A periodic signal f(t) is produced by periodically repeating the function alt) - S2t|t| for -1<t<1...
A periodic function f(x) with period 21 is defined by: X + -1<x< 0 2 f(x) = 0<x< 2 Determine the Fourier expansion of the periodic function f(x). X - TT
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):
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.
I really appreciate it. please explain in detail. Thank you. a) f(t) = r|t| -1<t<1 t = 1 Compute the Fourier integral representations of f(t). It > 1 NI b) g(t (t, ostsi t = 1 Compute the Fourier cosine integral representation of g. t> 0 c) Compute the Fourier sine integral representation
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
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...
Let x(t) = t, 0<t 1 and Fourier series coefficients a , be a periodic signal with fundamental period of T 2 -t,-1t0 dz(t) a) Sketch the waveform of r(t)d3 marks) b) Calculate ao (3 marks) c) Determine the Fourier series representation of gt)(4 rks) d) Using the results from Part (c) and the property of continuous-time Fourier series to dr(t) determine the Fourier series coefficients of r(t) (4 marks)
3) Find the exponential Fourier series for the periodic signal x(t)= e 1/2 over the range 0..1, periodically continued. 4) Plot the amplitude and phase spectra of this signal. How do they compare to (2) above?
87 The plot of a time-domain function shows tiro palses of a periodic, repeating wareform fit) t (a) The wav efcem is to be represented by a Fourier series. What are the ferst three nonzero Fourier series terms (A) 2 cos(0.5mt) + 2 sin(nt) + 읊 sin(1.5mt) (B) 0.5 + 2 sin(0.5rt)喙sin(1.5m) (C) 0.5 + 2 cos(0.5nt) + sin(1.5nt) (D) π sin(0.brt) + 읊 sín(1.5nt)壕sin(2.5nt) 3T The graph shows a pulse in a communications signal. xlt) 1 t (s) What...
Given the periodic function 5 f(1) = { 1 f (+4) 0<i and I<2 2 <r and I<4 otherwise and its graph is displayed below. 6 5 4 y 3 2 1 0 -2 2 4 6 00+ x The function may be approximated by the Fourier series f(t) = 40 + 1 (an cos ( 172 ) + bn sin where L is the half-period of the function. + bn sin ne :)), L Calculate the coefficients of the...