Given the Fourier Series cocfficients and fundamental frequency, find the signal using the Fourier Series synthesis...
The complex exponential Fourier series of a real even signal has non-zero coefficients for non- negative k given by k a_k 0 2 1 3 2 -1 3 0.5 4 1 5 -2 a. What are the values for negative k? b. What is the energy in the fundamental frequency? What is the energy in the third and fourth harmonics? d. What is the Fourier series in terms of sines and cosine if 0, = 3? C.
8. The complex exponential Fourier series of a real even signal has non-zero coefficients for non-negative k given by a. What are the values for negative k? b. What is the energy in the fundamental frequency? c. What is the energy in the third and fourth harmonics? d. What is the Fourier series in terms of sines and cosine if ? a_k 2 0 1 3 2 -1 3 0.5 4 1 5 -2 We were unable to transcribe this image
2- In cach of the following, we specify the Fourier series coefficients of a CT signal that i periodic with period To 4. Determine the signal x(t) in each case k 0 a) a sin ,k 0 km -j= ei= (j* = e#. Hint: using Euler's formula: Jkl3 jk b) a fo.0therwise -4 (1,k even c) a 2.k odd Hint: Suppose x(t) 8(t-kT) ke- is an impulse train with impulses spaced every T seconds apart (Figure 2). This is a...
GIven the signal s(t)- 3cos(2T30t1.5708) +4cos(2T210t 0.523599) find the Fourier series coefficients of the exponential representation Find the fundamental frequency radians Wo Give the indices and the values (polar representation) of the nonzero coefficients, starting with the most negative index and proceeding to the most positive index. For example if indices n = ±3 and n-±7 are the only nonzero terms, the order is-Z-3, 3, 7 S(n)l- S(n)l S(n) S(n)l ZS(n) - LS (n)- ZS(n) - LS (n)- radians radians...
Prob. 2 Discrete-Time Fourier Series (DTFs) (a) A periodic signal, rin] is shown below. Use the analysis equation to determine the discrete-time Fourier Series (DTFS) coefficients, a. Express the a in terms of cosines [72] -2 N= -3 (b) Sketch the spectrum, as vs. k for -5Sk s5. Please note each value. ak 2 5 Prob. 2 (cont.) -Discrete-Time Fourier Series (CTFS) (c) A periodic signal rafnl is given below. a2In] 2 1 E -3 what is the fundamental period...
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...
A periodic signal x(t) is shown below. We want to find the Fourier Series representation for this signal. x(t) AA -4 -2 1 2 4 6 8 (a) Find the period (T.) and radian frequency (wo) of (t). (b) Find the Trigonometric Series representation of X(t). These include: (a) Fourier coefficients ao, an, and bn ; (b) complete mathematical Fourier series expression for X(t); and (c) first five terms of the series.
2. If x(t) is a real periodic signal with fundamental period T and Fourier series coefficients ak, show that if r(t) is even, then its Fourier series coefficients must be real and even. [10 points]
2) The exponential Fourier series of a periodic signal x(t) is given as x(t) = (4 + j3)e-j6t + j3e-j4t + 2 - j3ej4t + (4 - j3) jót a) What is the fundamental frequency? b) By inspection write the signal x(t) in a compact trigonometric form. c) Find the power of the signal.
Determine the trigonometric Fourier series coefficients an and bn for signal x(t) sin(3m + 1) + 2 cos(7m-2) . Determine also the signal's fundamental radian frequency wo. No integration is required to solve this cos( ( ? problem