4. A periodic signal x (t) is represented by a trigonometrie Fourier series X(t) = 8...
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
For the periodic signal below, find the compact trigonometric fourier series and sketch the amplitude and phase spectra. If either the sine or cosine terms are absent in the Fourier series, explain why. Please provide a detailed solution. Thanks! For the periodi the amplitude and phase spectra. If either the sine or cosine terms a series, explain why 6.1-1. c signal shown below, find the compact trigonometric Fourier series and sketch re absent in the Fourier b) -20
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[
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...
4. Given that x(t) has the Fourier transform X(a), p(t) is a periodic signal with frequency of ??. p(t)-??--o nejnaot, where Cn is the Fourier series coefficient of p) (1) Assume y(t)-x(t)p(t), determine Y(?), the Fourier transform of the modulated signal y(t) in terms of X(). (2) Given the spectrum sketch of x(?) shown below, p(t)-cos(2t) cos(t), determine and sketch the Y() X(w) -1
6.3.6 Figure P6.3-6 shows the trigonometric Fourier spectra of a periodic signal x(t) a. By inspection of Fig. P6.3-6, find the trigonometric Fourier series representing x(t) D. By spectien of Eig P636 ketcir tne exponential Eourier spectra of x(t). Egunar specta obtained in part b find the expone Het Ferrer sense。「 X(t) 0, 1 2 3 4 Cn Figure P6.3-8 6.3.6 Figure P6.3-6 shows the trigonometric Fourier spectra of a periodic signal x(t) a. By inspection of Fig. P6.3-6, find...
Problem .3 Find the Fourier transform of the following periodic signal. Sketch the magnitude and phase spectra x(t) -4? -2? 2? 2 The exponential Fourier series of r(t) is n=0 -98 sin n- Odd 2 0, n- Even
The exponential Fourier series of a certain function is given as x(t) = (2+jl)e"]3+ + j3e-ft + 5 - Belt + (2-j1)e131 a) Sketch the exponential Fourier spectra b) By inspection of the spectra in part (a), sketch the trigonometric Fourier spectra for x(t). c) Find the compact trigonometric Fourier series from the spectra in part b.
Consider the Fourier series for the periodic function: x(t)= 3 + 5cos t +6 sin (2t) a.) Find the Fourier Coefficients of the exponential form b.) Find the Fourier Coefficients of the combined trigonometric form c.) Find the normalized average power using the Fourier series coefficient d.) Sketch the one sided Power Spectral Density
3. Determine the complex Fourier series to represent the function f(t) = 2t in the range T to + 4. Show that the complex Fourier series in problem 3 above is equivalent to: f (t) = 4( sin t – įsin 2t + eşsin 3t - sin 4t + ... III.