2, For the following periodic series, f(t) = t^2, ( -1<t<1), period = 2 (a) graph...
2, For the following periodic series, f(t) = t^2, ( -1<t<1), period = 2
(a) graph this periodic function, range is ( -8<t<8), and find a key point
(b)Even function or odd function?
(c ) find a Fourier series
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2, For the following periodic series, f(t) = t^2, (
-1<t<1), period = 2
(a) graph...
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,...
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
Problem 32: (20 points) Consider a periodic signal f(t), with fundamental period To, that has the...
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)...
Let f(t) be periodic function with period T = 1 defined over 1 period as
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.
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch...
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...
Q2. The following function f(t) is periodic with fundamental period To Sketch f(t) for at least...
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.
dan.curgul&key=72CW8gayu (1 point) Suppose that f(t) is periodic with period -x, x) and has the following...
dan.curgul&key=72CW8gayu (1 point) Suppose that f(t) is periodic with period -x, x) and has the following real Fourier coefficients: ao = 2, = -2, az = 3, az = 3, b, = 4, b2 = 4, bg =0, %3D ... (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) (B) Give the real Fourier coefficients for the following functions: (1) The derivative f'(t) , a2 = ,as by by b1 %3D (ii) The function...
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...
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...
1. Find the Fourier series for the following 1-periodic function f(t) = t, t < -- 2. Find the sum 24 3444 (Hint: Consider the Fourier series for the function f(t)-t2 on [- integer k.) 1) and f(t-k...
1. Find the Fourier series for the following 1-periodic function f(t) = t, t < -- 2. Find the sum 24 3444 (Hint: Consider the Fourier series for the function f(t)-t2 on [- integer k.) 1) and f(t-k)-f(t) for all
1. Find the Fourier series for the following 1-periodic function f(t) = t, t
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 th...
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...
For the function y 1-x for 0 s x s 1 Graph the function's 3 periods 1) Find its formulas for the Fourier series and Fourier coefficients 2) Write out the first three non-zero terms of the Four...
For the function y 1-x for 0 s x s 1 Graph the function's 3 periods 1) Find its formulas for the Fourier series and Fourier coefficients 2) Write out the first three non-zero terms of the Fourier Series 3) 4) Graph the even extension of the function 5) Find the Fourier series and Fourier coefficients for the even extension 6) Write out the first three non-zero terms of the even Fourier series 7) Graph the odd extension of the...
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
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)...
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...
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.
dan.curgul&key=72CW8gayu (1 point) Suppose that f(t) is periodic with period -x, x) and has the following real Fourier coefficients: ao = 2, = -2, az = 3, az = 3, b, = 4, b2 = 4, bg =0, %3D ... (A) Write the beginning of the real Fourier series of f(t) (through frequency 3): f(t) (B) Give the real Fourier coefficients for the following functions: (1) The derivative f'(t) , a2 = ,as by by b1 %3D (ii) The function...
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...
1. Find the Fourier series for the following 1-periodic function f(t) = t, t < -- 2. Find the sum 24 3444 (Hint: Consider the Fourier series for the function f(t)-t2 on [- integer k.) 1) and f(t-k)-f(t) for all
1. Find the Fourier series for the following 1-periodic function f(t) = t, t
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...
For the function y 1-x for 0 s x s 1 Graph the function's 3 periods 1) Find its formulas for the Fourier series and Fourier coefficients 2) Write out the first three non-zero terms of the Fourier Series 3) 4) Graph the even extension of the function 5) Find the Fourier series and Fourier coefficients for the even extension 6) Write out the first three non-zero terms of the even Fourier series 7) Graph the odd extension of the...
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