(z)= e-? f(3) = cosh(z) (a) (b) 12. Find the derivative of the following using Cauchy- Reimann equations: ali d [2z - i dz z + 2i Z + 2z3 (a) (b)
Consider the following complex-variable function cosh a < T f(z) la! cosh πχ, a) Find all its singularities, state their nature and compute the residues b) Consider the rectangular contour y with vertices at tR and tRi. Evaluate 6 6 dz cosh πχ c) Using the previous result take the limit R-to prove that cosh ax (10] 2 cos (g Hint: remember that cosh(a + b) -cosh a cosh b + sinh a sinh b d) Why is the above...
4. Consider the periodic function given below: f(x)-x 0 ㄨㄑㄧ (i) State its fundamental period, and sketch the function for 3 periods. (5 marks) i) Find the Fourier series of the given periodic function, and expand the series to give the first three non-zero a and b terms (15 marks) ii) Use the answer obtained in Q4(ii) and the given periodic function, find the sum of the series 4(2n-1 )2 (5 marks)
Let f(t) be periodic function with period T = 1 defined over 1 period as f(t) = {t -1/2 < t < 1/2} (a) Plot f(t) and find its Fourier series representation. (b) Find the first four terms of the fourier series.
Problem 3: a) Show that is f(t) is an even, real valued periodic function of time with period To, then 0 f(t)dt ao = T. Jo b) Show that is f(t) is an odd, real valued periodic function of time with period To, then an-0 f (t) sin(nwot)dt
Q4. For each signal, if it is periodic, find the fundamental period T. (in seconds) and the fundamental frequency (in rad/s). Otherwise prove that the signal is not periodic. [1 + 1 - 2 marks) a) X(t) = cos(5t) + sin(25t) b)x() = sin 91 + + sin(61 - 7) + cos(391)
l, f) is a periodic signal with period f(t)-n(t)-u(t-t/2 ) for 0 2π a.) Find the exponential Fourier series of f() and sketchf). What is the fundamental radian frequency. b.) Evaluate and sketch |Dml, the magnitude of the Fourier series coefficients vs.o in the range of -4s n S4 c.) Evaluate and sketch the phase angle of D, vs. co in the same range (-4S n S4) d.) Find the signal average power e) Find the approximate average power of...