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Problem 04: A voltage source is expressed by the following Fourier series: v(t) = -2 +...
3.11-For each of the following signals compute the complex exponential Fourier series by using trigonometric identities,and then sketch the amplitude and phase spectra for all values of k (a) x(t)-cos(5t-π/4) (b) x(t) sint+ cos t 756 Chapter & The Series and fourier Translorm 023 4 5 ibi FIGURE Pa P33 3.13 Problems 157 in 0 14 12 3 I) ain FIGURE ,3.3 (antísndj (c) sti)-cos(1-1) + sin(,-%) 3.12. Determine the exponential Fourier series tor the Following periodic signals 3.11-For each...
The Fourier series of a periodic signal s(2) of period T can be expressed as k s(x) = cxexp ( 21 - where the coefficients Ck are given by 7/2 CR 1 T -T/2 | $(z) exp (-27 k -27=cdc T (i) Consider s(2) of period T = 6 and amplitude A= 2: 8(z) = 2 * |< T 2 Compute the Fourier coefficients ok. (ii) Use the identities exp(Trik) + exp(-rik) cos(Tk) = 2 sin(Tk) exp(Trik) – exp(-rik) 2i...
4. A periodic signal x (t) is represented by a trigonometrie Fourier series X(t) = 8 + 4 cos (2t + 60°) + 2sin (3t+30°) - cos (4t + 150°) = 0 * +30°) - cos (4t+150°) = 3 +4 Cos(216)+2 Cart ( 6) Col413 (a) Sketch the trigonometric Fourier series spectra (both magnitude and phase). O i 2 3 (b) Sketch the exponential Fourier series spectra (both magnitude and phase). + Dol -3 -2 -1 0 1 2 3...
For each of the following signals, compute the complex exponential Fourier series by using trigonometric identities, and then sketch the amplitude and phase spectra for all values of k. (a) x() = cos(51 - 7/4) (b) X(t) = sin 1 + cost (c) x(0) cos(t – 1) + sin(t - 12) (d) x(t) = cos 2t sin 3t
3. [45] Compute the exponential Fourier series representation for the following signals and sketch the amplitude and phase spectra. x(t) -7 -6 -2 -1 4 5 6 x(t) b) c) x(t) periodic with period 4 and (sin(at),0 <t<2 x(0) = { 0,2 <t 54
P.3 The voltage across the terminals of a circuit is: v(t) = 30+ 20 cos(1207t +45°)+10 cos(120nt - 459) V and the current entering the terminal is: i(t) = 6+4 cos(120wt +10°) - 2 cos(120ft -60°) A a) Calculate the RMS value of the voltage b) Calculate the RMS value of the current c) Calculate the average value of the power absorbed by the circuit
Problem 3: (20 points) When a DC source is connected to a series RC cireuit the time constant is 15.0 ms. When an 18.0 V RMS AC source is connected to the same series RC circuit you measure 3.17 V RMS across the capacitor a) (3 points) What is the resistor voltage? c) (5 points) What is the frequency of the source? If the resistor is 750.0 Q, what is the value of C? d) (6 points) An inductor is...
signal and systems 3.11. For each of the following signals, compute the complex exponential Fourier series by using trigonometric identities, and then sketch the amplitude and phase spectra for all values of k , (a) x(t) = cos(51-7r/4) (b) x(1) sin! + cos[
Matlab Code if available Problem 04 mm us(0 In the circuit, the voltage source Vs(t) frequency, amplitude and phase are 22 kHz, 10 V and 0.25 rad correspondingly; Rs=4 Ohm, Ri=12 Ohm, R2=9 Ohm, R3=2 Ohm, L1=0.11 mH, L2=0.13 mH, C= 1.4 uF ("u"="micro"). Part A. Using any appropriate techniques, find the parameters of Thevenin equivalent circuit with respect to the ports "a" and "b". Present the Thevenin source in the polar form and the Thevenin impedance in the algebraic...
Problem 2: For the signal g(t) t, a) (25 points) Find the exponential Fourier series to represent g(t) over the interval (-π, π). Sketch the spectra (amplitude and phase of Fourier series coefficients). b) (25 points) Find the average power of g(t) within interval (- ,r). Using this result and given that Σ00.-6, verify the Parseval's theorem